# Quizbank/University Physics Semester 2/T7

University Physics Semester 2/T7 ID153341821922

Exams:

78 Tests = 3 versions x 26 variations: Each of the 26 variations (A, B, ...) represents a different random selection of questions taken from the study guide.The 3 versions (0,1,..) all have the same questions but in different order and with different numerical inputs. Unless all students take version "0" it is best to reserve it for the instructor because the questions are grouped according to the order in which they appear on the study guide.

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### T7 A0

1) A long solenoid has a radius of 0.845 m and 78 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$3 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 0.214 m from the axis at time t=0.0655 s ?

a) 1.160E-04 V/m
b) 1.276E-04 V/m
c) 1.403E-04 V/m
d) 1.544E-04 V/m
e) 1.698E-04 V/m

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.54 T and ${\displaystyle \omega =}$1.860E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.642 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 2.415E+04 V
b) 2.656E+04 V
c) 2.922E+04 V
d) 3.214E+04 V
e) 3.535E+04 V

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.78 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.22)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.74 s. What is the current in the coil if the impedance of the coil is 32.1 Ω?

a) 1.742E+00 A
b) 1.916E+00 A
c) 2.108E+00 A
d) 2.319E+00 A
e) 2.551E+00 A

4) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.14mm}$, and ${\displaystyle n=2.86}$. What is the volume of the washer?

a) 1.071E+00 cm3
b) 1.178E+00 cm3
c) 1.296E+00 cm3
d) 1.425E+00 cm3
e) 1.568E+00 cm3
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.69% of its maximum value if ε = 4.79 V , R = 4.18 Ω, and L = 2.7 H?
a) -8.773E-01 s
b) -9.651E-01 s
c) -1.062E+00 s
d) -1.168E+00 s
e) -1.284E+00 s

6) An ac generator produces an emf of amplitude 4 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 19 mF capacitor?

a) 6.946E-02 A
b) 7.640E-02 A
c) 8.404E-02 A
d) 9.245E-02 A
e) 1.017E-01 A

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.17 Ω, L= 4.40E-03H , and C=3.40E-06 F, respectively.

a) Q = 1.391E+02
b) Q = 1.600E+02
c) Q = 1.840E+02
d) Q = 2.116E+02
e) Q = 2.434E+02

8) The output of an ac generator connected to an RLC series combination has a frequency of 1.00E+03 Hz and an amplitude of 0.6 V;. If R =3 Ω, L= 1.70E-03H , and C=5.40E-04 F, what is the impedance?

a) 8.123E+00 Ω
b) 8.935E+00 Ω
c) 9.828E+00 Ω
d) 1.081E+01 Ω
e) 1.189E+01 Ω

9) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 A1

1) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.14 Ω, L= 5.20E-03H , and C=2.90E-06 F, respectively.

a) Q = 2.287E+02
b) Q = 2.630E+02
c) Q = 3.025E+02
d) Q = 3.478E+02
e) Q = 4.000E+02

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.59)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.58 s. What is the current in the coil if the impedance of the coil is 13.3 Ω?

a) 4.141E-01 A
b) 4.555E-01 A
c) 5.011E-01 A
d) 5.512E-01 A
e) 6.063E-01 A

3) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

4) A long solenoid has a radius of 0.861 m and 28 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 0.106 m from the axis at time t=0.055 s ?

a) 1.026E-05 V/m
b) 1.129E-05 V/m
c) 1.242E-05 V/m
d) 1.366E-05 V/m
e) 1.502E-05 V/m

5) A washer has an inner diameter of 2.42 cm and an outer diamter of 4.53 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.47mm}$, and ${\displaystyle n=2.8}$. What is the volume of the washer?

a) 8.932E-01 cm3
b) 9.825E-01 cm3
c) 1.081E+00 cm3
d) 1.189E+00 cm3
e) 1.308E+00 cm3

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.71 T and ${\displaystyle \omega =}$6.600E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.31 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 4.769E+04 V
b) 5.246E+04 V
c) 5.771E+04 V
d) 6.348E+04 V
e) 6.983E+04 V

7) The output of an ac generator connected to an RLC series combination has a frequency of 910 Hz and an amplitude of 0.88 V;. If R =7 Ω, L= 6.80E-03H , and C=9.60E-04 F, what is the impedance?

a) 3.575E+01 Ω
b) 3.933E+01 Ω
c) 4.326E+01 Ω
d) 4.758E+01 Ω
e) 5.234E+01 Ω

8) An ac generator produces an emf of amplitude 53 V at a frequency of 190 Hz. What is the maximum amplitude of the current if the generator is connected to a 85 mF capacitor?

a) 4.445E+00 A
b) 4.889E+00 A
c) 5.378E+00 A
d) 5.916E+00 A
e) 6.507E+00 A
9)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.63% of its maximum value if ε = 8.7 V , R = 8.35 Ω, and L = 1.44 H?
a) -3.137E-01 s
b) -3.451E-01 s
c) -3.796E-01 s
d) -4.176E-01 s
e) -4.593E-01 s

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 A2

1) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.34 T and ${\displaystyle \omega =}$2.670E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.646 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.905E+04 V
b) 2.096E+04 V
c) 2.305E+04 V
d) 2.536E+04 V
e) 2.790E+04 V

3) An ac generator produces an emf of amplitude 87 V at a frequency of 44 Hz. What is the maximum amplitude of the current if the generator is connected to a 9 mF capacitor?

a) 1.626E-01 A
b) 1.789E-01 A
c) 1.968E-01 A
d) 2.165E-01 A
e) 2.381E-01 A

4) The output of an ac generator connected to an RLC series combination has a frequency of 740 Hz and an amplitude of 0.66 V;. If R =3 Ω, L= 2.40E-03H , and C=5.70E-04 F, what is the impedance?

a) 1.119E+01 Ω
b) 1.231E+01 Ω
c) 1.354E+01 Ω
d) 1.490E+01 Ω
e) 1.639E+01 Ω

5) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.62 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.66mm}$, and ${\displaystyle n=2.61}$. What is the volume of the washer?

a) 6.960E-01 cm3
b) 7.656E-01 cm3
c) 8.421E-01 cm3
d) 9.264E-01 cm3
e) 1.019E+00 cm3

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.17 Ω, L= 4.40E-03H , and C=3.40E-06 F, respectively.

a) Q = 1.391E+02
b) Q = 1.600E+02
c) Q = 1.840E+02
d) Q = 2.116E+02
e) Q = 2.434E+02

7) An loop of wire with 92 turns has a radius of 0.39 meters, and is oriented with its axis parallel to a magetic field of 0.97 Tesla. What is the induced voltage if this field is reduced to 16% of its original value in 1.4 seconds?

a) 2.56 x 101 volts
b) 3.1 x 101 volts
c) 3.76 x 101 volts
d) 4.55 x 101 volts
e) 5.51 x 101 volts

8) A long solenoid has a radius of 0.793 m and 45 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$29 s−1.What is the induced electric fied at a distance 0.216 m from the axis at time t=0.0208 s ?

a) 1.456E-04 V/m
b) 1.601E-04 V/m
c) 1.762E-04 V/m
d) 1.938E-04 V/m
e) 2.132E-04 V/m

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.274 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (1.84)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.59 s. What is the current in the coil if the impedance of the coil is 33.0 Ω?

a) 7.007E-02 A
b) 7.708E-02 A
c) 8.479E-02 A
d) 9.327E-02 A
e) 1.026E-01 A
10)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.28% of its maximum value if ε = 7.39 V , R = 7.05 Ω, and L = 3.51 H?
a) -6.429E-01 s
b) -7.072E-01 s
c) -7.779E-01 s
d) -8.557E-01 s
e) -9.412E-01 s

### T7 B0

1) Calculate the motional emf induced along a 32.1 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 5.280E-05 Tesla magnetic field.

a) 1.093E+04 V
b) 1.202E+04 V
c) 1.322E+04 V
d) 1.454E+04 V
e) 1.600E+04 V

2) A long solenoid has a radius of 0.857 m and 58 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$21 s−1.What is the induced electric fied at a distance 0.144 m from the axis at time t=0.0898 s ?

a) 1.256E-05 V/m
b) 1.382E-05 V/m
c) 1.520E-05 V/m
d) 1.672E-05 V/m
e) 1.839E-05 V/m

3) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$1.89 T and ${\displaystyle \omega =}$1.710E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.476 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.262E+03 V
b) 7.988E+03 V
c) 8.787E+03 V
d) 9.666E+03 V
e) 1.063E+04 V
4)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =1.95 s if ε = 8.33 V , R = 6.96 Ω, and L = 2.66 H?
a) 5.736E-01 V
b) 6.884E-01 V
c) 8.260E-01 V
d) 9.912E-01 V
e) 1.189E+00 V
5)
A long solenoid has a length 0.759 meters, radius 4.51 cm, and 542 turns. It surrounds coil of radius 9.59 meters and 13turns. If the current in the solenoid is changing at a rate of 272 A/s, what is the emf induced in the surounding coil?
a) 5.791E-02 V
b) 6.370E-02 V
c) 7.007E-02 V
d) 7.708E-02 V
e) 8.478E-02 V

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.14 Ω, L= 5.20E-03H , and C=2.90E-06 F, respectively.

a) Q = 2.287E+02
b) Q = 2.630E+02
c) Q = 3.025E+02
d) Q = 3.478E+02
e) Q = 4.000E+02

7) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.25 V. The resistance, inductance, and capacitance are R =3 Ω, L= 2.20E-03H , and C=6.30E-04 F, respectively. What is the amplitude of the current?

a) 7.576E-02 A
b) 8.333E-02 A
c) 9.167E-02 A
d) 1.008E-01 A
e) 1.109E-01 A

8) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 Ω, L= 2.80E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 B1

1)
A long solenoid has a length 0.777 meters, radius 3.45 cm, and 557 turns. It surrounds coil of radius 6.01 meters and 10turns. If the current in the solenoid is changing at a rate of 184 A/s, what is the emf induced in the surounding coil?
a) 1.463E-02 V
b) 1.609E-02 V
c) 1.770E-02 V
d) 1.947E-02 V
e) 2.142E-02 V

2) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

3) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

4) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.77 V. The resistance, inductance, and capacitance are R =3 Ω, L= 6.70E-03H , and C=7.10E-04 F, respectively. What is the amplitude of the current?

a) 2.333E-01 A
b) 2.567E-01 A
c) 2.823E-01 A
d) 3.106E-01 A
e) 3.416E-01 A

5) Calculate the motional emf induced along a 25.2 km conductor moving at an orbital speed of 7.72 km/s perpendicular to Earth's 4.900E-05 Tesla magnetic field.

a) 7.162E+03 V
b) 7.878E+03 V
c) 8.666E+03 V
d) 9.533E+03 V
e) 1.049E+04 V

6) A long solenoid has a radius of 0.682 m and 38 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$27 s−1.What is the induced electric fied at a distance 0.16 m from the axis at time t=0.0736 s ?

a) 2.571E-05 V/m
b) 2.828E-05 V/m
c) 3.111E-05 V/m
d) 3.422E-05 V/m
e) 3.764E-05 V/m

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.13 Ω, L= 5.30E-03H , and C=2.60E-06 F, respectively.

a) Q = 1.986E+02
b) Q = 2.284E+02
c) Q = 2.626E+02
d) Q = 3.020E+02
e) Q = 3.473E+02
8)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =5.9 s if ε = 7.85 V , R = 6.89 Ω, and L = 7.36 H?
a) 6.567E-01 V
b) 7.880E-01 V
c) 9.456E-01 V
d) 1.135E+00 V
e) 1.362E+00 V

9) The output of an ac generator connected to an RLC series combination has a frequency of 360 Hz and an amplitude of 0.17 V;. If R =9 Ω, L= 2.60E-03H , and C=8.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

10) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$1.8 T and ${\displaystyle \omega =}$1.530E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.519 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.422E+03 V
b) 8.164E+03 V
c) 8.981E+03 V
d) 9.879E+03 V
e) 1.087E+04 V

#### T7 B2

1) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.62 V. The resistance, inductance, and capacitance are R =6 Ω, L= 8.10E-03H , and C=6.40E-04 F, respectively. What is the amplitude of the current?

a) 7.058E-02 A
b) 7.764E-02 A
c) 8.540E-02 A
d) 9.394E-02 A
e) 1.033E-01 A

2) Calculate the motional emf induced along a 11.9 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.870E-05 Tesla magnetic field.

a) 3.736E+03 V
b) 4.109E+03 V
c) 4.520E+03 V
d) 4.972E+03 V
e) 5.470E+03 V
3)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =13.6 s if ε = 6.56 V , R = 2.44 Ω, and L = 8.76 H?
a) 2.627E+00 V
b) 3.153E+00 V
c) 3.783E+00 V
d) 4.540E+00 V
e) 5.448E+00 V

4) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

5) An loop of wire with 54 turns has a radius of 0.8 meters, and is oriented with its axis parallel to a magetic field of 0.86 Tesla. What is the induced voltage if this field is reduced to 46% of its original value in 2.4 seconds?

a) 1.43 x 101 volts
b) 1.73 x 101 volts
c) 2.1 x 101 volts
d) 2.55 x 101 volts
e) 3.08 x 101 volts

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.25 T and ${\displaystyle \omega =}$8.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.227 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 2.657E+04 V
b) 2.923E+04 V
c) 3.215E+04 V
d) 3.537E+04 V
e) 3.890E+04 V
7)
A long solenoid has a length 0.759 meters, radius 4.51 cm, and 542 turns. It surrounds coil of radius 9.59 meters and 13turns. If the current in the solenoid is changing at a rate of 272 A/s, what is the emf induced in the surounding coil?
a) 5.791E-02 V
b) 6.370E-02 V
c) 7.007E-02 V
d) 7.708E-02 V
e) 8.478E-02 V

8) The output of an ac generator connected to an RLC series combination has a frequency of 360 Hz and an amplitude of 0.17 V;. If R =9 Ω, L= 2.60E-03H , and C=8.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.29 Ω, L= 4.80E-03H , and C=2.60E-06 F, respectively.

a) Q = 1.288E+02
b) Q = 1.482E+02
c) Q = 1.704E+02
d) Q = 1.959E+02
e) Q = 2.253E+02

10) A long solenoid has a radius of 0.793 m and 45 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$29 s−1.What is the induced electric fied at a distance 0.216 m from the axis at time t=0.0208 s ?

a) 1.456E-04 V/m
b) 1.601E-04 V/m
c) 1.762E-04 V/m
d) 1.938E-04 V/m
e) 2.132E-04 V/m

### T7 C0

1) A recangular coil with an area of 0.45 m2 and 18 turns is placed in a uniform magnetic field of 2.68 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.730E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 87 s?

a) 4.861E+04 V
b) 5.347E+04 V
c) 5.882E+04 V
d) 6.470E+04 V
e) 7.117E+04 V

2) A long solenoid has a radius of 0.447 m and 85 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 0.212 m from the axis at time t=0.0819 s ?

a) 1.893E-04 V/m
b) 2.082E-04 V/m
c) 2.290E-04 V/m
d) 2.519E-04 V/m
e) 2.771E-04 V/m

3) Calculate the motional emf induced along a 32.1 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 5.280E-05 Tesla magnetic field.

a) 1.093E+04 V
b) 1.202E+04 V
c) 1.322E+04 V
d) 1.454E+04 V
e) 1.600E+04 V

4) In an LC circuit, the self-inductance is 0.0237 H and the capacitance is 6.140E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.260E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.093E-04 s
b) 4.502E-04 s
c) 4.952E-04 s
d) 5.447E-04 s
e) 5.992E-04 s

5) An induced emf of 5.08V is measured across a coil of 78 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.07A in 0.681s. What is the self-inductance of the coil?

a) 4.660E-01 H
b) 5.127E-01 H
c) 5.639E-01 H
d) 6.203E-01 H
e) 6.823E-01 H

6) A step-down transformer steps 9 kV down to 210 V. The high-voltage input is provided by a 170 Ω power line that carries 5 A of currentWhat is the output current (at the 210 V side ?)

a) 1.948E+02 A
b) 2.143E+02 A
c) 2.357E+02 A
d) 2.593E+02 A
e) 2.852E+02 A

7) An ac generator produces an emf of amplitude 54 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 7 mF capacitor?

a) 2.850E-01 A
b) 3.135E-01 A
c) 3.449E-01 A
d) 3.793E-01 A
e) 4.173E-01 A

8) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.43 V;. If R =7 Ω, L= 7.40E-03H , and C=6.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) Two orbiting satellites are orbiting at a speed of 58 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 22 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 2.72 x 104 volts.
b) 3.3 x 104 volts.
c) 4 x 104 volts.
d) 4.84 x 104 volts.
e) 5.87 x 104 volts.

10) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

#### T7 C1

1) A long solenoid has a radius of 0.603 m and 51 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$26 s−1.What is the induced electric fied at a distance 0.105 m from the axis at time t=0.0659 s ?

a) 2.154E-05 V/m
b) 2.369E-05 V/m
c) 2.606E-05 V/m
d) 2.867E-05 V/m
e) 3.154E-05 V/m

2) The output of an ac generator connected to an RLC series combination has a frequency of 970 Hz and an amplitude of 0.11 V;. If R =9 Ω, L= 8.50E-03H , and C=7.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

3) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

4) Two orbiting satellites are orbiting at a speed of 52 km/s perpendicular to a magnetic field of 41 μT. They are connected by a cable that is 33 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 4.79 x 104 volts.
b) 5.81 x 104 volts.
c) 7.04 x 104 volts.
d) 8.52 x 104 volts.
e) 1.03 x 105 volts.

5) A step-down transformer steps 9 kV down to 160 V. The high-voltage input is provided by a 260 Ω power line that carries 7 A of currentWhat is the output current (at the 160 V side ?)

a) 3.938E+02 A
b) 4.331E+02 A
c) 4.764E+02 A
d) 5.241E+02 A
e) 5.765E+02 A

6) A recangular coil with an area of 0.897 m2 and 8 turns is placed in a uniform magnetic field of 2.83 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 8.740E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 3 s?

a) 4.695E+04 V
b) 5.165E+04 V
c) 5.681E+04 V
d) 6.249E+04 V
e) 6.874E+04 V

7) Calculate the motional emf induced along a 21.3 km conductor moving at an orbital speed of 7.75 km/s perpendicular to Earth's 5.320E-05 Tesla magnetic field.

a) 6.598E+03 V
b) 7.258E+03 V
c) 7.984E+03 V
d) 8.782E+03 V
e) 9.660E+03 V

8) An ac generator produces an emf of amplitude 53 V at a frequency of 190 Hz. What is the maximum amplitude of the current if the generator is connected to a 85 mF capacitor?

a) 4.445E+00 A
b) 4.889E+00 A
c) 5.378E+00 A
d) 5.916E+00 A
e) 6.507E+00 A

9) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?

a) 6.230E-04 s
b) 6.853E-04 s
c) 7.538E-04 s
d) 8.292E-04 s
e) 9.121E-04 s

10) An induced emf of 6.75V is measured across a coil of 79 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.76A in 0.115s. What is the self-inductance of the coil?

a) 9.094E-02 H
b) 1.000E-01 H
c) 1.100E-01 H
d) 1.210E-01 H
e) 1.331E-01 H

#### T7 C2

1) A recangular coil with an area of 0.45 m2 and 18 turns is placed in a uniform magnetic field of 2.68 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.730E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 87 s?

a) 4.861E+04 V
b) 5.347E+04 V
c) 5.882E+04 V
d) 6.470E+04 V
e) 7.117E+04 V

2) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

3) In an LC circuit, the self-inductance is 0.025 H and the capacitance is 3.530E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.770E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.856E-04 s
b) 4.242E-04 s
c) 4.666E-04 s
d) 5.133E-04 s
e) 5.646E-04 s

4) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.23 V;. If R =4 Ω, L= 7.70E-03H , and C=9.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

5) Calculate the motional emf induced along a 11.9 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.870E-05 Tesla magnetic field.

a) 3.736E+03 V
b) 4.109E+03 V
c) 4.520E+03 V
d) 4.972E+03 V
e) 5.470E+03 V

6) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

7) A long solenoid has a radius of 0.845 m and 78 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$3 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 0.214 m from the axis at time t=0.0655 s ?

a) 1.160E-04 V/m
b) 1.276E-04 V/m
c) 1.403E-04 V/m
d) 1.544E-04 V/m
e) 1.698E-04 V/m

8) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a 99 mF capacitor?

a) 1.644E+00 A
b) 1.808E+00 A
c) 1.989E+00 A
d) 2.188E+00 A
e) 2.407E+00 A

9) An induced emf of 8.76V is measured across a coil of 62 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.59A in 0.611s. What is the self-inductance of the coil?

a) 7.913E-01 H
b) 8.704E-01 H
c) 9.575E-01 H
d) 1.053E+00 H
e) 1.159E+00 H

10) A step-down transformer steps 15 kV down to 250 V. The high-voltage input is provided by a 130 Ω power line that carries 4 A of currentWhat is the output current (at the 250 V side ?)

a) 1.983E+02 A
b) 2.182E+02 A
c) 2.400E+02 A
d) 2.640E+02 A
e) 2.904E+02 A

### T7 D0

1) A square coil has sides that are L= 0.308 m long and is tightly wound with N=969 turns of wire. The resistance of the coil is R=8.64 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0498 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 4.817E-01 A
b) 5.298E-01 A
c) 5.828E-01 A
d) 6.411E-01 A
e) 7.052E-01 A

2) Calculate the motional emf induced along a 30.3 km conductor moving at an orbital speed of 7.76 km/s perpendicular to Earth's 5.100E-05 Tesla magnetic field.

a) 1.090E+04 V
b) 1.199E+04 V
c) 1.319E+04 V
d) 1.451E+04 V
e) 1.596E+04 V

3) A recangular coil with an area of 0.137 m2 and 18 turns is placed in a uniform magnetic field of 1.18 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.120E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 47 s?

a) 1.086E+04 V
b) 1.195E+04 V
c) 1.314E+04 V
d) 1.446E+04 V
e) 1.590E+04 V
4)
A long solenoid has a length 0.559 meters, radius 4.6 cm, and 515 turns. It surrounds coil of radius 9.72 meters and 17turns. If the current in the solenoid is changing at a rate of 189 A/s, what is the emf induced in the surounding coil?
a) 7.062E-02 V
b) 7.768E-02 V
c) 8.545E-02 V
d) 9.400E-02 V
e) 1.034E-01 V
5)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =6.01 s if ε = 5.75 V , R = 5.73 Ω, and L = 7.46 H?
a) 9.936E-01 V
b) 1.192E+00 V
c) 1.431E+00 V
d) 1.717E+00 V
e) 2.060E+00 V

6) An ac generator produces an emf of amplitude 69 V at a frequency of 180 Hz. What is the maximum amplitude of the current if the generator is connected to a 57 mF inductor?

a) 1.070E+00 A
b) 1.177E+00 A
c) 1.295E+00 A
d) 1.425E+00 A
e) 1.567E+00 A

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=6 V. The resistance, inductance, and capacitance are R =0.27 Ω, L= 4.20E-03H , and C=3.70E-06 F, respectively.

a) Q = 7.135E+01
b) Q = 8.205E+01
c) Q = 9.435E+01
d) Q = 1.085E+02
e) Q = 1.248E+02

8) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.23 V;. If R =4 Ω, L= 7.70E-03H , and C=9.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 D1

1) The output of an ac generator connected to an RLC series combination has a frequency of 720 Hz and an amplitude of 0.63 V;. If R =5 Ω, L= 4.20E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

2) A square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.661E+00 A
b) 4.028E+00 A
c) 4.430E+00 A
d) 4.873E+00 A
e) 5.361E+00 A

3) Calculate the motional emf induced along a 50.7 km conductor moving at an orbital speed of 7.88 km/s perpendicular to Earth's 4.930E-05 Tesla magnetic field.

a) 1.791E+04 V
b) 1.970E+04 V
c) 2.167E+04 V
d) 2.383E+04 V
e) 2.622E+04 V

4) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.29 Ω, L= 4.80E-03H , and C=2.60E-06 F, respectively.

a) Q = 1.288E+02
b) Q = 1.482E+02
c) Q = 1.704E+02
d) Q = 1.959E+02
e) Q = 2.253E+02

5) An ac generator produces an emf of amplitude 40 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a 52 mF inductor?

a) 7.783E-01 A
b) 8.561E-01 A
c) 9.417E-01 A
d) 1.036E+00 A
e) 1.140E+00 A

6) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.
7)
A long solenoid has a length 0.841 meters, radius 3.81 cm, and 516 turns. It surrounds coil of radius 9.2 meters and 11turns. If the current in the solenoid is changing at a rate of 190 A/s, what is the emf induced in the surounding coil?
a) 1.735E-02 V
b) 1.908E-02 V
c) 2.099E-02 V
d) 2.309E-02 V
e) 2.540E-02 V

8) A recangular coil with an area of 0.449 m2 and 20 turns is placed in a uniform magnetic field of 3.58 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.990E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 66 s?

a) 7.734E+04 V
b) 8.507E+04 V
c) 9.358E+04 V
d) 1.029E+05 V
e) 1.132E+05 V
9)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =1.55 s if ε = 5.97 V , R = 7.74 Ω, and L = 2.62 H?
a) 3.682E-01 V
b) 4.418E-01 V
c) 5.301E-01 V
d) 6.362E-01 V
e) 7.634E-01 V

10) An loop of wire with 31 turns has a radius of 0.9 meters, and is oriented with its axis parallel to a magetic field of 0.83 Tesla. What is the induced voltage if this field is reduced to 35% of its original value in 1.7 seconds?

a) 2.07 x 101 volts
b) 2.5 x 101 volts
c) 3.03 x 101 volts
d) 3.67 x 101 volts
e) 4.45 x 101 volts

#### T7 D2

1) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.22 Ω, L= 5.10E-03H , and C=2.50E-06 F, respectively.

a) Q = 2.053E+02
b) Q = 2.361E+02
c) Q = 2.715E+02
d) Q = 3.122E+02
e) Q = 3.591E+02

2) Calculate the motional emf induced along a 24.6 km conductor moving at an orbital speed of 7.89 km/s perpendicular to Earth's 5.180E-05 Tesla magnetic field.

a) 9.140E+03 V
b) 1.005E+04 V
c) 1.106E+04 V
d) 1.217E+04 V
e) 1.338E+04 V
3)
A long solenoid has a length 0.974 meters, radius 4.72 cm, and 587 turns. It surrounds coil of radius 8.65 meters and 17turns. If the current in the solenoid is changing at a rate of 146 A/s, what is the emf induced in the surounding coil?
a) 2.823E-02 V
b) 3.105E-02 V
c) 3.416E-02 V
d) 3.757E-02 V
e) 4.133E-02 V

4) The output of an ac generator connected to an RLC series combination has a frequency of 160 Hz and an amplitude of 0.47 V;. If R =8 Ω, L= 1.30E-03H , and C=6.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

5) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

6) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

7) A recangular coil with an area of 0.432 m2 and 16 turns is placed in a uniform magnetic field of 3.7 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.020E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 55 s?

a) 1.055E+05 V
b) 1.161E+05 V
c) 1.277E+05 V
d) 1.405E+05 V
e) 1.545E+05 V
8)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =3.96 s if ε = 4.92 V , R = 5.02 Ω, and L = 5.0 H?
a) 9.618E-01 V
b) 1.154E+00 V
c) 1.385E+00 V
d) 1.662E+00 V
e) 1.994E+00 V

9) A square coil has sides that are L= 0.561 m long and is tightly wound with N=930 turns of wire. The resistance of the coil is R=5.08 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 2.609E+00 A
b) 2.870E+00 A
c) 3.157E+00 A
d) 3.473E+00 A
e) 3.820E+00 A

10) An ac generator produces an emf of amplitude 69 V at a frequency of 180 Hz. What is the maximum amplitude of the current if the generator is connected to a 57 mF inductor?

a) 1.070E+00 A
b) 1.177E+00 A
c) 1.295E+00 A
d) 1.425E+00 A
e) 1.567E+00 A

### T7 E0

1) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.58 T and ${\displaystyle \omega =}$4.310E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.879 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.043E+04 V
b) 7.747E+04 V
c) 8.522E+04 V
d) 9.374E+04 V
e) 1.031E+05 V

2) A long solenoid has a radius of 0.793 m and 45 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$29 s−1.What is the induced electric fied at a distance 0.216 m from the axis at time t=0.0208 s ?

a) 1.456E-04 V/m
b) 1.601E-04 V/m
c) 1.762E-04 V/m
d) 1.938E-04 V/m
e) 2.132E-04 V/m

3) A recangular coil with an area of 0.587 m2 and 13 turns is placed in a uniform magnetic field of 1.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.800E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 93 s?

a) 2.512E+04 V
b) 2.763E+04 V
c) 3.039E+04 V
d) 3.343E+04 V
e) 3.677E+04 V

4) In an LC circuit, the self-inductance is 0.0237 H and the capacitance is 6.140E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.260E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.093E-04 s
b) 4.502E-04 s
c) 4.952E-04 s
d) 5.447E-04 s
e) 5.992E-04 s
5)
A long solenoid has a length 0.896 meters, radius 4.28 cm, and 550 turns. It surrounds coil of radius 6.65 meters and 9turns. If the current in the solenoid is changing at a rate of 204 A/s, what is the emf induced in the surounding coil?
a) 2.328E-02 V
b) 2.560E-02 V
c) 2.817E-02 V
d) 3.098E-02 V
e) 3.408E-02 V

6) The output of an ac generator connected to an RLC series combination has a frequency of 360 Hz and an amplitude of 0.17 V;. If R =9 Ω, L= 2.60E-03H , and C=8.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

7) The output of an ac generator connected to an RLC series combination has a frequency of 680 Hz and an amplitude of 0.79 V;. If R =5 Ω, L= 2.40E-03H , and C=9.10E-04 F, what is the impedance?

a) 8.398E+00 Ω
b) 9.238E+00 Ω
c) 1.016E+01 Ω
d) 1.118E+01 Ω
e) 1.230E+01 Ω

8) The output of an ac generator connected to an RLC series combination has a frequency of 4.30E+04 Hz and an amplitude of 6 V. If R =6 Ω, L= 5.20E-03H , and C=8.60E-06 F, what is the rms power transferred to the resistor?

a) 1.511E-03 Watts
b) 1.662E-03 Watts
c) 1.828E-03 Watts
d) 2.011E-03 Watts
e) 2.212E-03 Watts

9) An loop of wire with 43 turns has a radius of 0.27 meters, and is oriented with its axis parallel to a magetic field of 0.68 Tesla. What is the induced voltage if this field is reduced to 36% of its original value in 3.8 seconds?

a) 6.34 x 10-1 volts
b) 7.68 x 10-1 volts
c) 9.31 x 10-1 volts
d) 1.13 x 100 volts
e) 1.37 x 100 volts

10) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

#### T7 E1

1) The output of an ac generator connected to an RLC series combination has a frequency of 490 Hz and an amplitude of 0.68 V;. If R =9 Ω, L= 5.80E-03H , and C=9.50E-04 F, what is the impedance?

a) 1.969E+01 Ω
b) 2.166E+01 Ω
c) 2.383E+01 Ω
d) 2.621E+01 Ω
e) 2.883E+01 Ω

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.34 T and ${\displaystyle \omega =}$2.670E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.646 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.905E+04 V
b) 2.096E+04 V
c) 2.305E+04 V
d) 2.536E+04 V
e) 2.790E+04 V

3) The output of an ac generator connected to an RLC series combination has a frequency of 860 Hz and an amplitude of 0.59 V;. If R =9 Ω, L= 8.40E-03H , and C=8.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

4) An loop of wire with 92 turns has a radius of 0.39 meters, and is oriented with its axis parallel to a magetic field of 0.97 Tesla. What is the induced voltage if this field is reduced to 16% of its original value in 1.4 seconds?

a) 2.56 x 101 volts
b) 3.1 x 101 volts
c) 3.76 x 101 volts
d) 4.55 x 101 volts
e) 5.51 x 101 volts
5)
A long solenoid has a length 0.805 meters, radius 4.24 cm, and 536 turns. It surrounds coil of radius 8.5 meters and 16turns. If the current in the solenoid is changing at a rate of 278 A/s, what is the emf induced in the surounding coil?
a) 6.604E-02 V
b) 7.264E-02 V
c) 7.990E-02 V
d) 8.789E-02 V
e) 9.668E-02 V

6) The output of an ac generator connected to an RLC series combination has a frequency of 5.00E+04 Hz and an amplitude of 5 V. If R =6 Ω, L= 2.50E-03H , and C=5.20E-06 F, what is the rms power transferred to the resistor?

a) 5.097E-03 Watts
b) 5.607E-03 Watts
c) 6.167E-03 Watts
d) 6.784E-03 Watts
e) 7.463E-03 Watts

7) A recangular coil with an area of 0.446 m2 and 13 turns is placed in a uniform magnetic field of 3.17 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.060E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 54 s?

a) 1.957E+03 V
b) 2.153E+03 V
c) 2.368E+03 V
d) 2.605E+03 V
e) 2.865E+03 V

8) In an LC circuit, the self-inductance is 0.0156 H and the capacitance is 6.950E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 4.830E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.886E-04 s
b) 4.275E-04 s
c) 4.702E-04 s
d) 5.172E-04 s
e) 5.689E-04 s

9) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

10) A long solenoid has a radius of 0.749 m and 62 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$25 s−1.What is the induced electric fied at a distance 0.139 m from the axis at time t=0.071 s ?

a) 2.065E-04 V/m
b) 2.271E-04 V/m
c) 2.499E-04 V/m
d) 2.748E-04 V/m
e) 3.023E-04 V/m

#### T7 E2

1) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$1.97 T and ${\displaystyle \omega =}$5.410E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.244 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.485E+04 V
b) 1.634E+04 V
c) 1.797E+04 V
d) 1.977E+04 V
e) 2.175E+04 V
2)
A long solenoid has a length 0.89 meters, radius 3.01 cm, and 505 turns. It surrounds coil of radius 8.65 meters and 18turns. If the current in the solenoid is changing at a rate of 279 A/s, what is the emf induced in the surounding coil?
a) 2.646E-02 V
b) 2.911E-02 V
c) 3.202E-02 V
d) 3.522E-02 V
e) 3.874E-02 V

3) The output of an ac generator connected to an RLC series combination has a frequency of 370 Hz and an amplitude of 0.14 V;. If R =3 Ω, L= 5.30E-03H , and C=5.50E-04 F, what is the impedance?

a) 8.958E+00 Ω
b) 9.854E+00 Ω
c) 1.084E+01 Ω
d) 1.192E+01 Ω
e) 1.312E+01 Ω

4) In an LC circuit, the self-inductance is 0.0237 H and the capacitance is 6.140E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.260E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.093E-04 s
b) 4.502E-04 s
c) 4.952E-04 s
d) 5.447E-04 s
e) 5.992E-04 s

5) The output of an ac generator connected to an RLC series combination has a frequency of 280 Hz and an amplitude of 0.35 V;. If R =5 Ω, L= 9.50E-03H , and C=6.90E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

6) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

7) A long solenoid has a radius of 0.682 m and 38 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$27 s−1.What is the induced electric fied at a distance 0.16 m from the axis at time t=0.0736 s ?

a) 2.571E-05 V/m
b) 2.828E-05 V/m
c) 3.111E-05 V/m
d) 3.422E-05 V/m
e) 3.764E-05 V/m

8) A recangular coil with an area of 0.446 m2 and 13 turns is placed in a uniform magnetic field of 3.17 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.060E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 54 s?

a) 1.957E+03 V
b) 2.153E+03 V
c) 2.368E+03 V
d) 2.605E+03 V
e) 2.865E+03 V

9) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

10) The output of an ac generator connected to an RLC series combination has a frequency of 3.60E+04 Hz and an amplitude of 9 V. If R =2 Ω, L= 7.60E-03H , and C=7.50E-06 F, what is the rms power transferred to the resistor?

a) 1.011E-03 Watts
b) 1.112E-03 Watts
c) 1.223E-03 Watts
d) 1.345E-03 Watts
e) 1.480E-03 Watts

### T7 F0

1) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.25 T and ${\displaystyle \omega =}$8.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.227 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 2.657E+04 V
b) 2.923E+04 V
c) 3.215E+04 V
d) 3.537E+04 V
e) 3.890E+04 V

2) A long solenoid has a radius of 0.413 m and 17 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$21 s−1.What is the induced electric fied at a distance 2.25 m from the axis at time t=0.0689 s ?

a) 3.006E-06 V/m
b) 3.307E-06 V/m
c) 3.637E-06 V/m
d) 4.001E-06 V/m
e) 4.401E-06 V/m

3) Calculate the motional emf induced along a 49.5 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 5.310E-05 Tesla magnetic field.

a) 1.395E+04 V
b) 1.534E+04 V
c) 1.688E+04 V
d) 1.857E+04 V
e) 2.042E+04 V

4) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?

a) 6.166E-04 s
b) 6.783E-04 s
c) 7.461E-04 s
d) 8.207E-04 s
e) 9.028E-04 s
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.7% of its maximum value if ε = 7.67 V , R = 2.45 Ω, and L = 7.81 H?
a) -5.757E+00 s
b) -6.333E+00 s
c) -6.966E+00 s
d) -7.663E+00 s
e) -8.429E+00 s

6) The output of an ac generator connected to an RLC series combination has a frequency of 2.30E+04 Hz and an amplitude of 3 V. If R =5 Ω, L= 3.90E-03H , and C=9.00E-06 F, what is the rms power transferred to the resistor?

a) 2.339E-03 Watts
b) 2.573E-03 Watts
c) 2.830E-03 Watts
d) 3.113E-03 Watts
e) 3.424E-03 Watts

7) An ac generator produces an emf of amplitude 93 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF capacitor?

a) 4.917E+00 A
b) 5.409E+00 A
c) 5.950E+00 A
d) 6.545E+00 A
e) 7.199E+00 A

8) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.25 V. The resistance, inductance, and capacitance are R =7 Ω, L= 5.00E-03H , and C=7.70E-04 F, respectively. What is the amplitude of the current?

a) 2.439E-02 A
b) 2.683E-02 A
c) 2.952E-02 A
d) 3.247E-02 A
e) 3.571E-02 A

9) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 F1

1) Calculate the motional emf induced along a 50.7 km conductor moving at an orbital speed of 7.88 km/s perpendicular to Earth's 4.930E-05 Tesla magnetic field.

a) 1.791E+04 V
b) 1.970E+04 V
c) 2.167E+04 V
d) 2.383E+04 V
e) 2.622E+04 V

2) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

3) The output of an ac generator connected to an RLC series combination has a frequency of 2.70E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 9.10E-03H , and C=9.60E-06 F, what is the rms power transferred to the resistor?

a) 2.188E-03 Watts
b) 2.407E-03 Watts
c) 2.647E-03 Watts
d) 2.912E-03 Watts
e) 3.203E-03 Watts

4) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.25 V. The resistance, inductance, and capacitance are R =3 Ω, L= 2.20E-03H , and C=6.30E-04 F, respectively. What is the amplitude of the current?

a) 7.576E-02 A
b) 8.333E-02 A
c) 9.167E-02 A
d) 1.008E-01 A
e) 1.109E-01 A

5) In an LC circuit, the self-inductance is 0.0464 H and the capacitance is 7.350E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.280E-05 C. How long does it take for the capacitor to become completely discharged?

a) 8.339E-04 s
b) 9.173E-04 s
c) 1.009E-03 s
d) 1.110E-03 s
e) 1.221E-03 s

6) A long solenoid has a radius of 0.624 m and 84 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 1.78 m from the axis at time t=0.0579 s ?

a) 3.597E-04 V/m
b) 3.956E-04 V/m
c) 4.352E-04 V/m
d) 4.787E-04 V/m
e) 5.266E-04 V/m

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$1.8 T and ${\displaystyle \omega =}$1.530E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.519 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.422E+03 V
b) 8.164E+03 V
c) 8.981E+03 V
d) 9.879E+03 V
e) 1.087E+04 V
8)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.23% of its maximum value if ε = 3.13 V , R = 3.59 Ω, and L = 3.38 H?
a) -1.345E+00 s
b) -1.480E+00 s
c) -1.628E+00 s
d) -1.790E+00 s
e) -1.969E+00 s

9) An ac generator produces an emf of amplitude 64 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

a) 1.170E+00 A
b) 1.287E+00 A
c) 1.415E+00 A
d) 1.557E+00 A
e) 1.713E+00 A

10) Two orbiting satellites are orbiting at a speed of 58 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 22 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 2.72 x 104 volts.
b) 3.3 x 104 volts.
c) 4 x 104 volts.
d) 4.84 x 104 volts.
e) 5.87 x 104 volts.

#### T7 F2

1) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

2) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a 99 mF capacitor?

a) 1.644E+00 A
b) 1.808E+00 A
c) 1.989E+00 A
d) 2.188E+00 A
e) 2.407E+00 A

3) Calculate the motional emf induced along a 37.9 km conductor moving at an orbital speed of 7.84 km/s perpendicular to Earth's 5.410E-05 Tesla magnetic field.

a) 1.208E+04 V
b) 1.329E+04 V
c) 1.461E+04 V
d) 1.608E+04 V
e) 1.768E+04 V

4) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

5) A long solenoid has a radius of 0.45 m and 35 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$28 s−1.What is the induced electric fied at a distance 2.35 m from the axis at time t=0.0709 s ?

a) 5.475E-06 V/m
b) 6.023E-06 V/m
c) 6.625E-06 V/m
d) 7.288E-06 V/m
e) 8.017E-06 V/m
6)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.44% of its maximum value if ε = 5.95 V , R = 7.26 Ω, and L = 1.29 H?
a) -3.114E-01 s
b) -3.425E-01 s
c) -3.767E-01 s
d) -4.144E-01 s
e) -4.559E-01 s

7) The output of an ac generator connected to an RLC series combination has a frequency of 5.00E+04 Hz and an amplitude of 5 V. If R =6 Ω, L= 2.50E-03H , and C=5.20E-06 F, what is the rms power transferred to the resistor?

a) 5.097E-03 Watts
b) 5.607E-03 Watts
c) 6.167E-03 Watts
d) 6.784E-03 Watts
e) 7.463E-03 Watts

8) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.34 T and ${\displaystyle \omega =}$2.670E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.646 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.905E+04 V
b) 2.096E+04 V
c) 2.305E+04 V
d) 2.536E+04 V
e) 2.790E+04 V

9) In an LC circuit, the self-inductance is 0.025 H and the capacitance is 3.530E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.770E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.856E-04 s
b) 4.242E-04 s
c) 4.666E-04 s
d) 5.133E-04 s
e) 5.646E-04 s

10) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.82 V. The resistance, inductance, and capacitance are R =3 Ω, L= 6.20E-03H , and C=6.70E-04 F, respectively. What is the amplitude of the current?

a) 2.259E-01 A
b) 2.485E-01 A
c) 2.733E-01 A
d) 3.007E-01 A
e) 3.307E-01 A

### T7 G0

1) A square coil has sides that are L= 0.245 m long and is tightly wound with N=925 turns of wire. The resistance of the coil is R=8.0 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.545E-01 A
b) 3.899E-01 A
c) 4.289E-01 A
d) 4.718E-01 A
e) 5.190E-01 A

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.869 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.01)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.66 s. What is the current in the coil if the impedance of the coil is 32.8 Ω?

a) 9.191E-01 A
b) 1.011E+00 A
c) 1.112E+00 A
d) 1.223E+00 A
e) 1.346E+00 A

3) A recangular coil with an area of 0.291 m2 and 6 turns is placed in a uniform magnetic field of 2.63 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.130E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 35 s?

a) 1.490E+04 V
b) 1.639E+04 V
c) 1.803E+04 V
d) 1.983E+04 V
e) 2.181E+04 V
4)
A long solenoid has a length 0.896 meters, radius 4.28 cm, and 550 turns. It surrounds coil of radius 6.65 meters and 9turns. If the current in the solenoid is changing at a rate of 204 A/s, what is the emf induced in the surounding coil?
a) 2.328E-02 V
b) 2.560E-02 V
c) 2.817E-02 V
d) 3.098E-02 V
e) 3.408E-02 V

5) In an LC circuit, the self-inductance is 0.0795 H and the capacitance is 7.930E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 2.420E-05 C. How long does it take for the capacitor to become completely discharged?

a) 9.370E-04 s
b) 1.031E-03 s
c) 1.134E-03 s
d) 1.247E-03 s
e) 1.372E-03 s

6) The output of an ac generator connected to an RLC series combination has a frequency of 4.00E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 7.00E-03H , and C=6.60E-06 F, what is the rms power transferred to the resistor?

a) 1.146E-03 Watts
b) 1.260E-03 Watts
c) 1.386E-03 Watts
d) 1.525E-03 Watts
e) 1.677E-03 Watts

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=6 V. The resistance, inductance, and capacitance are R =0.3 Ω, L= 5.90E-03H , and C=3.80E-06 F, respectively.

a) Q = 7.510E+01
b) Q = 8.636E+01
c) Q = 9.932E+01
d) Q = 1.142E+02
e) Q = 1.313E+02

8) An ac generator produces an emf of amplitude 4 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 19 mF capacitor?

a) 6.946E-02 A
b) 7.640E-02 A
c) 8.404E-02 A
d) 9.245E-02 A
e) 1.017E-01 A

9) An loop of wire with 43 turns has a radius of 0.27 meters, and is oriented with its axis parallel to a magetic field of 0.68 Tesla. What is the induced voltage if this field is reduced to 36% of its original value in 3.8 seconds?

a) 6.34 x 10-1 volts
b) 7.68 x 10-1 volts
c) 9.31 x 10-1 volts
d) 1.13 x 100 volts
e) 1.37 x 100 volts

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 G1

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.708 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.16)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$6.34 s. What is the current in the coil if the impedance of the coil is 89.8 Ω?

a) 2.313E-01 A
b) 2.544E-01 A
c) 2.798E-01 A
d) 3.078E-01 A
e) 3.386E-01 A

2) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?

a) 6.166E-04 s
b) 6.783E-04 s
c) 7.461E-04 s
d) 8.207E-04 s
e) 9.028E-04 s

3) The output of an ac generator connected to an RLC series combination has a frequency of 5.70E+04 Hz and an amplitude of 5 V. If R =9 Ω, L= 6.10E-03H , and C=6.60E-06 F, what is the rms power transferred to the resistor?

a) 9.443E-04 Watts
b) 1.039E-03 Watts
c) 1.143E-03 Watts
d) 1.257E-03 Watts
e) 1.383E-03 Watts

4) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.
5)
A long solenoid has a length 0.634 meters, radius 3.04 cm, and 522 turns. It surrounds coil of radius 9.17 meters and 9turns. If the current in the solenoid is changing at a rate of 283 A/s, what is the emf induced in the surounding coil?
a) 1.986E-02 V
b) 2.185E-02 V
c) 2.404E-02 V
d) 2.644E-02 V
e) 2.908E-02 V

6) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=4 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 4.80E-03H , and C=2.60E-06 F, respectively.

a) Q = 1.300E+02
b) Q = 1.495E+02
c) Q = 1.719E+02
d) Q = 1.976E+02
e) Q = 2.273E+02

8) An ac generator produces an emf of amplitude 87 V at a frequency of 44 Hz. What is the maximum amplitude of the current if the generator is connected to a 9 mF capacitor?

a) 1.626E-01 A
b) 1.789E-01 A
c) 1.968E-01 A
d) 2.165E-01 A
e) 2.381E-01 A

9) A square coil has sides that are L= 0.259 m long and is tightly wound with N=628 turns of wire. The resistance of the coil is R=6.51 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0372 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.809E-01 A
b) 1.989E-01 A
c) 2.188E-01 A
d) 2.407E-01 A
e) 2.648E-01 A

10) A recangular coil with an area of 0.45 m2 and 18 turns is placed in a uniform magnetic field of 2.68 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.730E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 87 s?

a) 4.861E+04 V
b) 5.347E+04 V
c) 5.882E+04 V
d) 6.470E+04 V
e) 7.117E+04 V

#### T7 G2

1) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?

a) 6.166E-04 s
b) 6.783E-04 s
c) 7.461E-04 s
d) 8.207E-04 s
e) 9.028E-04 s

2) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.22 Ω, L= 5.10E-03H , and C=2.50E-06 F, respectively.

a) Q = 2.053E+02
b) Q = 2.361E+02
c) Q = 2.715E+02
d) Q = 3.122E+02
e) Q = 3.591E+02

3) An loop of wire with 43 turns has a radius of 0.27 meters, and is oriented with its axis parallel to a magetic field of 0.68 Tesla. What is the induced voltage if this field is reduced to 36% of its original value in 3.8 seconds?

a) 6.34 x 10-1 volts
b) 7.68 x 10-1 volts
c) 9.31 x 10-1 volts
d) 1.13 x 100 volts
e) 1.37 x 100 volts

4) A square coil has sides that are L= 0.547 m long and is tightly wound with N=198 turns of wire. The resistance of the coil is R=4.62 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0768 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 8.953E-01 A
b) 9.848E-01 A
c) 1.083E+00 A
d) 1.192E+00 A
e) 1.311E+00 A
5)
A long solenoid has a length 0.567 meters, radius 3.35 cm, and 555 turns. It surrounds coil of radius 5.73 meters and 9turns. If the current in the solenoid is changing at a rate of 281 A/s, what is the emf induced in the surounding coil?
a) 3.446E-02 V
b) 3.790E-02 V
c) 4.169E-02 V
d) 4.586E-02 V
e) 5.045E-02 V

6) An ac generator produces an emf of amplitude 64 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 32 mF capacitor?

a) 1.170E+00 A
b) 1.287E+00 A
c) 1.415E+00 A
d) 1.557E+00 A
e) 1.713E+00 A

7) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.274 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (1.84)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.59 s. What is the current in the coil if the impedance of the coil is 33.0 Ω?

a) 7.007E-02 A
b) 7.708E-02 A
c) 8.479E-02 A
d) 9.327E-02 A
e) 1.026E-01 A

8) The output of an ac generator connected to an RLC series combination has a frequency of 8.00E+04 Hz and an amplitude of 2 V. If R =7 Ω, L= 4.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

a) 1.047E-04 Watts
b) 1.151E-04 Watts
c) 1.267E-04 Watts
d) 1.393E-04 Watts
e) 1.533E-04 Watts

9) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

10) A recangular coil with an area of 0.479 m2 and 11 turns is placed in a uniform magnetic field of 1.34 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.200E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 38 s?

a) 2.148E+04 V
b) 2.363E+04 V
c) 2.599E+04 V
d) 2.859E+04 V
e) 3.145E+04 V

### T7 H0

1) A long solenoid has a radius of 0.732 m and 55 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$25 s−1.What is the induced electric fied at a distance 0.203 m from the axis at time t=0.0448 s ?

a) 5.150E-04 V/m
b) 5.665E-04 V/m
c) 6.232E-04 V/m
d) 6.855E-04 V/m
e) 7.540E-04 V/m

2) Calculate the motional emf induced along a 21.3 km conductor moving at an orbital speed of 7.75 km/s perpendicular to Earth's 5.320E-05 Tesla magnetic field.

a) 6.598E+03 V
b) 7.258E+03 V
c) 7.984E+03 V
d) 8.782E+03 V
e) 9.660E+03 V

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.655 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (5.62)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.62 s. What is the current in the coil if the impedance of the coil is 48.9 Ω?

a) 7.890E-01 A
b) 8.679E-01 A
c) 9.547E-01 A
d) 1.050E+00 A
e) 1.155E+00 A

4) A washer has an inner diameter of 2.2 cm and an outer diamter of 4.11 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.23mm}$, and ${\displaystyle n=2.74}$. What is the volume of the washer?

a) 7.110E-01 cm3
b) 7.821E-01 cm3
c) 8.603E-01 cm3
d) 9.463E-01 cm3
e) 1.041E+00 cm3
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.23% of its maximum value if ε = 3.13 V , R = 3.59 Ω, and L = 3.38 H?
a) -1.345E+00 s
b) -1.480E+00 s
c) -1.628E+00 s
d) -1.790E+00 s
e) -1.969E+00 s

6) A step-down transformer steps 18 kV down to 230 V. The high-voltage input is provided by a 250 Ω power line that carries 8 A of currentWhat is the output current (at the 230 V side ?)

a) 5.174E+02 A
b) 5.692E+02 A
c) 6.261E+02 A
d) 6.887E+02 A
e) 7.576E+02 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.18 V;. If R =6 Ω, L= 7.50E-03H , and C=7.50E-04 F, what is the impedance?

a) 2.708E+01 Ω
b) 2.978E+01 Ω
c) 3.276E+01 Ω
d) 3.604E+01 Ω
e) 3.964E+01 Ω

8) An ac generator produces an emf of amplitude 71 V at a frequency of 68 Hz. What is the maximum amplitude of the current if the generator is connected to a 35 mF capacitor?

a) 7.252E-01 A
b) 7.977E-01 A
c) 8.775E-01 A
d) 9.652E-01 A
e) 1.062E+00 A

9) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

10) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

#### T7 H1

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.43 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.73)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.61 s. What is the current in the coil if the impedance of the coil is 4.89 Ω?

a) 1.134E+00 A
b) 1.248E+00 A
c) 1.373E+00 A
d) 1.510E+00 A
e) 1.661E+00 A

2) An ac generator produces an emf of amplitude 17 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 6 mF capacitor?

a) 5.253E-02 A
b) 5.778E-02 A
c) 6.356E-02 A
d) 6.991E-02 A
e) 7.691E-02 A

3) A step-down transformer steps 9 kV down to 160 V. The high-voltage input is provided by a 260 Ω power line that carries 7 A of currentWhat is the output current (at the 160 V side ?)

a) 3.938E+02 A
b) 4.331E+02 A
c) 4.764E+02 A
d) 5.241E+02 A
e) 5.765E+02 A

4) A long solenoid has a radius of 0.851 m and 12 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$3 A and ${\displaystyle \alpha =}$30 s−1.What is the induced electric fied at a distance 0.14 m from the axis at time t=0.0531 s ?

a) 1.319E-05 V/m
b) 1.451E-05 V/m
c) 1.596E-05 V/m
d) 1.756E-05 V/m
e) 1.932E-05 V/m

5) The output of an ac generator connected to an RLC series combination has a frequency of 910 Hz and an amplitude of 0.88 V;. If R =7 Ω, L= 6.80E-03H , and C=9.60E-04 F, what is the impedance?

a) 3.575E+01 Ω
b) 3.933E+01 Ω
c) 4.326E+01 Ω
d) 4.758E+01 Ω
e) 5.234E+01 Ω
6)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.54% of its maximum value if ε = 2.46 V , R = 2.8 Ω, and L = 5.67 H?
a) -2.540E+00 s
b) -2.794E+00 s
c) -3.073E+00 s
d) -3.381E+00 s
e) -3.719E+00 s

7) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

8) A washer has an inner diameter of 2.74 cm and an outer diamter of 4.71 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.9mm}$, and ${\displaystyle n=2.85}$. What is the volume of the washer?

a) 8.141E-01 cm3
b) 8.955E-01 cm3
c) 9.850E-01 cm3
d) 1.084E+00 cm3
e) 1.192E+00 cm3

9) Calculate the motional emf induced along a 49.5 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 5.310E-05 Tesla magnetic field.

a) 1.395E+04 V
b) 1.534E+04 V
c) 1.688E+04 V
d) 1.857E+04 V
e) 2.042E+04 V

10) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

#### T7 H2

1)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.63% of its maximum value if ε = 8.7 V , R = 8.35 Ω, and L = 1.44 H?
a) -3.137E-01 s
b) -3.451E-01 s
c) -3.796E-01 s
d) -4.176E-01 s
e) -4.593E-01 s

2) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

3) An ac generator produces an emf of amplitude 32 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 14 mF capacitor?

a) 3.378E-01 A
b) 3.716E-01 A
c) 4.087E-01 A
d) 4.496E-01 A
e) 4.945E-01 A

4) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.87 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.39mm}$, and ${\displaystyle n=2.55}$. What is the volume of the washer?

a) 7.754E-01 cm3
b) 8.530E-01 cm3
c) 9.383E-01 cm3
d) 1.032E+00 cm3
e) 1.135E+00 cm3

5) Two orbiting satellites are orbiting at a speed of 52 km/s perpendicular to a magnetic field of 41 μT. They are connected by a cable that is 33 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 4.79 x 104 volts.
b) 5.81 x 104 volts.
c) 7.04 x 104 volts.
d) 8.52 x 104 volts.
e) 1.03 x 105 volts.

6) A step-down transformer steps 18 kV down to 230 V. The high-voltage input is provided by a 250 Ω power line that carries 8 A of currentWhat is the output current (at the 230 V side ?)

a) 5.174E+02 A
b) 5.692E+02 A
c) 6.261E+02 A
d) 6.887E+02 A
e) 7.576E+02 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 540 Hz and an amplitude of 0.18 V;. If R =3 Ω, L= 2.50E-03H , and C=8.20E-04 F, what is the impedance?

a) 7.872E+00 Ω
b) 8.659E+00 Ω
c) 9.525E+00 Ω
d) 1.048E+01 Ω
e) 1.153E+01 Ω

8) A long solenoid has a radius of 0.645 m and 37 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 0.189 m from the axis at time t=0.0698 s ?

a) 1.372E-04 V/m
b) 1.509E-04 V/m
c) 1.660E-04 V/m
d) 1.826E-04 V/m
e) 2.009E-04 V/m

9) Calculate the motional emf induced along a 48.8 km conductor moving at an orbital speed of 7.88 km/s perpendicular to Earth's 4.660E-05 Tesla magnetic field.

a) 1.224E+04 V
b) 1.346E+04 V
c) 1.481E+04 V
d) 1.629E+04 V
e) 1.792E+04 V

10) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.59)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.58 s. What is the current in the coil if the impedance of the coil is 13.3 Ω?

a) 4.141E-01 A
b) 4.555E-01 A
c) 5.011E-01 A
d) 5.512E-01 A
e) 6.063E-01 A

### T7 I0

1) A long solenoid has a radius of 0.306 m and 98 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$22 s−1.What is the induced electric fied at a distance 2.52 m from the axis at time t=0.0246 s ?

a) 1.598E-04 V/m
b) 1.758E-04 V/m
c) 1.934E-04 V/m
d) 2.127E-04 V/m
e) 2.340E-04 V/m

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.708 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.16)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$6.34 s. What is the current in the coil if the impedance of the coil is 89.8 Ω?

a) 2.313E-01 A
b) 2.544E-01 A
c) 2.798E-01 A
d) 3.078E-01 A
e) 3.386E-01 A

3) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 2.081E-04 V
b) 2.289E-04 V
c) 2.518E-04 V
d) 2.770E-04 V
e) 3.047E-04 V
4)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?
a) -1.700E+00 s
b) -1.870E+00 s
c) -2.057E+00 s
d) -2.262E+00 s
e) -2.489E+00 s
5)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =6.45 s if ε = 7.01 V , R = 7.04 Ω, and L = 8.75 H?
a) 9.902E-01 V
b) 1.188E+00 V
c) 1.426E+00 V
d) 1.711E+00 V
e) 2.053E+00 V

6) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.23 V;. If R =4 Ω, L= 7.70E-03H , and C=9.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

7) The output of an ac generator connected to an RLC series combination has a frequency of 4.00E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 7.00E-03H , and C=6.60E-06 F, what is the rms power transferred to the resistor?

a) 1.146E-03 Watts
b) 1.260E-03 Watts
c) 1.386E-03 Watts
d) 1.525E-03 Watts
e) 1.677E-03 Watts

8) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.21 Ω, L= 5.40E-03H , and C=3.20E-06 F, respectively.

a) Q = 1.286E+02
b) Q = 1.479E+02
c) Q = 1.701E+02
d) Q = 1.956E+02
e) Q = 2.250E+02

9) Two orbiting satellites are orbiting at a speed of 70 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 30 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 4.48 x 104 volts.
b) 5.43 x 104 volts.
c) 6.58 x 104 volts.
d) 7.97 x 104 volts.
e) 9.66 x 104 volts.

10) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

#### T7 I1

1) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 Ω, L= 2.80E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

2)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =3.8 s if ε = 3.36 V , R = 5.2 Ω, and L = 3.37 H?
a) 5.369E-01 V
b) 6.443E-01 V
c) 7.732E-01 V
d) 9.278E-01 V
e) 1.113E+00 V

3) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

4) The current through the windings of a solenoid with n= 2.840E+03 turns per meter is changing at a rate dI/dt=19 A/s. The solenoid is 65 cm long and has a cross-sectional diameter of 2.18 cm. A small coil consisting of N=25turns wraped in a circle of diameter 1.35 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 2.206E-04 V
b) 2.426E-04 V
c) 2.669E-04 V
d) 2.936E-04 V
e) 3.230E-04 V

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (1.95)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

a) 7.402E-01 A
b) 8.142E-01 A
c) 8.956E-01 A
d) 9.852E-01 A
e) 1.084E+00 A

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.22 Ω, L= 5.10E-03H , and C=2.50E-06 F, respectively.

a) Q = 2.053E+02
b) Q = 2.361E+02
c) Q = 2.715E+02
d) Q = 3.122E+02
e) Q = 3.591E+02
7)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.67% of its maximum value if ε = 5.07 V , R = 7.8 Ω, and L = 4.39 H?
a) -1.047E+00 s
b) -1.152E+00 s
c) -1.267E+00 s
d) -1.393E+00 s
e) -1.533E+00 s

8) A long solenoid has a radius of 0.521 m and 46 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$30 s−1.What is the induced electric fied at a distance 2.42 m from the axis at time t=0.0449 s ?

a) 2.529E-05 V/m
b) 2.782E-05 V/m
c) 3.060E-05 V/m
d) 3.366E-05 V/m
e) 3.703E-05 V/m

9) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

10) The output of an ac generator connected to an RLC series combination has a frequency of 8.00E+04 Hz and an amplitude of 2 V. If R =7 Ω, L= 4.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

a) 1.047E-04 Watts
b) 1.151E-04 Watts
c) 1.267E-04 Watts
d) 1.393E-04 Watts
e) 1.533E-04 Watts

#### T7 I2

1) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

2) The output of an ac generator connected to an RLC series combination has a frequency of 890 Hz and an amplitude of 0.58 V;. If R =9 Ω, L= 2.90E-03H , and C=8.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

3) The output of an ac generator connected to an RLC series combination has a frequency of 8.00E+04 Hz and an amplitude of 2 V. If R =7 Ω, L= 4.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

a) 1.047E-04 Watts
b) 1.151E-04 Watts
c) 1.267E-04 Watts
d) 1.393E-04 Watts
e) 1.533E-04 Watts

4) Two orbiting satellites are orbiting at a speed of 66 km/s perpendicular to a magnetic field of 64 μT. They are connected by a cable that is 37 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 1.29 x 105 volts.
b) 1.56 x 105 volts.
c) 1.89 x 105 volts.
d) 2.29 x 105 volts.
e) 2.78 x 105 volts.

5) A long solenoid has a radius of 0.434 m and 41 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$28 s−1.What is the induced electric fied at a distance 2.28 m from the axis at time t=0.0392 s ?

a) 1.479E-04 V/m
b) 1.627E-04 V/m
c) 1.789E-04 V/m
d) 1.968E-04 V/m
e) 2.165E-04 V/m

6) The current through the windings of a solenoid with n= 2.590E+03 turns per meter is changing at a rate dI/dt=11 A/s. The solenoid is 95 cm long and has a cross-sectional diameter of 2.29 cm. A small coil consisting of N=25turns wraped in a circle of diameter 1.15 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 6.985E-05 V
b) 7.683E-05 V
c) 8.452E-05 V
d) 9.297E-05 V
e) 1.023E-04 V

7) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.549 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.97)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.0 s. What is the current in the coil if the impedance of the coil is 46.7 Ω?

a) 2.032E-01 A
b) 2.235E-01 A
c) 2.458E-01 A
d) 2.704E-01 A
e) 2.975E-01 A
8)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =7.72 s if ε = 2.79 V , R = 1.56 Ω, and L = 3.16 H?
a) 1.214E+00 V
b) 1.457E+00 V
c) 1.749E+00 V
d) 2.099E+00 V
e) 2.518E+00 V

9) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.21 Ω, L= 5.40E-03H , and C=3.20E-06 F, respectively.

a) Q = 1.286E+02
b) Q = 1.479E+02
c) Q = 1.701E+02
d) Q = 1.956E+02
e) Q = 2.250E+02
10)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.78% of its maximum value if ε = 1.39 V , R = 2.88 Ω, and L = 4.06 H?
a) -2.296E+00 s
b) -2.525E+00 s
c) -2.778E+00 s
d) -3.056E+00 s
e) -3.361E+00 s

### T7 J0

1) A recangular coil with an area of 0.412 m2 and 18 turns is placed in a uniform magnetic field of 3.81 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 2.120E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 79 s?

a) 4.465E+04 V
b) 4.912E+04 V
c) 5.403E+04 V
d) 5.943E+04 V
e) 6.538E+04 V

2) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 6.581E-01 A
b) 7.239E-01 A
c) 7.963E-01 A
d) 8.759E-01 A
e) 9.635E-01 A

3) Calculate the motional emf induced along a 46.2 km conductor moving at an orbital speed of 7.9 km/s perpendicular to Earth's 4.630E-05 Tesla magnetic field.

a) 1.536E+04 V
b) 1.690E+04 V
c) 1.859E+04 V
d) 2.045E+04 V
e) 2.249E+04 V

4) A washer has an inner diameter of 2.16 cm and an outer diamter of 4.82 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.22mm}$, and ${\displaystyle n=2.8}$. What is the volume of the washer?

a) 1.342E+00 cm3
b) 1.477E+00 cm3
c) 1.624E+00 cm3
d) 1.787E+00 cm3
e) 1.965E+00 cm3
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.56% of its maximum value if ε = 4.22 V , R = 1.89 Ω, and L = 6.57 H?
a) -4.939E+00 s
b) -5.433E+00 s
c) -5.976E+00 s
d) -6.574E+00 s
e) -7.231E+00 s

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.27 Ω, L= 4.30E-03H , and C=2.20E-06 F, respectively.

a) Q = 1.238E+02
b) Q = 1.424E+02
c) Q = 1.637E+02
d) Q = 1.883E+02
e) Q = 2.165E+02

7) A step-down transformer steps 9 kV down to 160 V. The high-voltage input is provided by a 260 Ω power line that carries 7 A of currentWhat is the output current (at the 160 V side ?)

a) 3.938E+02 A
b) 4.331E+02 A
c) 4.764E+02 A
d) 5.241E+02 A
e) 5.765E+02 A

8) The output of an ac generator connected to an RLC series combination has a frequency of 360 Hz and an amplitude of 0.17 V;. If R =9 Ω, L= 2.60E-03H , and C=8.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) An loop of wire with 31 turns has a radius of 0.9 meters, and is oriented with its axis parallel to a magetic field of 0.83 Tesla. What is the induced voltage if this field is reduced to 35% of its original value in 1.7 seconds?

a) 2.07 x 101 volts
b) 2.5 x 101 volts
c) 3.03 x 101 volts
d) 3.67 x 101 volts
e) 4.45 x 101 volts

10) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

#### T7 J1

1) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.25 Ω, L= 4.70E-03H , and C=3.30E-06 F, respectively.

a) Q = 1.313E+02
b) Q = 1.510E+02
c) Q = 1.736E+02
d) Q = 1.996E+02
e) Q = 2.296E+02

2) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.
3)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.78% of its maximum value if ε = 1.39 V , R = 2.88 Ω, and L = 4.06 H?
a) -2.296E+00 s
b) -2.525E+00 s
c) -2.778E+00 s
d) -3.056E+00 s
e) -3.361E+00 s

4) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

5) A step-down transformer steps 18 kV down to 260 V. The high-voltage input is provided by a 290 Ω power line that carries 3 A of currentWhat is the output current (at the 260 V side ?)

a) 1.888E+02 A
b) 2.077E+02 A
c) 2.285E+02 A
d) 2.513E+02 A
e) 2.764E+02 A

6) A recangular coil with an area of 0.897 m2 and 8 turns is placed in a uniform magnetic field of 2.83 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 8.740E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 3 s?

a) 4.695E+04 V
b) 5.165E+04 V
c) 5.681E+04 V
d) 6.249E+04 V
e) 6.874E+04 V

7) A washer has an inner diameter of 2.3 cm and an outer diamter of 4.44 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.31mm}$, and ${\displaystyle n=2.66}$. What is the volume of the washer?

a) 1.089E+00 cm3
b) 1.198E+00 cm3
c) 1.318E+00 cm3
d) 1.449E+00 cm3
e) 1.594E+00 cm3

8) A square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.661E+00 A
b) 4.028E+00 A
c) 4.430E+00 A
d) 4.873E+00 A
e) 5.361E+00 A

9) The output of an ac generator connected to an RLC series combination has a frequency of 860 Hz and an amplitude of 0.59 V;. If R =9 Ω, L= 8.40E-03H , and C=8.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

10) Calculate the motional emf induced along a 49.5 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 5.310E-05 Tesla magnetic field.

a) 1.395E+04 V
b) 1.534E+04 V
c) 1.688E+04 V
d) 1.857E+04 V
e) 2.042E+04 V

#### T7 J2

1) A recangular coil with an area of 0.39 m2 and 16 turns is placed in a uniform magnetic field of 3.07 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.320E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 44 s?

a) 3.792E+04 V
b) 4.172E+04 V
c) 4.589E+04 V
d) 5.048E+04 V
e) 5.552E+04 V

2) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

3) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

4) A square coil has sides that are L= 0.325 m long and is tightly wound with N=697 turns of wire. The resistance of the coil is R=4.87 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0842 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.157E+00 A
b) 1.273E+00 A
c) 1.400E+00 A
d) 1.540E+00 A
e) 1.694E+00 A
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.01% of its maximum value if ε = 1.45 V , R = 4.4 Ω, and L = 2.36 H?
a) -8.659E-01 s
b) -9.525E-01 s
c) -1.048E+00 s
d) -1.153E+00 s
e) -1.268E+00 s

6) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 Ω, L= 2.80E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

7) A step-down transformer steps 18 kV down to 170 V. The high-voltage input is provided by a 240 Ω power line that carries 5 A of currentWhat is the output current (at the 170 V side ?)

a) 5.294E+02 A
b) 5.824E+02 A
c) 6.406E+02 A
d) 7.046E+02 A
e) 7.751E+02 A

8) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.21 Ω, L= 4.70E-03H , and C=3.70E-06 F, respectively.

a) Q = 1.476E+02
b) Q = 1.697E+02
c) Q = 1.952E+02
d) Q = 2.245E+02
e) Q = 2.581E+02

9) A washer has an inner diameter of 2.37 cm and an outer diamter of 4.84 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.67mm}$, and ${\displaystyle n=2.56}$. What is the volume of the washer?

a) 1.570E+00 cm3
b) 1.727E+00 cm3
c) 1.900E+00 cm3
d) 2.090E+00 cm3
e) 2.299E+00 cm3

10) Calculate the motional emf induced along a 24.4 km conductor moving at an orbital speed of 7.79 km/s perpendicular to Earth's 4.790E-05 Tesla magnetic field.

a) 6.840E+03 V
b) 7.524E+03 V
c) 8.277E+03 V
d) 9.105E+03 V
e) 1.002E+04 V

### T7 K0

1) A square coil has sides that are L= 0.325 m long and is tightly wound with N=697 turns of wire. The resistance of the coil is R=4.87 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0842 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.157E+00 A
b) 1.273E+00 A
c) 1.400E+00 A
d) 1.540E+00 A
e) 1.694E+00 A

2) A long solenoid has a radius of 0.757 m and 90 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \alpha =}$30 s−1.What is the induced electric fied at a distance 2.08 m from the axis at time t=0.0442 s ?

a) 6.527E-04 V/m
b) 7.180E-04 V/m
c) 7.898E-04 V/m
d) 8.688E-04 V/m
e) 9.556E-04 V/m

3) A recangular coil with an area of 0.157 m2 and 17 turns is placed in a uniform magnetic field of 3.64 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.890E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 9 s?

a) 4.464E+04 V
b) 4.911E+04 V
c) 5.402E+04 V
d) 5.942E+04 V
e) 6.536E+04 V

4) An induced emf of 3.78V is measured across a coil of 99 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.36A in 0.821s. What is the self-inductance of the coil?

a) 4.033E-01 H
b) 4.436E-01 H
c) 4.880E-01 H
d) 5.367E-01 H
e) 5.904E-01 H
5)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =0.919 s if ε = 6.65 V , R = 6.34 Ω, and L = 1.14 H?
a) 6.033E-01 V
b) 7.240E-01 V
c) 8.688E-01 V
d) 1.043E+00 V
e) 1.251E+00 V

6) An ac generator produces an emf of amplitude 70 V at a frequency of 63 Hz. What is the maximum amplitude of the current if the generator is connected to a 34 mF inductor?

a) 3.908E+00 A
b) 4.298E+00 A
c) 4.728E+00 A
d) 5.201E+00 A
e) 5.721E+00 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 840 Hz and an amplitude of 0.55 V;. If R =4 Ω, L= 9.30E-03H , and C=9.40E-04 F, what is the impedance?

a) 3.685E+01 Ω
b) 4.053E+01 Ω
c) 4.459E+01 Ω
d) 4.905E+01 Ω
e) 5.395E+01 Ω

8) An ac generator produces an emf of amplitude 4 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 19 mF capacitor?

a) 6.946E-02 A
b) 7.640E-02 A
c) 8.404E-02 A
d) 9.245E-02 A
e) 1.017E-01 A

9) An loop of wire with 92 turns has a radius of 0.39 meters, and is oriented with its axis parallel to a magetic field of 0.97 Tesla. What is the induced voltage if this field is reduced to 16% of its original value in 1.4 seconds?

a) 2.56 x 101 volts
b) 3.1 x 101 volts
c) 3.76 x 101 volts
d) 4.55 x 101 volts
e) 5.51 x 101 volts

10) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

#### T7 K1

1) An induced emf of 5.33V is measured across a coil of 77 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.57A in 0.648s. What is the self-inductance of the coil?

a) 4.779E-01 H
b) 5.257E-01 H
c) 5.783E-01 H
d) 6.361E-01 H
e) 6.997E-01 H

2) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

3) An ac generator produces an emf of amplitude 97 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 55 mF inductor?

a) 4.386E+00 A
b) 4.824E+00 A
c) 5.307E+00 A
d) 5.838E+00 A
e) 6.421E+00 A
4)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =13.6 s if ε = 6.56 V , R = 2.44 Ω, and L = 8.76 H?
a) 2.627E+00 V
b) 3.153E+00 V
c) 3.783E+00 V
d) 4.540E+00 V
e) 5.448E+00 V

5) A square coil has sides that are L= 0.738 m long and is tightly wound with N=717 turns of wire. The resistance of the coil is R=5.25 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0655 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.660E+00 A
b) 4.027E+00 A
c) 4.429E+00 A
d) 4.872E+00 A
e) 5.359E+00 A

6) A recangular coil with an area of 0.412 m2 and 18 turns is placed in a uniform magnetic field of 3.81 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 2.120E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 79 s?

a) 4.465E+04 V
b) 4.912E+04 V
c) 5.403E+04 V
d) 5.943E+04 V
e) 6.538E+04 V

7) An loop of wire with 92 turns has a radius of 0.39 meters, and is oriented with its axis parallel to a magetic field of 0.97 Tesla. What is the induced voltage if this field is reduced to 16% of its original value in 1.4 seconds?

a) 2.56 x 101 volts
b) 3.1 x 101 volts
c) 3.76 x 101 volts
d) 4.55 x 101 volts
e) 5.51 x 101 volts

8) An ac generator produces an emf of amplitude 90 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 16 mF capacitor?

a) 4.351E-01 A
b) 4.786E-01 A
c) 5.264E-01 A
d) 5.791E-01 A
e) 6.370E-01 A

9) The output of an ac generator connected to an RLC series combination has a frequency of 710 Hz and an amplitude of 0.88 V;. If R =2 Ω, L= 2.60E-03H , and C=8.00E-04 F, what is the impedance?

a) 1.045E+01 Ω
b) 1.149E+01 Ω
c) 1.264E+01 Ω
d) 1.391E+01 Ω
e) 1.530E+01 Ω

10) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$21 s−1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?

a) 1.605E-04 V/m
b) 1.766E-04 V/m
c) 1.942E-04 V/m
d) 2.136E-04 V/m
e) 2.350E-04 V/m

#### T7 K2

1) A recangular coil with an area of 0.446 m2 and 13 turns is placed in a uniform magnetic field of 3.17 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.060E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 54 s?

a) 1.957E+03 V
b) 2.153E+03 V
c) 2.368E+03 V
d) 2.605E+03 V
e) 2.865E+03 V

2) An ac generator produces an emf of amplitude 32 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 14 mF capacitor?

a) 3.378E-01 A
b) 3.716E-01 A
c) 4.087E-01 A
d) 4.496E-01 A
e) 4.945E-01 A

3) A square coil has sides that are L= 0.638 m long and is tightly wound with N=927 turns of wire. The resistance of the coil is R=8.34 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 2.685E+00 A
b) 2.953E+00 A
c) 3.248E+00 A
d) 3.573E+00 A
e) 3.931E+00 A

4) An ac generator produces an emf of amplitude 73 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF inductor?

a) 1.134E+00 A
b) 1.247E+00 A
c) 1.372E+00 A
d) 1.509E+00 A
e) 1.660E+00 A

5) An induced emf of 7.94V is measured across a coil of 94 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.65A in 0.478s. What is the self-inductance of the coil?

a) 5.047E-01 H
b) 5.552E-01 H
c) 6.107E-01 H
d) 6.717E-01 H
e) 7.389E-01 H
6)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =0.741 s if ε = 7.36 V , R = 5.33 Ω, and L = 1.27 H?
a) 7.635E-01 V
b) 9.162E-01 V
c) 1.099E+00 V
d) 1.319E+00 V
e) 1.583E+00 V

7) An loop of wire with 54 turns has a radius of 0.8 meters, and is oriented with its axis parallel to a magetic field of 0.86 Tesla. What is the induced voltage if this field is reduced to 46% of its original value in 2.4 seconds?

a) 1.43 x 101 volts
b) 1.73 x 101 volts
c) 2.1 x 101 volts
d) 2.55 x 101 volts
e) 3.08 x 101 volts

8) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$5 A and ${\displaystyle \alpha =}$28 s−1.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?

a) 1.616E-04 V/m
b) 1.778E-04 V/m
c) 1.955E-04 V/m
d) 2.151E-04 V/m
e) 2.366E-04 V/m

9) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

10) The output of an ac generator connected to an RLC series combination has a frequency of 910 Hz and an amplitude of 0.88 V;. If R =7 Ω, L= 6.80E-03H , and C=9.60E-04 F, what is the impedance?

a) 3.575E+01 Ω
b) 3.933E+01 Ω
c) 4.326E+01 Ω
d) 4.758E+01 Ω
e) 5.234E+01 Ω

### T7 L0

1) The current through the windings of a solenoid with n= 2.590E+03 turns per meter is changing at a rate dI/dt=11 A/s. The solenoid is 95 cm long and has a cross-sectional diameter of 2.29 cm. A small coil consisting of N=25turns wraped in a circle of diameter 1.15 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 6.985E-05 V
b) 7.683E-05 V
c) 8.452E-05 V
d) 9.297E-05 V
e) 1.023E-04 V

2) A long solenoid has a radius of 0.645 m and 37 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 0.189 m from the axis at time t=0.0698 s ?

a) 1.372E-04 V/m
b) 1.509E-04 V/m
c) 1.660E-04 V/m
d) 1.826E-04 V/m
e) 2.009E-04 V/m

3) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$5 A and ${\displaystyle \alpha =}$28 s−1.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?

a) 1.616E-04 V/m
b) 1.778E-04 V/m
c) 1.955E-04 V/m
d) 2.151E-04 V/m
e) 2.366E-04 V/m

4) An induced emf of 6.75V is measured across a coil of 79 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.76A in 0.115s. What is the self-inductance of the coil?

a) 9.094E-02 H
b) 1.000E-01 H
c) 1.100E-01 H
d) 1.210E-01 H
e) 1.331E-01 H

5) A washer has an inner diameter of 2.74 cm and an outer diamter of 4.71 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.9mm}$, and ${\displaystyle n=2.85}$. What is the volume of the washer?

a) 8.141E-01 cm3
b) 8.955E-01 cm3
c) 9.850E-01 cm3
d) 1.084E+00 cm3
e) 1.192E+00 cm3

6) An ac generator produces an emf of amplitude 73 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF inductor?

a) 1.134E+00 A
b) 1.247E+00 A
c) 1.372E+00 A
d) 1.509E+00 A
e) 1.660E+00 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 860 Hz and an amplitude of 0.59 V;. If R =9 Ω, L= 8.40E-03H , and C=8.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

8) An ac generator produces an emf of amplitude 7 V at a frequency of 95 Hz. What is the maximum amplitude of the current if the generator is connected to a 50 mF capacitor?

a) 1.427E-01 A
b) 1.570E-01 A
c) 1.727E-01 A
d) 1.899E-01 A
e) 2.089E-01 A

9) An loop of wire with 54 turns has a radius of 0.8 meters, and is oriented with its axis parallel to a magetic field of 0.86 Tesla. What is the induced voltage if this field is reduced to 46% of its original value in 2.4 seconds?

a) 1.43 x 101 volts
b) 1.73 x 101 volts
c) 2.1 x 101 volts
d) 2.55 x 101 volts
e) 3.08 x 101 volts

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 L1

1) An induced emf of 6.78V is measured across a coil of 58 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.98A in 0.726s. What is the self-inductance of the coil?

a) 1.022E+00 H
b) 1.124E+00 H
c) 1.237E+00 H
d) 1.360E+00 H
e) 1.496E+00 H

2) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$5 A and ${\displaystyle \alpha =}$28 s−1.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?

a) 1.616E-04 V/m
b) 1.778E-04 V/m
c) 1.955E-04 V/m
d) 2.151E-04 V/m
e) 2.366E-04 V/m

3) A long solenoid has a radius of 0.793 m and 45 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$29 s−1.What is the induced electric fied at a distance 0.216 m from the axis at time t=0.0208 s ?

a) 1.456E-04 V/m
b) 1.601E-04 V/m
c) 1.762E-04 V/m
d) 1.938E-04 V/m
e) 2.132E-04 V/m

4) An ac generator produces an emf of amplitude 8 V at a frequency of 85 Hz. What is the maximum amplitude of the current if the generator is connected to a 16 mF capacitor?

a) 4.669E-02 A
b) 5.136E-02 A
c) 5.650E-02 A
d) 6.215E-02 A
e) 6.836E-02 A

5) A washer has an inner diameter of 2.37 cm and an outer diamter of 4.84 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.67mm}$, and ${\displaystyle n=2.56}$. What is the volume of the washer?

a) 1.570E+00 cm3
b) 1.727E+00 cm3
c) 1.900E+00 cm3
d) 2.090E+00 cm3
e) 2.299E+00 cm3

6) An ac generator produces an emf of amplitude 90 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a 20 mF inductor?

a) 5.008E+00 A
b) 5.509E+00 A
c) 6.060E+00 A
d) 6.666E+00 A
e) 7.333E+00 A

7) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

8) The current through the windings of a solenoid with n= 2.980E+03 turns per meter is changing at a rate dI/dt=9 A/s. The solenoid is 88 cm long and has a cross-sectional diameter of 2.69 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.64 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.498E-04 V
b) 1.647E-04 V
c) 1.812E-04 V
d) 1.993E-04 V
e) 2.193E-04 V

9) An loop of wire with 92 turns has a radius of 0.39 meters, and is oriented with its axis parallel to a magetic field of 0.97 Tesla. What is the induced voltage if this field is reduced to 16% of its original value in 1.4 seconds?

a) 2.56 x 101 volts
b) 3.1 x 101 volts
c) 3.76 x 101 volts
d) 4.55 x 101 volts
e) 5.51 x 101 volts

10) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 Ω, L= 2.80E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

#### T7 L2

1) An loop of wire with 43 turns has a radius of 0.27 meters, and is oriented with its axis parallel to a magetic field of 0.68 Tesla. What is the induced voltage if this field is reduced to 36% of its original value in 3.8 seconds?

a) 6.34 x 10-1 volts
b) 7.68 x 10-1 volts
c) 9.31 x 10-1 volts
d) 1.13 x 100 volts
e) 1.37 x 100 volts

2) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.45 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.066E-04 V
b) 1.173E-04 V
c) 1.290E-04 V
d) 1.419E-04 V
e) 1.561E-04 V

3) A long solenoid has a radius of 0.624 m and 84 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 1.78 m from the axis at time t=0.0579 s ?

a) 3.597E-04 V/m
b) 3.956E-04 V/m
c) 4.352E-04 V/m
d) 4.787E-04 V/m
e) 5.266E-04 V/m

4) An induced emf of 7.94V is measured across a coil of 94 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.65A in 0.478s. What is the self-inductance of the coil?

a) 5.047E-01 H
b) 5.552E-01 H
c) 6.107E-01 H
d) 6.717E-01 H
e) 7.389E-01 H

5) The output of an ac generator connected to an RLC series combination has a frequency of 860 Hz and an amplitude of 0.59 V;. If R =9 Ω, L= 8.40E-03H , and C=8.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

6) An ac generator produces an emf of amplitude 58 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 66 mF capacitor?

a) 3.976E+00 A
b) 4.373E+00 A
c) 4.810E+00 A
d) 5.291E+00 A
e) 5.821E+00 A

7) A long solenoid has a radius of 0.517 m and 23 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$30 s−1.What is the induced electric fied at a distance 0.162 m from the axis at time t=0.0679 s ?

a) 6.256E-06 V/m
b) 6.882E-06 V/m
c) 7.570E-06 V/m
d) 8.327E-06 V/m
e) 9.160E-06 V/m

8) A washer has an inner diameter of 2.12 cm and an outer diamter of 4.47 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.7mm}$, and ${\displaystyle n=2.72}$. What is the volume of the washer?

a) 1.228E+00 cm3
b) 1.351E+00 cm3
c) 1.486E+00 cm3
d) 1.634E+00 cm3
e) 1.798E+00 cm3

9) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

10) An ac generator produces an emf of amplitude 97 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 55 mF inductor?

a) 4.386E+00 A
b) 4.824E+00 A
c) 5.307E+00 A
d) 5.838E+00 A
e) 6.421E+00 A

### T7 M0

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.274 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (1.84)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.59 s. What is the current in the coil if the impedance of the coil is 33.0 Ω?

a) 7.007E-02 A
b) 7.708E-02 A
c) 8.479E-02 A
d) 9.327E-02 A
e) 1.026E-01 A

2) A square coil has sides that are L= 0.561 m long and is tightly wound with N=930 turns of wire. The resistance of the coil is R=5.08 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 2.609E+00 A
b) 2.870E+00 A
c) 3.157E+00 A
d) 3.473E+00 A
e) 3.820E+00 A

3) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.79 T and ${\displaystyle \omega =}$7.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.668 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.910E+04 V
b) 8.701E+04 V
c) 9.571E+04 V
d) 1.053E+05 V
e) 1.158E+05 V

4) A washer has an inner diameter of 2.21 cm and an outer diamter of 4.5 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.29mm}$, and ${\displaystyle n=2.62}$. What is the volume of the washer?

a) 1.325E+00 cm3
b) 1.457E+00 cm3
c) 1.603E+00 cm3
d) 1.763E+00 cm3
e) 1.939E+00 cm3
5)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =1.95 s if ε = 8.33 V , R = 6.96 Ω, and L = 2.66 H?
a) 5.736E-01 V
b) 6.884E-01 V
c) 8.260E-01 V
d) 9.912E-01 V
e) 1.189E+00 V

6) The output of an ac generator connected to an RLC series combination has a frequency of 6.10E+04 Hz and an amplitude of 9 V. If R =4 Ω, L= 3.40E-03H , and C=8.10E-06 F, what is the rms power transferred to the resistor?

a) 3.839E-03 Watts
b) 4.223E-03 Watts
c) 4.646E-03 Watts
d) 5.110E-03 Watts
e) 5.621E-03 Watts

7) The output of an ac generator connected to an RLC series combination has a frequency of 490 Hz and an amplitude of 0.68 V;. If R =9 Ω, L= 5.80E-03H , and C=9.50E-04 F, what is the impedance?

a) 1.969E+01 Ω
b) 2.166E+01 Ω
c) 2.383E+01 Ω
d) 2.621E+01 Ω
e) 2.883E+01 Ω

8) The output of an ac generator connected to an RLC series combination has a frequency of 510 Hz and an amplitude of 0.24 V;. If R =7 Ω, L= 2.90E-03H , and C=9.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

10) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

#### T7 M1

1) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

2) A washer has an inner diameter of 2.37 cm and an outer diamter of 4.84 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.67mm}$, and ${\displaystyle n=2.56}$. What is the volume of the washer?

a) 1.570E+00 cm3
b) 1.727E+00 cm3
c) 1.900E+00 cm3
d) 2.090E+00 cm3
e) 2.299E+00 cm3

3) The output of an ac generator connected to an RLC series combination has a frequency of 5.70E+04 Hz and an amplitude of 5 V. If R =9 Ω, L= 6.10E-03H , and C=6.60E-06 F, what is the rms power transferred to the resistor?

a) 9.443E-04 Watts
b) 1.039E-03 Watts
c) 1.143E-03 Watts
d) 1.257E-03 Watts
e) 1.383E-03 Watts

4) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.84 T and ${\displaystyle \omega =}$4.410E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.379 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 3.333E+04 V
b) 3.666E+04 V
c) 4.033E+04 V
d) 4.436E+04 V
e) 4.879E+04 V

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.78 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.22)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.74 s. What is the current in the coil if the impedance of the coil is 32.1 Ω?

a) 1.742E+00 A
b) 1.916E+00 A
c) 2.108E+00 A
d) 2.319E+00 A
e) 2.551E+00 A

6) The output of an ac generator connected to an RLC series combination has a frequency of 910 Hz and an amplitude of 0.88 V;. If R =7 Ω, L= 6.80E-03H , and C=9.60E-04 F, what is the impedance?

a) 3.575E+01 Ω
b) 3.933E+01 Ω
c) 4.326E+01 Ω
d) 4.758E+01 Ω
e) 5.234E+01 Ω

7) A square coil has sides that are L= 0.259 m long and is tightly wound with N=628 turns of wire. The resistance of the coil is R=6.51 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0372 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.809E-01 A
b) 1.989E-01 A
c) 2.188E-01 A
d) 2.407E-01 A
e) 2.648E-01 A

8) Two orbiting satellites are orbiting at a speed of 66 km/s perpendicular to a magnetic field of 64 μT. They are connected by a cable that is 37 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 1.29 x 105 volts.
b) 1.56 x 105 volts.
c) 1.89 x 105 volts.
d) 2.29 x 105 volts.
e) 2.78 x 105 volts.

9) The output of an ac generator connected to an RLC series combination has a frequency of 410 Hz and an amplitude of 0.82 V;. If R =7 Ω, L= 9.70E-03H , and C=9.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

10)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =20.1 s if ε = 5.77 V , R = 1.38 Ω, and L = 5.45 H?
a) 3.463E+00 V
b) 4.156E+00 V
c) 4.987E+00 V
d) 5.984E+00 V
e) 7.181E+00 V

#### T7 M2

1) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.58 T and ${\displaystyle \omega =}$4.310E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.879 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.043E+04 V
b) 7.747E+04 V
c) 8.522E+04 V
d) 9.374E+04 V
e) 1.031E+05 V

3) A washer has an inner diameter of 2.46 cm and an outer diamter of 4.24 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.32mm}$, and ${\displaystyle n=2.63}$. What is the volume of the washer?

a) 7.499E-01 cm3
b) 8.249E-01 cm3
c) 9.074E-01 cm3
d) 9.982E-01 cm3
e) 1.098E+00 cm3

4) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 Ω, L= 2.80E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.594 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.89)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.6 s. What is the current in the coil if the impedance of the coil is 6.65 Ω?

a) 2.088E+00 A
b) 2.297E+00 A
c) 2.527E+00 A
d) 2.779E+00 A
e) 3.057E+00 A

6) A square coil has sides that are L= 0.894 m long and is tightly wound with N=255 turns of wire. The resistance of the coil is R=8.83 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0682 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.301E+00 A
b) 1.431E+00 A
c) 1.574E+00 A
d) 1.732E+00 A
e) 1.905E+00 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 1.00E+03 Hz and an amplitude of 0.6 V;. If R =3 Ω, L= 1.70E-03H , and C=5.40E-04 F, what is the impedance?

a) 8.123E+00 Ω
b) 8.935E+00 Ω
c) 9.828E+00 Ω
d) 1.081E+01 Ω
e) 1.189E+01 Ω

8) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 6.60E-03H , and C=5.30E-06 F, what is the rms power transferred to the resistor?

a) 2.007E-03 Watts
b) 2.208E-03 Watts
c) 2.429E-03 Watts
d) 2.672E-03 Watts
e) 2.939E-03 Watts
9)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =3.96 s if ε = 4.92 V , R = 5.02 Ω, and L = 5.0 H?
a) 9.618E-01 V
b) 1.154E+00 V
c) 1.385E+00 V
d) 1.662E+00 V
e) 1.994E+00 V

10) Two orbiting satellites are orbiting at a speed of 58 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 22 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 2.72 x 104 volts.
b) 3.3 x 104 volts.
c) 4 x 104 volts.
d) 4.84 x 104 volts.
e) 5.87 x 104 volts.

### T7 N0

1) The current through the windings of a solenoid with n= 2.400E+03 turns per meter is changing at a rate dI/dt=3 A/s. The solenoid is 93 cm long and has a cross-sectional diameter of 2.13 cm. A small coil consisting of N=30turns wraped in a circle of diameter 1.35 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 3.885E-05 V
b) 4.274E-05 V
c) 4.701E-05 V
d) 5.171E-05 V
e) 5.688E-05 V

2) Calculate the motional emf induced along a 49.5 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 5.310E-05 Tesla magnetic field.

a) 1.395E+04 V
b) 1.534E+04 V
c) 1.688E+04 V
d) 1.857E+04 V
e) 2.042E+04 V

3) A long solenoid has a radius of 0.306 m and 98 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$22 s−1.What is the induced electric fied at a distance 2.52 m from the axis at time t=0.0246 s ?

a) 1.598E-04 V/m
b) 1.758E-04 V/m
c) 1.934E-04 V/m
d) 2.127E-04 V/m
e) 2.340E-04 V/m
4)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =5.67 s if ε = 5.58 V , R = 3.81 Ω, and L = 3.85 H?
a) 7.037E-01 V
b) 8.444E-01 V
c) 1.013E+00 V
d) 1.216E+00 V
e) 1.459E+00 V
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.54% of its maximum value if ε = 2.46 V , R = 2.8 Ω, and L = 5.67 H?
a) -2.540E+00 s
b) -2.794E+00 s
c) -3.073E+00 s
d) -3.381E+00 s
e) -3.719E+00 s

6) The output of an ac generator connected to an RLC series combination has a frequency of 810 Hz and an amplitude of 0.64 V;. If R =6 Ω, L= 8.70E-03H , and C=8.20E-04 F, what is the impedance?

a) 4.444E+01 Ω
b) 4.889E+01 Ω
c) 5.378E+01 Ω
d) 5.916E+01 Ω
e) 6.507E+01 Ω

7) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 59 mF capacitor?

a) 5.042E+00 A
b) 5.546E+00 A
c) 6.100E+00 A
d) 6.710E+00 A
e) 7.381E+00 A

8) A step-down transformer steps 16 kV down to 210 V. The high-voltage input is provided by a 200 Ω power line that carries 7 A of currentWhat is the output current (at the 210 V side ?)

a) 4.007E+02 A
b) 4.408E+02 A
c) 4.848E+02 A
d) 5.333E+02 A
e) 5.867E+02 A

9) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

10) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

#### T7 N1

1)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.54% of its maximum value if ε = 2.46 V , R = 2.8 Ω, and L = 5.67 H?
a) -2.540E+00 s
b) -2.794E+00 s
c) -3.073E+00 s
d) -3.381E+00 s
e) -3.719E+00 s

2) An ac generator produces an emf of amplitude 17 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 6 mF capacitor?

a) 5.253E-02 A
b) 5.778E-02 A
c) 6.356E-02 A
d) 6.991E-02 A
e) 7.691E-02 A

3) The output of an ac generator connected to an RLC series combination has a frequency of 900 Hz and an amplitude of 0.43 V;. If R =7 Ω, L= 5.60E-03H , and C=6.30E-04 F, what is the impedance?

a) 2.658E+01 Ω
b) 2.923E+01 Ω
c) 3.216E+01 Ω
d) 3.537E+01 Ω
e) 3.891E+01 Ω

4) A long solenoid has a radius of 0.45 m and 35 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$28 s−1.What is the induced electric fied at a distance 2.35 m from the axis at time t=0.0709 s ?

a) 5.475E-06 V/m
b) 6.023E-06 V/m
c) 6.625E-06 V/m
d) 7.288E-06 V/m
e) 8.017E-06 V/m

5) A step-down transformer steps 18 kV down to 230 V. The high-voltage input is provided by a 250 Ω power line that carries 8 A of currentWhat is the output current (at the 230 V side ?)

a) 5.174E+02 A
b) 5.692E+02 A
c) 6.261E+02 A
d) 6.887E+02 A
e) 7.576E+02 A

6) The current through the windings of a solenoid with n= 2.840E+03 turns per meter is changing at a rate dI/dt=19 A/s. The solenoid is 65 cm long and has a cross-sectional diameter of 2.18 cm. A small coil consisting of N=25turns wraped in a circle of diameter 1.35 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 2.206E-04 V
b) 2.426E-04 V
c) 2.669E-04 V
d) 2.936E-04 V
e) 3.230E-04 V

7) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

8) Calculate the motional emf induced along a 49.5 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 5.310E-05 Tesla magnetic field.

a) 1.395E+04 V
b) 1.534E+04 V
c) 1.688E+04 V
d) 1.857E+04 V
e) 2.042E+04 V

9) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.
10)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =7.72 s if ε = 2.79 V , R = 1.56 Ω, and L = 3.16 H?
a) 1.214E+00 V
b) 1.457E+00 V
c) 1.749E+00 V
d) 2.099E+00 V
e) 2.518E+00 V

#### T7 N2

1) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

2) An ac generator produces an emf of amplitude 4 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 19 mF capacitor?

a) 6.946E-02 A
b) 7.640E-02 A
c) 8.404E-02 A
d) 9.245E-02 A
e) 1.017E-01 A

3) Calculate the motional emf induced along a 24.9 km conductor moving at an orbital speed of 7.82 km/s perpendicular to Earth's 5.040E-05 Tesla magnetic field.

a) 8.111E+03 V
b) 8.922E+03 V
c) 9.814E+03 V
d) 1.080E+04 V
e) 1.187E+04 V

4) The output of an ac generator connected to an RLC series combination has a frequency of 890 Hz and an amplitude of 0.12 V;. If R =8 Ω, L= 8.60E-03H , and C=9.90E-04 F, what is the impedance?

a) 3.318E+01 Ω
b) 3.649E+01 Ω
c) 4.014E+01 Ω
d) 4.416E+01 Ω
e) 4.857E+01 Ω
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.67% of its maximum value if ε = 5.07 V , R = 7.8 Ω, and L = 4.39 H?
a) -1.047E+00 s
b) -1.152E+00 s
c) -1.267E+00 s
d) -1.393E+00 s
e) -1.533E+00 s

6) The current through the windings of a solenoid with n= 2.980E+03 turns per meter is changing at a rate dI/dt=9 A/s. The solenoid is 88 cm long and has a cross-sectional diameter of 2.69 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.64 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.498E-04 V
b) 1.647E-04 V
c) 1.812E-04 V
d) 1.993E-04 V
e) 2.193E-04 V

7) A long solenoid has a radius of 0.887 m and 43 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \alpha =}$28 s−1.What is the induced electric fied at a distance 2.66 m from the axis at time t=0.0332 s ?

a) 6.182E-04 V/m
b) 6.801E-04 V/m
c) 7.481E-04 V/m
d) 8.229E-04 V/m
e) 9.052E-04 V/m
8)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.53 s if ε = 6.14 V , R = 4.22 Ω, and L = 1.91 H?
a) 1.007E+00 V
b) 1.208E+00 V
c) 1.450E+00 V
d) 1.739E+00 V
e) 2.087E+00 V

9) Two orbiting satellites are orbiting at a speed of 66 km/s perpendicular to a magnetic field of 64 μT. They are connected by a cable that is 37 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 1.29 x 105 volts.
b) 1.56 x 105 volts.
c) 1.89 x 105 volts.
d) 2.29 x 105 volts.
e) 2.78 x 105 volts.

10) A step-down transformer steps 9 kV down to 160 V. The high-voltage input is provided by a 260 Ω power line that carries 7 A of currentWhat is the output current (at the 160 V side ?)

a) 3.938E+02 A
b) 4.331E+02 A
c) 4.764E+02 A
d) 5.241E+02 A
e) 5.765E+02 A

### T7 O0

1) A long solenoid has a radius of 0.645 m and 37 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 0.189 m from the axis at time t=0.0698 s ?

a) 1.372E-04 V/m
b) 1.509E-04 V/m
c) 1.660E-04 V/m
d) 1.826E-04 V/m
e) 2.009E-04 V/m

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.84 T and ${\displaystyle \omega =}$4.410E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.379 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 3.333E+04 V
b) 3.666E+04 V
c) 4.033E+04 V
d) 4.436E+04 V
e) 4.879E+04 V

3) A square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.661E+00 A
b) 4.028E+00 A
c) 4.430E+00 A
d) 4.873E+00 A
e) 5.361E+00 A
4)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =3.96 s if ε = 4.92 V , R = 5.02 Ω, and L = 5.0 H?
a) 9.618E-01 V
b) 1.154E+00 V
c) 1.385E+00 V
d) 1.662E+00 V
e) 1.994E+00 V
5)
A long solenoid has a length 0.841 meters, radius 3.81 cm, and 516 turns. It surrounds coil of radius 9.2 meters and 11turns. If the current in the solenoid is changing at a rate of 190 A/s, what is the emf induced in the surounding coil?
a) 1.735E-02 V
b) 1.908E-02 V
c) 2.099E-02 V
d) 2.309E-02 V
e) 2.540E-02 V

6) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.82 V. The resistance, inductance, and capacitance are R =3 Ω, L= 6.20E-03H , and C=6.70E-04 F, respectively. What is the amplitude of the current?

a) 2.259E-01 A
b) 2.485E-01 A
c) 2.733E-01 A
d) 3.007E-01 A
e) 3.307E-01 A

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.13 Ω, L= 5.30E-03H , and C=2.60E-06 F, respectively.

a) Q = 1.986E+02
b) Q = 2.284E+02
c) Q = 2.626E+02
d) Q = 3.020E+02
e) Q = 3.473E+02

8) The output of an ac generator connected to an RLC series combination has a frequency of 6.10E+04 Hz and an amplitude of 8 V. If R =5 Ω, L= 9.10E-03H , and C=8.80E-06 F, what is the rms power transferred to the resistor?

a) 4.320E-04 Watts
b) 4.752E-04 Watts
c) 5.227E-04 Watts
d) 5.750E-04 Watts
e) 6.325E-04 Watts

9) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

10) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

#### T7 O1

1) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.76 V. The resistance, inductance, and capacitance are R =8 Ω, L= 3.80E-03H , and C=5.60E-04 F, respectively. What is the amplitude of the current?

a) 8.636E-02 A
b) 9.500E-02 A
c) 1.045E-01 A
d) 1.150E-01 A
e) 1.264E-01 A

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.7 T and ${\displaystyle \omega =}$8.100E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.827 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.416E+05 V
b) 1.557E+05 V
c) 1.713E+05 V
d) 1.884E+05 V
e) 2.073E+05 V

3) A long solenoid has a radius of 0.603 m and 51 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$26 s−1.What is the induced electric fied at a distance 0.105 m from the axis at time t=0.0659 s ?

a) 2.154E-05 V/m
b) 2.369E-05 V/m
c) 2.606E-05 V/m
d) 2.867E-05 V/m
e) 3.154E-05 V/m
4)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =1.0 s if ε = 4.14 V , R = 7.92 Ω, and L = 2.26 H?
a) 3.523E-01 V
b) 4.227E-01 V
c) 5.073E-01 V
d) 6.087E-01 V
e) 7.304E-01 V
5)
A long solenoid has a length 0.805 meters, radius 4.24 cm, and 536 turns. It surrounds coil of radius 8.5 meters and 16turns. If the current in the solenoid is changing at a rate of 278 A/s, what is the emf induced in the surounding coil?
a) 6.604E-02 V
b) 7.264E-02 V
c) 7.990E-02 V
d) 8.789E-02 V
e) 9.668E-02 V

6) An loop of wire with 92 turns has a radius of 0.39 meters, and is oriented with its axis parallel to a magetic field of 0.97 Tesla. What is the induced voltage if this field is reduced to 16% of its original value in 1.4 seconds?

a) 2.56 x 101 volts
b) 3.1 x 101 volts
c) 3.76 x 101 volts
d) 4.55 x 101 volts
e) 5.51 x 101 volts

7) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

8) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=4 V. The resistance, inductance, and capacitance are R =0.2 Ω, L= 5.00E-03H , and C=3.20E-06 F, respectively.

a) Q = 1.300E+02
b) Q = 1.494E+02
c) Q = 1.719E+02
d) Q = 1.976E+02
e) Q = 2.273E+02

9) A square coil has sides that are L= 0.738 m long and is tightly wound with N=717 turns of wire. The resistance of the coil is R=5.25 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0655 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 3.660E+00 A
b) 4.027E+00 A
c) 4.429E+00 A
d) 4.872E+00 A
e) 5.359E+00 A

10) The output of an ac generator connected to an RLC series combination has a frequency of 3.60E+04 Hz and an amplitude of 9 V. If R =2 Ω, L= 7.60E-03H , and C=7.50E-06 F, what is the rms power transferred to the resistor?

a) 1.011E-03 Watts
b) 1.112E-03 Watts
c) 1.223E-03 Watts
d) 1.345E-03 Watts
e) 1.480E-03 Watts

#### T7 O2

1) The output of an ac generator connected to an RLC series combination has a frequency of 2.30E+04 Hz and an amplitude of 7 V. If R =3 Ω, L= 4.10E-03H , and C=8.70E-06 F, what is the rms power transferred to the resistor?

a) 8.369E-03 Watts
b) 9.206E-03 Watts
c) 1.013E-02 Watts
d) 1.114E-02 Watts
e) 1.225E-02 Watts
2)
A long solenoid has a length 0.841 meters, radius 3.81 cm, and 516 turns. It surrounds coil of radius 9.2 meters and 11turns. If the current in the solenoid is changing at a rate of 190 A/s, what is the emf induced in the surounding coil?
a) 1.735E-02 V
b) 1.908E-02 V
c) 2.099E-02 V
d) 2.309E-02 V
e) 2.540E-02 V

3) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

4) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.44 V. The resistance, inductance, and capacitance are R =7 Ω, L= 5.40E-03H , and C=5.70E-04 F, respectively. What is the amplitude of the current?

a) 4.723E-02 A
b) 5.195E-02 A
c) 5.714E-02 A
d) 6.286E-02 A
e) 6.914E-02 A
5)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =5.9 s if ε = 7.85 V , R = 6.89 Ω, and L = 7.36 H?
a) 6.567E-01 V
b) 7.880E-01 V
c) 9.456E-01 V
d) 1.135E+00 V
e) 1.362E+00 V

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.21 Ω, L= 4.70E-03H , and C=3.70E-06 F, respectively.

a) Q = 1.476E+02
b) Q = 1.697E+02
c) Q = 1.952E+02
d) Q = 2.245E+02
e) Q = 2.581E+02

7) A long solenoid has a radius of 0.596 m and 19 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$5 A and ${\displaystyle \alpha =}$29 s−1.What is the induced electric fied at a distance 0.209 m from the axis at time t=0.0604 s ?

a) 6.277E-05 V/m
b) 6.904E-05 V/m
c) 7.595E-05 V/m
d) 8.354E-05 V/m
e) 9.190E-05 V/m

8) A square coil has sides that are L= 0.894 m long and is tightly wound with N=255 turns of wire. The resistance of the coil is R=8.83 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0682 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.301E+00 A
b) 1.431E+00 A
c) 1.574E+00 A
d) 1.732E+00 A
e) 1.905E+00 A

9) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

10) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.71 T and ${\displaystyle \omega =}$6.600E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.31 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 4.769E+04 V
b) 5.246E+04 V
c) 5.771E+04 V
d) 6.348E+04 V
e) 6.983E+04 V

### T7 P0

1) A square coil has sides that are L= 0.259 m long and is tightly wound with N=628 turns of wire. The resistance of the coil is R=6.51 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0372 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.809E-01 A
b) 1.989E-01 A
c) 2.188E-01 A
d) 2.407E-01 A
e) 2.648E-01 A

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.84 T and ${\displaystyle \omega =}$4.410E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.379 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 3.333E+04 V
b) 3.666E+04 V
c) 4.033E+04 V
d) 4.436E+04 V
e) 4.879E+04 V

3) A recangular coil with an area of 0.39 m2 and 16 turns is placed in a uniform magnetic field of 3.07 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.320E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 44 s?

a) 3.792E+04 V
b) 4.172E+04 V
c) 4.589E+04 V
d) 5.048E+04 V
e) 5.552E+04 V

4) In an LC circuit, the self-inductance is 0.0116 H and the capacitance is 7.040E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.140E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.489E-04 s
b) 4.938E-04 s
c) 5.432E-04 s
d) 5.975E-04 s
e) 6.572E-04 s

5) A washer has an inner diameter of 2.21 cm and an outer diamter of 4.5 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.29mm}$, and ${\displaystyle n=2.62}$. What is the volume of the washer?

a) 1.325E+00 cm3
b) 1.457E+00 cm3
c) 1.603E+00 cm3
d) 1.763E+00 cm3
e) 1.939E+00 cm3

6) An ac generator produces an emf of amplitude 90 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a 20 mF inductor?

a) 5.008E+00 A
b) 5.509E+00 A
c) 6.060E+00 A
d) 6.666E+00 A
e) 7.333E+00 A

7) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.31 V. The resistance, inductance, and capacitance are R =5 Ω, L= 9.00E-03H , and C=5.10E-04 F, respectively. What is the amplitude of the current?

a) 4.235E-02 A
b) 4.658E-02 A
c) 5.124E-02 A
d) 5.636E-02 A
e) 6.200E-02 A

8) The output of an ac generator connected to an RLC series combination has a frequency of 280 Hz and an amplitude of 0.35 V;. If R =5 Ω, L= 9.50E-03H , and C=6.90E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) An loop of wire with 31 turns has a radius of 0.9 meters, and is oriented with its axis parallel to a magetic field of 0.83 Tesla. What is the induced voltage if this field is reduced to 35% of its original value in 1.7 seconds?

a) 2.07 x 101 volts
b) 2.5 x 101 volts
c) 3.03 x 101 volts
d) 3.67 x 101 volts
e) 4.45 x 101 volts

10) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

#### T7 P1

1) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.16 V. The resistance, inductance, and capacitance are R =8 Ω, L= 5.40E-03H , and C=5.40E-04 F, respectively. What is the amplitude of the current?

a) 2.000E-02 A
b) 2.200E-02 A
c) 2.420E-02 A
d) 2.662E-02 A
e) 2.928E-02 A

2) The output of an ac generator connected to an RLC series combination has a frequency of 360 Hz and an amplitude of 0.17 V;. If R =9 Ω, L= 2.60E-03H , and C=8.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

3) A recangular coil with an area of 0.449 m2 and 20 turns is placed in a uniform magnetic field of 3.58 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.990E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 66 s?

a) 7.734E+04 V
b) 8.507E+04 V
c) 9.358E+04 V
d) 1.029E+05 V
e) 1.132E+05 V

4) An ac generator produces an emf of amplitude 46 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 63 mF inductor?

a) 4.961E-01 A
b) 5.457E-01 A
c) 6.002E-01 A
d) 6.603E-01 A
e) 7.263E-01 A

5) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

6) A square coil has sides that are L= 0.861 m long and is tightly wound with N=538 turns of wire. The resistance of the coil is R=9.04 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0433 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.737E+00 A
b) 1.910E+00 A
c) 2.101E+00 A
d) 2.311E+00 A
e) 2.543E+00 A

7) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

8) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$1.8 T and ${\displaystyle \omega =}$1.530E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.519 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.422E+03 V
b) 8.164E+03 V
c) 8.981E+03 V
d) 9.879E+03 V
e) 1.087E+04 V

9) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.85 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.7mm}$, and ${\displaystyle n=2.76}$. What is the volume of the washer?

a) 1.038E+00 cm3
b) 1.142E+00 cm3
c) 1.256E+00 cm3
d) 1.381E+00 cm3
e) 1.520E+00 cm3

10) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?

a) 6.166E-04 s
b) 6.783E-04 s
c) 7.461E-04 s
d) 8.207E-04 s
e) 9.028E-04 s

#### T7 P2

1) A washer has an inner diameter of 2.46 cm and an outer diamter of 4.24 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.32mm}$, and ${\displaystyle n=2.63}$. What is the volume of the washer?

a) 7.499E-01 cm3
b) 8.249E-01 cm3
c) 9.074E-01 cm3
d) 9.982E-01 cm3
e) 1.098E+00 cm3

2) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.3 V. The resistance, inductance, and capacitance are R =2 Ω, L= 8.10E-03H , and C=9.40E-04 F, respectively. What is the amplitude of the current?

a) 1.364E-01 A
b) 1.500E-01 A
c) 1.650E-01 A
d) 1.815E-01 A
e) 1.997E-01 A

3) In an LC circuit, the self-inductance is 0.025 H and the capacitance is 3.530E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.770E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.856E-04 s
b) 4.242E-04 s
c) 4.666E-04 s
d) 5.133E-04 s
e) 5.646E-04 s

4) The output of an ac generator connected to an RLC series combination has a frequency of 750 Hz and an amplitude of 0.88 V;. If R =4 Ω, L= 5.60E-03H , and C=9.70E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

5) An ac generator produces an emf of amplitude 75 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 22 mF inductor?

a) 2.466E+00 A
b) 2.713E+00 A
c) 2.984E+00 A
d) 3.283E+00 A
e) 3.611E+00 A

6) A recangular coil with an area of 0.39 m2 and 16 turns is placed in a uniform magnetic field of 3.07 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.320E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 44 s?

a) 3.792E+04 V
b) 4.172E+04 V
c) 4.589E+04 V
d) 5.048E+04 V
e) 5.552E+04 V

7) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.75 T and ${\displaystyle \omega =}$1.740E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.417 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.168E+04 V
b) 1.284E+04 V
c) 1.413E+04 V
d) 1.554E+04 V
e) 1.710E+04 V

8) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

9) A square coil has sides that are L= 0.308 m long and is tightly wound with N=969 turns of wire. The resistance of the coil is R=8.64 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0498 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 4.817E-01 A
b) 5.298E-01 A
c) 5.828E-01 A
d) 6.411E-01 A
e) 7.052E-01 A

10) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

### T7 Q0

1) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm. A small coil consisting of N=28turns wraped in a circle of diameter 1.5 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 2.081E-04 V
b) 2.289E-04 V
c) 2.518E-04 V
d) 2.770E-04 V
e) 3.047E-04 V

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.869 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.01)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.66 s. What is the current in the coil if the impedance of the coil is 32.8 Ω?

a) 9.191E-01 A
b) 1.011E+00 A
c) 1.112E+00 A
d) 1.223E+00 A
e) 1.346E+00 A

3) A long solenoid has a radius of 0.716 m and 96 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?

a) 1.426E-03 V/m
b) 1.568E-03 V/m
c) 1.725E-03 V/m
d) 1.897E-03 V/m
e) 2.087E-03 V/m

4) A washer has an inner diameter of 2.62 cm and an outer diamter of 4.79 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.08mm}$, and ${\displaystyle n=2.68}$. What is the volume of the washer?

a) 1.056E+00 cm3
b) 1.161E+00 cm3
c) 1.278E+00 cm3
d) 1.405E+00 cm3
e) 1.546E+00 cm3
5)
A long solenoid has a length 0.896 meters, radius 4.28 cm, and 550 turns. It surrounds coil of radius 6.65 meters and 9turns. If the current in the solenoid is changing at a rate of 204 A/s, what is the emf induced in the surounding coil?
a) 2.328E-02 V
b) 2.560E-02 V
c) 2.817E-02 V
d) 3.098E-02 V
e) 3.408E-02 V

6) A step-down transformer steps 7 kV down to 190 V. The high-voltage input is provided by a 240 Ω power line that carries 5 A of currentWhat is the output current (at the 190 V side ?)

a) 1.675E+02 A
b) 1.842E+02 A
c) 2.026E+02 A
d) 2.229E+02 A
e) 2.452E+02 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 680 Hz and an amplitude of 0.79 V;. If R =5 Ω, L= 2.40E-03H , and C=9.10E-04 F, what is the impedance?

a) 8.398E+00 Ω
b) 9.238E+00 Ω
c) 1.016E+01 Ω
d) 1.118E+01 Ω
e) 1.230E+01 Ω

8) The output of an ac generator connected to an RLC series combination has a frequency of 5.70E+04 Hz and an amplitude of 5 V. If R =9 Ω, L= 6.10E-03H , and C=6.60E-06 F, what is the rms power transferred to the resistor?

a) 9.443E-04 Watts
b) 1.039E-03 Watts
c) 1.143E-03 Watts
d) 1.257E-03 Watts
e) 1.383E-03 Watts

9) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 Q1

1) The output of an ac generator connected to an RLC series combination has a frequency of 7.60E+04 Hz and an amplitude of 5 V. If R =6 Ω, L= 3.70E-03H , and C=5.80E-06 F, what is the rms power transferred to the resistor?

a) 7.239E-04 Watts
b) 7.963E-04 Watts
c) 8.759E-04 Watts
d) 9.635E-04 Watts
e) 1.060E-03 Watts

2) The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 85 cm long and has a cross-sectional diameter of 3.12 cm. A small coil consisting of N=32turns wraped in a circle of diameter 1.44 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.602E-04 V
b) 1.762E-04 V
c) 1.939E-04 V
d) 2.132E-04 V
e) 2.346E-04 V

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.8 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.6)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$8.91 s. What is the current in the coil if the impedance of the coil is 61.7 Ω?

a) 5.369E-01 A
b) 5.906E-01 A
c) 6.496E-01 A
d) 7.146E-01 A
e) 7.860E-01 A

4) A step-down transformer steps 9 kV down to 160 V. The high-voltage input is provided by a 260 Ω power line that carries 7 A of currentWhat is the output current (at the 160 V side ?)

a) 3.938E+02 A
b) 4.331E+02 A
c) 4.764E+02 A
d) 5.241E+02 A
e) 5.765E+02 A
5)
A long solenoid has a length 0.667 meters, radius 4.41 cm, and 517 turns. It surrounds coil of radius 9.18 meters and 9turns. If the current in the solenoid is changing at a rate of 296 A/s, what is the emf induced in the surounding coil?
a) 4.116E-02 V
b) 4.528E-02 V
c) 4.981E-02 V
d) 5.479E-02 V
e) 6.027E-02 V

6) A long solenoid has a radius of 0.644 m and 20 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \alpha =}$27 s−1.What is the induced electric fied at a distance 2.84 m from the axis at time t=0.083 s ?

a) 3.353E-05 V/m
b) 3.689E-05 V/m
c) 4.058E-05 V/m
d) 4.463E-05 V/m
e) 4.910E-05 V/m

7) The output of an ac generator connected to an RLC series combination has a frequency of 490 Hz and an amplitude of 0.68 V;. If R =9 Ω, L= 5.80E-03H , and C=9.50E-04 F, what is the impedance?

a) 1.969E+01 Ω
b) 2.166E+01 Ω
c) 2.383E+01 Ω
d) 2.621E+01 Ω
e) 2.883E+01 Ω

8) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

9) An loop of wire with 31 turns has a radius of 0.9 meters, and is oriented with its axis parallel to a magetic field of 0.83 Tesla. What is the induced voltage if this field is reduced to 35% of its original value in 1.7 seconds?

a) 2.07 x 101 volts
b) 2.5 x 101 volts
c) 3.03 x 101 volts
d) 3.67 x 101 volts
e) 4.45 x 101 volts

10) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.87 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.39mm}$, and ${\displaystyle n=2.55}$. What is the volume of the washer?

a) 7.754E-01 cm3
b) 8.530E-01 cm3
c) 9.383E-01 cm3
d) 1.032E+00 cm3
e) 1.135E+00 cm3

#### T7 Q2

1) A step-down transformer steps 8 kV down to 220 V. The high-voltage input is provided by a 110 Ω power line that carries 8 A of currentWhat is the output current (at the 220 V side ?)

a) 2.404E+02 A
b) 2.645E+02 A
c) 2.909E+02 A
d) 3.200E+02 A
e) 3.520E+02 A

2) The output of an ac generator connected to an RLC series combination has a frequency of 5.70E+04 Hz and an amplitude of 5 V. If R =9 Ω, L= 6.10E-03H , and C=6.60E-06 F, what is the rms power transferred to the resistor?

a) 9.443E-04 Watts
b) 1.039E-03 Watts
c) 1.143E-03 Watts
d) 1.257E-03 Watts
e) 1.383E-03 Watts

3) A washer has an inner diameter of 2.2 cm and an outer diamter of 4.11 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.23mm}$, and ${\displaystyle n=2.74}$. What is the volume of the washer?

a) 7.110E-01 cm3
b) 7.821E-01 cm3
c) 8.603E-01 cm3
d) 9.463E-01 cm3
e) 1.041E+00 cm3

4) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

5) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

6) The current through the windings of a solenoid with n= 2.040E+03 turns per meter is changing at a rate dI/dt=19 A/s. The solenoid is 76 cm long and has a cross-sectional diameter of 3.23 cm. A small coil consisting of N=25turns wraped in a circle of diameter 1.67 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 2.204E-04 V
b) 2.425E-04 V
c) 2.667E-04 V
d) 2.934E-04 V
e) 3.227E-04 V
7)
A long solenoid has a length 0.703 meters, radius 4.03 cm, and 542 turns. It surrounds coil of radius 6.58 meters and 9turns. If the current in the solenoid is changing at a rate of 208 A/s, what is the emf induced in the surounding coil?
a) 2.643E-02 V
b) 2.907E-02 V
c) 3.198E-02 V
d) 3.518E-02 V
e) 3.869E-02 V

8) The output of an ac generator connected to an RLC series combination has a frequency of 680 Hz and an amplitude of 0.79 V;. If R =5 Ω, L= 2.40E-03H , and C=9.10E-04 F, what is the impedance?

a) 8.398E+00 Ω
b) 9.238E+00 Ω
c) 1.016E+01 Ω
d) 1.118E+01 Ω
e) 1.230E+01 Ω

9) A long solenoid has a radius of 0.777 m and 67 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 2.39 m from the axis at time t=0.0399 s ?

a) 3.924E-04 V/m
b) 4.317E-04 V/m
c) 4.748E-04 V/m
d) 5.223E-04 V/m
e) 5.745E-04 V/m

10) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.869 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.01)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.66 s. What is the current in the coil if the impedance of the coil is 32.8 Ω?

a) 9.191E-01 A
b) 1.011E+00 A
c) 1.112E+00 A
d) 1.223E+00 A
e) 1.346E+00 A

### T7 R0

1) A square coil has sides that are L= 0.458 m long and is tightly wound with N=742 turns of wire. The resistance of the coil is R=6.81 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0559 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.056E+00 A
b) 1.161E+00 A
c) 1.278E+00 A
d) 1.405E+00 A
e) 1.546E+00 A

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.25 T and ${\displaystyle \omega =}$8.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.227 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 2.657E+04 V
b) 2.923E+04 V
c) 3.215E+04 V
d) 3.537E+04 V
e) 3.890E+04 V

3) Calculate the motional emf induced along a 34.3 km conductor moving at an orbital speed of 7.86 km/s perpendicular to Earth's 4.780E-05 Tesla magnetic field.

a) 8.802E+03 V
b) 9.682E+03 V
c) 1.065E+04 V
d) 1.172E+04 V
e) 1.289E+04 V

4) A washer has an inner diameter of 2.12 cm and an outer diamter of 4.47 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.7mm}$, and ${\displaystyle n=2.72}$. What is the volume of the washer?

a) 1.228E+00 cm3
b) 1.351E+00 cm3
c) 1.486E+00 cm3
d) 1.634E+00 cm3
e) 1.798E+00 cm3

5) In an LC circuit, the self-inductance is 0.0116 H and the capacitance is 7.040E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.140E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.489E-04 s
b) 4.938E-04 s
c) 5.432E-04 s
d) 5.975E-04 s
e) 6.572E-04 s

6) The output of an ac generator connected to an RLC series combination has a frequency of 300 Hz and an amplitude of 0.76 V;. If R =5 Ω, L= 6.10E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.14 Ω, L= 5.20E-03H , and C=2.90E-06 F, respectively.

a) Q = 2.287E+02
b) Q = 2.630E+02
c) Q = 3.025E+02
d) Q = 3.478E+02
e) Q = 4.000E+02

8) The output of an ac generator connected to an RLC series combination has a frequency of 470 Hz and an amplitude of 0.67 V;. If R =4 Ω, L= 2.40E-03H , and C=5.10E-04 F, what is the impedance?

a) 6.254E+00 Ω
b) 6.879E+00 Ω
c) 7.567E+00 Ω
d) 8.324E+00 Ω
e) 9.156E+00 Ω

9) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 R1

1) The output of an ac generator connected to an RLC series combination has a frequency of 720 Hz and an amplitude of 0.63 V;. If R =5 Ω, L= 4.20E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

2) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 6.581E-01 A
b) 7.239E-01 A
c) 7.963E-01 A
d) 8.759E-01 A
e) 9.635E-01 A

3) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.31 T and ${\displaystyle \omega =}$8.360E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.547 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.145E+04 V
b) 7.860E+04 V
c) 8.646E+04 V
d) 9.510E+04 V
e) 1.046E+05 V

4) Calculate the motional emf induced along a 48.8 km conductor moving at an orbital speed of 7.88 km/s perpendicular to Earth's 4.660E-05 Tesla magnetic field.

a) 1.224E+04 V
b) 1.346E+04 V
c) 1.481E+04 V
d) 1.629E+04 V
e) 1.792E+04 V

5) In an LC circuit, the self-inductance is 0.0237 H and the capacitance is 6.140E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.260E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.093E-04 s
b) 4.502E-04 s
c) 4.952E-04 s
d) 5.447E-04 s
e) 5.992E-04 s

6) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

7) A washer has an inner diameter of 2.6 cm and an outer diamter of 4.17 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.38mm}$, and ${\displaystyle n=2.62}$. What is the volume of the washer?

a) 7.196E-01 cm3
b) 7.916E-01 cm3
c) 8.707E-01 cm3
d) 9.578E-01 cm3
e) 1.054E+00 cm3

8) The output of an ac generator connected to an RLC series combination has a frequency of 1.00E+03 Hz and an amplitude of 0.6 V;. If R =3 Ω, L= 1.70E-03H , and C=5.40E-04 F, what is the impedance?

a) 8.123E+00 Ω
b) 8.935E+00 Ω
c) 9.828E+00 Ω
d) 1.081E+01 Ω
e) 1.189E+01 Ω

9) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

10) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.17 Ω, L= 4.40E-03H , and C=3.40E-06 F, respectively.

a) Q = 1.391E+02
b) Q = 1.600E+02
c) Q = 1.840E+02
d) Q = 2.116E+02
e) Q = 2.434E+02

#### T7 R2

1) In an LC circuit, the self-inductance is 0.0735 H and the capacitance is 2.300E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.220E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.411E-04 s
b) 4.852E-04 s
c) 5.338E-04 s
d) 5.871E-04 s
e) 6.458E-04 s

2) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

3) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.84 T and ${\displaystyle \omega =}$4.410E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.379 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 3.333E+04 V
b) 3.666E+04 V
c) 4.033E+04 V
d) 4.436E+04 V
e) 4.879E+04 V

4) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

5) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.14 Ω, L= 5.20E-03H , and C=2.90E-06 F, respectively.

a) Q = 2.287E+02
b) Q = 2.630E+02
c) Q = 3.025E+02
d) Q = 3.478E+02
e) Q = 4.000E+02

6) The output of an ac generator connected to an RLC series combination has a frequency of 720 Hz and an amplitude of 0.63 V;. If R =5 Ω, L= 4.20E-03H , and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

7) Calculate the motional emf induced along a 50.7 km conductor moving at an orbital speed of 7.88 km/s perpendicular to Earth's 4.930E-05 Tesla magnetic field.

a) 1.791E+04 V
b) 1.970E+04 V
c) 2.167E+04 V
d) 2.383E+04 V
e) 2.622E+04 V

8) A square coil has sides that are L= 0.458 m long and is tightly wound with N=742 turns of wire. The resistance of the coil is R=6.81 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0559 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.056E+00 A
b) 1.161E+00 A
c) 1.278E+00 A
d) 1.405E+00 A
e) 1.546E+00 A

9) The output of an ac generator connected to an RLC series combination has a frequency of 810 Hz and an amplitude of 0.64 V;. If R =6 Ω, L= 8.70E-03H , and C=8.20E-04 F, what is the impedance?

a) 4.444E+01 Ω
b) 4.889E+01 Ω
c) 5.378E+01 Ω
d) 5.916E+01 Ω
e) 6.507E+01 Ω

10) A washer has an inner diameter of 2.62 cm and an outer diamter of 4.79 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.08mm}$, and ${\displaystyle n=2.68}$. What is the volume of the washer?

a) 1.056E+00 cm3
b) 1.161E+00 cm3
c) 1.278E+00 cm3
d) 1.405E+00 cm3
e) 1.546E+00 cm3

### T7 S0

1) A recangular coil with an area of 0.815 m2 and 11 turns is placed in a uniform magnetic field of 3.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.700E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 59 s?

a) 1.197E+05 V
b) 1.316E+05 V
c) 1.448E+05 V
d) 1.593E+05 V
e) 1.752E+05 V

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.18 T and ${\displaystyle \omega =}$4.840E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.387 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.928E+04 V
b) 2.120E+04 V
c) 2.332E+04 V
d) 2.566E+04 V
e) 2.822E+04 V

3) A square coil has sides that are L= 0.259 m long and is tightly wound with N=628 turns of wire. The resistance of the coil is R=6.51 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0372 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.809E-01 A
b) 1.989E-01 A
c) 2.188E-01 A
d) 2.407E-01 A
e) 2.648E-01 A
4)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?
a) -1.700E+00 s
b) -1.870E+00 s
c) -2.057E+00 s
d) -2.262E+00 s
e) -2.489E+00 s
5)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =1.95 s if ε = 8.33 V , R = 6.96 Ω, and L = 2.66 H?
a) 5.736E-01 V
b) 6.884E-01 V
c) 8.260E-01 V
d) 9.912E-01 V
e) 1.189E+00 V

6) An ac generator produces an emf of amplitude 50 V at a frequency of 47 Hz. What is the maximum amplitude of the current if the generator is connected to a 88 mF capacitor?

a) 1.074E+00 A
b) 1.181E+00 A
c) 1.299E+00 A
d) 1.429E+00 A
e) 1.572E+00 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 200 Hz and an amplitude of 0.14 V;. If R =3 Ω, L= 1.70E-03H , and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

8) An ac generator produces an emf of amplitude 37 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 86 mF inductor?

a) 4.677E-01 A
b) 5.145E-01 A
c) 5.659E-01 A
d) 6.225E-01 A
e) 6.847E-01 A

9) An loop of wire with 31 turns has a radius of 0.9 meters, and is oriented with its axis parallel to a magetic field of 0.83 Tesla. What is the induced voltage if this field is reduced to 35% of its original value in 1.7 seconds?

a) 2.07 x 101 volts
b) 2.5 x 101 volts
c) 3.03 x 101 volts
d) 3.67 x 101 volts
e) 4.45 x 101 volts

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 S1

1) The output of an ac generator connected to an RLC series combination has a frequency of 360 Hz and an amplitude of 0.17 V;. If R =9 Ω, L= 2.60E-03H , and C=8.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

2)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.59% of its maximum value if ε = 1.14 V , R = 6.17 Ω, and L = 5.45 H?
a) -1.614E+00 s
b) -1.775E+00 s
c) -1.952E+00 s
d) -2.148E+00 s
e) -2.362E+00 s

3) A square coil has sides that are L= 0.219 m long and is tightly wound with N=508 turns of wire. The resistance of the coil is R=8.42 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0619 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.791E-01 A
b) 1.970E-01 A
c) 2.167E-01 A
d) 2.384E-01 A
e) 2.622E-01 A

4) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.79 T and ${\displaystyle \omega =}$7.280E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.668 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 7.910E+04 V
b) 8.701E+04 V
c) 9.571E+04 V
d) 1.053E+05 V
e) 1.158E+05 V

5) An loop of wire with 92 turns has a radius of 0.39 meters, and is oriented with its axis parallel to a magetic field of 0.97 Tesla. What is the induced voltage if this field is reduced to 16% of its original value in 1.4 seconds?

a) 2.56 x 101 volts
b) 3.1 x 101 volts
c) 3.76 x 101 volts
d) 4.55 x 101 volts
e) 5.51 x 101 volts

6) A recangular coil with an area of 0.219 m2 and 14 turns is placed in a uniform magnetic field of 3.71 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.540E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 15 s?

a) 2.959E+04 V
b) 3.255E+04 V
c) 3.581E+04 V
d) 3.939E+04 V
e) 4.332E+04 V
7)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =20.1 s if ε = 5.77 V , R = 1.38 Ω, and L = 5.45 H?
a) 3.463E+00 V
b) 4.156E+00 V
c) 4.987E+00 V
d) 5.984E+00 V
e) 7.181E+00 V

8) An ac generator produces an emf of amplitude 37 V at a frequency of 100 Hz. What is the maximum amplitude of the current if the generator is connected to a 86 mF inductor?

a) 4.677E-01 A
b) 5.145E-01 A
c) 5.659E-01 A
d) 6.225E-01 A
e) 6.847E-01 A

9) An ac generator produces an emf of amplitude 93 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF capacitor?

a) 4.917E+00 A
b) 5.409E+00 A
c) 5.950E+00 A
d) 6.545E+00 A
e) 7.199E+00 A

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

#### T7 S2

1) An ac generator produces an emf of amplitude 7 V at a frequency of 95 Hz. What is the maximum amplitude of the current if the generator is connected to a 50 mF capacitor?

a) 1.427E-01 A
b) 1.570E-01 A
c) 1.727E-01 A
d) 1.899E-01 A
e) 2.089E-01 A

2) A recangular coil with an area of 0.178 m2 and 17 turns is placed in a uniform magnetic field of 2.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.380E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 45 s?

a) 1.068E+04 V
b) 1.175E+04 V
c) 1.293E+04 V
d) 1.422E+04 V
e) 1.564E+04 V
3)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =13.6 s if ε = 6.56 V , R = 2.44 Ω, and L = 8.76 H?
a) 2.627E+00 V
b) 3.153E+00 V
c) 3.783E+00 V
d) 4.540E+00 V
e) 5.448E+00 V

4) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$1.97 T and ${\displaystyle \omega =}$5.410E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.244 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.485E+04 V
b) 1.634E+04 V
c) 1.797E+04 V
d) 1.977E+04 V
e) 2.175E+04 V
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.65% of its maximum value if ε = 3.62 V , R = 4.07 Ω, and L = 7.19 H?
a) -2.476E+00 s
b) -2.724E+00 s
c) -2.996E+00 s
d) -3.296E+00 s
e) -3.625E+00 s

6) A square coil has sides that are L= 0.325 m long and is tightly wound with N=697 turns of wire. The resistance of the coil is R=4.87 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0842 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.157E+00 A
b) 1.273E+00 A
c) 1.400E+00 A
d) 1.540E+00 A
e) 1.694E+00 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 160 Hz and an amplitude of 0.47 V;. If R =8 Ω, L= 1.30E-03H , and C=6.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

8) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

9) An ac generator produces an emf of amplitude 58 V at a frequency of 99 Hz. What is the maximum amplitude of the current if the generator is connected to a 35 mF inductor?

a) 2.422E+00 A
b) 2.664E+00 A
c) 2.930E+00 A
d) 3.224E+00 A
e) 3.546E+00 A

10) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

### T7 T0

1) A long solenoid has a radius of 0.793 m and 45 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$29 s−1.What is the induced electric fied at a distance 0.216 m from the axis at time t=0.0208 s ?

a) 1.456E-04 V/m
b) 1.601E-04 V/m
c) 1.762E-04 V/m
d) 1.938E-04 V/m
e) 2.132E-04 V/m

2) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 5.743E-01 A
b) 6.318E-01 A
c) 6.950E-01 A
d) 7.645E-01 A
e) 8.409E-01 A

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.594 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.89)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.6 s. What is the current in the coil if the impedance of the coil is 6.65 Ω?

a) 2.088E+00 A
b) 2.297E+00 A
c) 2.527E+00 A
d) 2.779E+00 A
e) 3.057E+00 A

4) An induced emf of 7.48V is measured across a coil of 95 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.33A in 0.304s. What is the self-inductance of the coil?

a) 2.914E-01 H
b) 3.205E-01 H
c) 3.526E-01 H
d) 3.878E-01 H
e) 4.266E-01 H
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.63% of its maximum value if ε = 8.7 V , R = 8.35 Ω, and L = 1.44 H?
a) -3.137E-01 s
b) -3.451E-01 s
c) -3.796E-01 s
d) -4.176E-01 s
e) -4.593E-01 s

6) A step-down transformer steps 9 kV down to 210 V. The high-voltage input is provided by a 170 Ω power line that carries 5 A of currentWhat is the output current (at the 210 V side ?)

a) 1.948E+02 A
b) 2.143E+02 A
c) 2.357E+02 A
d) 2.593E+02 A
e) 2.852E+02 A

7) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.77 V. The resistance, inductance, and capacitance are R =3 Ω, L= 6.70E-03H , and C=7.10E-04 F, respectively. What is the amplitude of the current?

a) 2.333E-01 A
b) 2.567E-01 A
c) 2.823E-01 A
d) 3.106E-01 A
e) 3.416E-01 A

8) The output of an ac generator connected to an RLC series combination has a frequency of 540 Hz and an amplitude of 0.18 V;. If R =3 Ω, L= 2.50E-03H , and C=8.20E-04 F, what is the impedance?

a) 7.872E+00 Ω
b) 8.659E+00 Ω
c) 9.525E+00 Ω
d) 1.048E+01 Ω
e) 1.153E+01 Ω

9) Two orbiting satellites are orbiting at a speed of 58 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 22 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 2.72 x 104 volts.
b) 3.3 x 104 volts.
c) 4 x 104 volts.
d) 4.84 x 104 volts.
e) 5.87 x 104 volts.

10) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

#### T7 T1

1) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.25 V. The resistance, inductance, and capacitance are R =7 Ω, L= 5.00E-03H , and C=7.70E-04 F, respectively. What is the amplitude of the current?

a) 2.439E-02 A
b) 2.683E-02 A
c) 2.952E-02 A
d) 3.247E-02 A
e) 3.571E-02 A

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.419 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.48)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.15 s. What is the current in the coil if the impedance of the coil is 67.8 Ω?

a) 1.240E-01 A
b) 1.364E-01 A
c) 1.500E-01 A
d) 1.650E-01 A
e) 1.815E-01 A

3) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.
4)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.78% of its maximum value if ε = 1.39 V , R = 2.88 Ω, and L = 4.06 H?
a) -2.296E+00 s
b) -2.525E+00 s
c) -2.778E+00 s
d) -3.056E+00 s
e) -3.361E+00 s

5) A square coil has sides that are L= 0.894 m long and is tightly wound with N=255 turns of wire. The resistance of the coil is R=8.83 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0682 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.301E+00 A
b) 1.431E+00 A
c) 1.574E+00 A
d) 1.732E+00 A
e) 1.905E+00 A

6) Two orbiting satellites are orbiting at a speed of 70 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 30 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 4.48 x 104 volts.
b) 5.43 x 104 volts.
c) 6.58 x 104 volts.
d) 7.97 x 104 volts.
e) 9.66 x 104 volts.

7) The output of an ac generator connected to an RLC series combination has a frequency of 1.00E+03 Hz and an amplitude of 0.6 V;. If R =3 Ω, L= 1.70E-03H , and C=5.40E-04 F, what is the impedance?

a) 8.123E+00 Ω
b) 8.935E+00 Ω
c) 9.828E+00 Ω
d) 1.081E+01 Ω
e) 1.189E+01 Ω

8) A long solenoid has a radius of 0.517 m and 23 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$30 s−1.What is the induced electric fied at a distance 0.162 m from the axis at time t=0.0679 s ?

a) 6.256E-06 V/m
b) 6.882E-06 V/m
c) 7.570E-06 V/m
d) 8.327E-06 V/m
e) 9.160E-06 V/m

9) An induced emf of 1.7V is measured across a coil of 81 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.07A in 0.174s. What is the self-inductance of the coil?

a) 3.458E-02 H
b) 3.804E-02 H
c) 4.184E-02 H
d) 4.602E-02 H
e) 5.062E-02 H

10) A step-down transformer steps 6 kV down to 190 V. The high-voltage input is provided by a 130 Ω power line that carries 6 A of currentWhat is the output current (at the 190 V side ?)

a) 1.424E+02 A
b) 1.566E+02 A
c) 1.722E+02 A
d) 1.895E+02 A
e) 2.084E+02 A

#### T7 T2

1)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?
a) -1.700E+00 s
b) -1.870E+00 s
c) -2.057E+00 s
d) -2.262E+00 s
e) -2.489E+00 s

2) The output of an ac generator connected to an RLC series combination has a frequency of 680 Hz and an amplitude of 0.79 V;. If R =5 Ω, L= 2.40E-03H , and C=9.10E-04 F, what is the impedance?

a) 8.398E+00 Ω
b) 9.238E+00 Ω
c) 1.016E+01 Ω
d) 1.118E+01 Ω
e) 1.230E+01 Ω

3) An induced emf of 5.08V is measured across a coil of 78 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.07A in 0.681s. What is the self-inductance of the coil?

a) 4.660E-01 H
b) 5.127E-01 H
c) 5.639E-01 H
d) 6.203E-01 H
e) 6.823E-01 H

4) A step-down transformer steps 18 kV down to 260 V. The high-voltage input is provided by a 290 Ω power line that carries 3 A of currentWhat is the output current (at the 260 V side ?)

a) 1.888E+02 A
b) 2.077E+02 A
c) 2.285E+02 A
d) 2.513E+02 A
e) 2.764E+02 A

5) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

6) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.8 V. The resistance, inductance, and capacitance are R =7 Ω, L= 4.90E-03H , and C=8.50E-04 F, respectively. What is the amplitude of the current?

a) 1.039E-01 A
b) 1.143E-01 A
c) 1.257E-01 A
d) 1.383E-01 A
e) 1.521E-01 A

7) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 5.743E-01 A
b) 6.318E-01 A
c) 6.950E-01 A
d) 7.645E-01 A
e) 8.409E-01 A

8) A long solenoid has a radius of 0.442 m and 41 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$4 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 0.2 m from the axis at time t=0.0833 s ?

a) 6.438E-05 V/m
b) 7.082E-05 V/m
c) 7.790E-05 V/m
d) 8.569E-05 V/m
e) 9.426E-05 V/m

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.227 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (5.55)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$3.92 s. What is the current in the coil if the impedance of the coil is 22.7 Ω?

a) 1.082E-01 A
b) 1.190E-01 A
c) 1.309E-01 A
d) 1.440E-01 A
e) 1.584E-01 A

10) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

### T7 U0

1)
A cylinder of height 1.19 cm and radius 4.51 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.7 cm from point O and moves at a speed of 8.35 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 3.093E+01 cm3/s
b) 3.403E+01 cm3/s
c) 3.743E+01 cm3/s
d) 4.117E+01 cm3/s
e) 4.529E+01 cm3/s

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (1.95)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

a) 7.402E-01 A
b) 8.142E-01 A
c) 8.956E-01 A
d) 9.852E-01 A
e) 1.084E+00 A

3) A long solenoid has a radius of 0.624 m and 84 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 1.78 m from the axis at time t=0.0579 s ?

a) 3.597E-04 V/m
b) 3.956E-04 V/m
c) 4.352E-04 V/m
d) 4.787E-04 V/m
e) 5.266E-04 V/m

4) In an LC circuit, the self-inductance is 0.0126 H and the capacitance is 3.350E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.420E-05 C. How long does it take for the capacitor to become completely discharged?

a) 2.204E-04 s
b) 2.425E-04 s
c) 2.667E-04 s
d) 2.934E-04 s
e) 3.227E-04 s
5)
A long solenoid has a length 0.89 meters, radius 3.01 cm, and 505 turns. It surrounds coil of radius 8.65 meters and 18turns. If the current in the solenoid is changing at a rate of 279 A/s, what is the emf induced in the surounding coil?
a) 2.646E-02 V
b) 2.911E-02 V
c) 3.202E-02 V
d) 3.522E-02 V
e) 3.874E-02 V

6) An ac generator produces an emf of amplitude 24 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 96 mF inductor?

a) 3.014E-01 A
b) 3.316E-01 A
c) 3.647E-01 A
d) 4.012E-01 A
e) 4.413E-01 A

7) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.82 V. The resistance, inductance, and capacitance are R =8 Ω, L= 6.40E-03H , and C=5.70E-04 F, respectively. What is the amplitude of the current?

a) 7.701E-02 A
b) 8.471E-02 A
c) 9.318E-02 A
d) 1.025E-01 A
e) 1.128E-01 A

8) An ac generator produces an emf of amplitude 93 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF capacitor?

a) 4.917E+00 A
b) 5.409E+00 A
c) 5.950E+00 A
d) 6.545E+00 A
e) 7.199E+00 A

9) Two orbiting satellites are orbiting at a speed of 70 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 30 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 4.48 x 104 volts.
b) 5.43 x 104 volts.
c) 6.58 x 104 volts.
d) 7.97 x 104 volts.
e) 9.66 x 104 volts.

10) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

#### T7 U1

1) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.3 V. The resistance, inductance, and capacitance are R =2 Ω, L= 8.10E-03H , and C=9.40E-04 F, respectively. What is the amplitude of the current?

a) 1.364E-01 A
b) 1.500E-01 A
c) 1.650E-01 A
d) 1.815E-01 A
e) 1.997E-01 A
2)
A cylinder of height 1.34 cm and radius 2.47 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.23 cm from point O and moves at a speed of 6.23 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.414E+01 cm3/s
b) 1.556E+01 cm3/s
c) 1.711E+01 cm3/s
d) 1.882E+01 cm3/s
e) 2.070E+01 cm3/s

3) Two orbiting satellites are orbiting at a speed of 66 km/s perpendicular to a magnetic field of 64 μT. They are connected by a cable that is 37 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 1.29 x 105 volts.
b) 1.56 x 105 volts.
c) 1.89 x 105 volts.
d) 2.29 x 105 volts.
e) 2.78 x 105 volts.

4) An ac generator produces an emf of amplitude 40 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a 52 mF inductor?

a) 7.783E-01 A
b) 8.561E-01 A
c) 9.417E-01 A
d) 1.036E+00 A
e) 1.140E+00 A

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (1.95)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

a) 7.402E-01 A
b) 8.142E-01 A
c) 8.956E-01 A
d) 9.852E-01 A
e) 1.084E+00 A
6)
A long solenoid has a length 0.89 meters, radius 3.01 cm, and 505 turns. It surrounds coil of radius 8.65 meters and 18turns. If the current in the solenoid is changing at a rate of 279 A/s, what is the emf induced in the surounding coil?
a) 2.646E-02 V
b) 2.911E-02 V
c) 3.202E-02 V
d) 3.522E-02 V
e) 3.874E-02 V

7) A long solenoid has a radius of 0.521 m and 46 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$30 s−1.What is the induced electric fied at a distance 2.42 m from the axis at time t=0.0449 s ?

a) 2.529E-05 V/m
b) 2.782E-05 V/m
c) 3.060E-05 V/m
d) 3.366E-05 V/m
e) 3.703E-05 V/m

8) In an LC circuit, the self-inductance is 0.0307 H and the capacitance is 5.330E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 1.840E-05 C. How long does it take for the capacitor to become completely discharged?

a) 5.251E-04 s
b) 5.776E-04 s
c) 6.354E-04 s
d) 6.989E-04 s
e) 7.688E-04 s

9) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

10) An ac generator produces an emf of amplitude 98 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a 2 mF capacitor?

a) 1.232E-01 A
b) 1.355E-01 A
c) 1.490E-01 A
d) 1.639E-01 A
e) 1.803E-01 A

#### T7 U2

1)
A cylinder of height 2.63 cm and radius 6.27 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.35 cm from point O and moves at a speed of 2.7 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 4.057E+01 cm3/s
b) 4.463E+01 cm3/s
c) 4.909E+01 cm3/s
d) 5.400E+01 cm3/s
e) 5.940E+01 cm3/s

2) An ac generator produces an emf of amplitude 66 V at a frequency of 180 Hz. What is the maximum amplitude of the current if the generator is connected to a 97 mF inductor?

a) 4.972E-01 A
b) 5.469E-01 A
c) 6.016E-01 A
d) 6.618E-01 A
e) 7.280E-01 A

3) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

4) In an LC circuit, the self-inductance is 0.0464 H and the capacitance is 7.350E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.280E-05 C. How long does it take for the capacitor to become completely discharged?

a) 8.339E-04 s
b) 9.173E-04 s
c) 1.009E-03 s
d) 1.110E-03 s
e) 1.221E-03 s

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.8 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.6)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$8.91 s. What is the current in the coil if the impedance of the coil is 61.7 Ω?

a) 5.369E-01 A
b) 5.906E-01 A
c) 6.496E-01 A
d) 7.146E-01 A
e) 7.860E-01 A

6) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.83 V. The resistance, inductance, and capacitance are R =4 Ω, L= 4.60E-03H , and C=8.10E-04 F, respectively. What is the amplitude of the current?

a) 1.417E-01 A
b) 1.559E-01 A
c) 1.715E-01 A
d) 1.886E-01 A
e) 2.075E-01 A

7) A long solenoid has a radius of 0.845 m and 65 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$30 s−1.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0561 s ?

a) 3.371E-04 V/m
b) 3.709E-04 V/m
c) 4.079E-04 V/m
d) 4.487E-04 V/m
e) 4.936E-04 V/m
8)
A long solenoid has a length 0.759 meters, radius 4.51 cm, and 542 turns. It surrounds coil of radius 9.59 meters and 13turns. If the current in the solenoid is changing at a rate of 272 A/s, what is the emf induced in the surounding coil?
a) 5.791E-02 V
b) 6.370E-02 V
c) 7.007E-02 V
d) 7.708E-02 V
e) 8.478E-02 V

9) An ac generator produces an emf of amplitude 58 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 66 mF capacitor?

a) 3.976E+00 A
b) 4.373E+00 A
c) 4.810E+00 A
d) 5.291E+00 A
e) 5.821E+00 A

10) Two orbiting satellites are orbiting at a speed of 83 km/s perpendicular to a magnetic field of 57 μT. They are connected by a cable that is 23 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 8.98 x 104 volts.
b) 1.09 x 105 volts.
c) 1.32 x 105 volts.
d) 1.6 x 105 volts.
e) 1.93 x 105 volts.

### T7 V0

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.655 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (5.62)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.62 s. What is the current in the coil if the impedance of the coil is 48.9 Ω?

a) 7.890E-01 A
b) 8.679E-01 A
c) 9.547E-01 A
d) 1.050E+00 A
e) 1.155E+00 A

2) A square coil has sides that are L= 0.325 m long and is tightly wound with N=697 turns of wire. The resistance of the coil is R=4.87 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0842 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.157E+00 A
b) 1.273E+00 A
c) 1.400E+00 A
d) 1.540E+00 A
e) 1.694E+00 A
3)
A cylinder of height 2.94 cm and radius 5.05 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.37 cm from point O and moves at a speed of 7.29 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.153E+02 cm3/s
b) 1.268E+02 cm3/s
c) 1.395E+02 cm3/s
d) 1.535E+02 cm3/s
e) 1.688E+02 cm3/s
4)
A long solenoid has a length 0.974 meters, radius 4.72 cm, and 587 turns. It surrounds coil of radius 8.65 meters and 17turns. If the current in the solenoid is changing at a rate of 146 A/s, what is the emf induced in the surounding coil?
a) 2.823E-02 V
b) 3.105E-02 V
c) 3.416E-02 V
d) 3.757E-02 V
e) 4.133E-02 V

5) A washer has an inner diameter of 2.62 cm and an outer diamter of 4.79 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.08mm}$, and ${\displaystyle n=2.68}$. What is the volume of the washer?

a) 1.056E+00 cm3
b) 1.161E+00 cm3
c) 1.278E+00 cm3
d) 1.405E+00 cm3
e) 1.546E+00 cm3

6) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 59 mF capacitor?

a) 5.042E+00 A
b) 5.546E+00 A
c) 6.100E+00 A
d) 6.710E+00 A
e) 7.381E+00 A

7) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.64 V. The resistance, inductance, and capacitance are R =2 Ω, L= 4.00E-03H , and C=8.30E-04 F, respectively. What is the amplitude of the current?

a) 3.200E-01 A
b) 3.520E-01 A
c) 3.872E-01 A
d) 4.259E-01 A
e) 4.685E-01 A

8) An ac generator produces an emf of amplitude 8 V at a frequency of 80 Hz. What is the maximum amplitude of the current if the generator is connected to a 14 mF inductor?

a) 8.541E-01 A
b) 9.395E-01 A
c) 1.033E+00 A
d) 1.137E+00 A
e) 1.251E+00 A

9) Two orbiting satellites are orbiting at a speed of 83 km/s perpendicular to a magnetic field of 57 μT. They are connected by a cable that is 23 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 8.98 x 104 volts.
b) 1.09 x 105 volts.
c) 1.32 x 105 volts.
d) 1.6 x 105 volts.
e) 1.93 x 105 volts.

10) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

#### T7 V1

1)
A cylinder of height 2.58 cm and radius 9.47 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.62 cm from point O and moves at a speed of 4.7 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.128E+02 cm3/s
b) 1.241E+02 cm3/s
c) 1.365E+02 cm3/s
d) 1.502E+02 cm3/s
e) 1.652E+02 cm3/s

2) An ac generator produces an emf of amplitude 50 V at a frequency of 47 Hz. What is the maximum amplitude of the current if the generator is connected to a 88 mF capacitor?

a) 1.074E+00 A
b) 1.181E+00 A
c) 1.299E+00 A
d) 1.429E+00 A
e) 1.572E+00 A

3) An ac generator produces an emf of amplitude 70 V at a frequency of 63 Hz. What is the maximum amplitude of the current if the generator is connected to a 34 mF inductor?

a) 3.908E+00 A
b) 4.298E+00 A
c) 4.728E+00 A
d) 5.201E+00 A
e) 5.721E+00 A

4) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 5.743E-01 A
b) 6.318E-01 A
c) 6.950E-01 A
d) 7.645E-01 A
e) 8.409E-01 A

5) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.655 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (5.62)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.62 s. What is the current in the coil if the impedance of the coil is 48.9 Ω?

a) 7.890E-01 A
b) 8.679E-01 A
c) 9.547E-01 A
d) 1.050E+00 A
e) 1.155E+00 A

6) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

7) Two orbiting satellites are orbiting at a speed of 83 km/s perpendicular to a magnetic field of 57 μT. They are connected by a cable that is 23 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 8.98 x 104 volts.
b) 1.09 x 105 volts.
c) 1.32 x 105 volts.
d) 1.6 x 105 volts.
e) 1.93 x 105 volts.

8) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.62 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.66mm}$, and ${\displaystyle n=2.61}$. What is the volume of the washer?

a) 6.960E-01 cm3
b) 7.656E-01 cm3
c) 8.421E-01 cm3
d) 9.264E-01 cm3
e) 1.019E+00 cm3
9)
A long solenoid has a length 0.974 meters, radius 4.72 cm, and 587 turns. It surrounds coil of radius 8.65 meters and 17turns. If the current in the solenoid is changing at a rate of 146 A/s, what is the emf induced in the surounding coil?
a) 2.823E-02 V
b) 3.105E-02 V
c) 3.416E-02 V
d) 3.757E-02 V
e) 4.133E-02 V

10) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.82 V. The resistance, inductance, and capacitance are R =3 Ω, L= 6.20E-03H , and C=6.70E-04 F, respectively. What is the amplitude of the current?

a) 2.259E-01 A
b) 2.485E-01 A
c) 2.733E-01 A
d) 3.007E-01 A
e) 3.307E-01 A

#### T7 V2

1) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.752 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (1.95)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.47 s. What is the current in the coil if the impedance of the coil is 18.0 Ω?

a) 7.402E-01 A
b) 8.142E-01 A
c) 8.956E-01 A
d) 9.852E-01 A
e) 1.084E+00 A

2) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.14mm}$, and ${\displaystyle n=2.86}$. What is the volume of the washer?

a) 1.071E+00 cm3
b) 1.178E+00 cm3
c) 1.296E+00 cm3
d) 1.425E+00 cm3
e) 1.568E+00 cm3

3) Two orbiting satellites are orbiting at a speed of 83 km/s perpendicular to a magnetic field of 57 μT. They are connected by a cable that is 23 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 8.98 x 104 volts.
b) 1.09 x 105 volts.
c) 1.32 x 105 volts.
d) 1.6 x 105 volts.
e) 1.93 x 105 volts.

4) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 6.581E-01 A
b) 7.239E-01 A
c) 7.963E-01 A
d) 8.759E-01 A
e) 9.635E-01 A
5)
A long solenoid has a length 0.794 meters, radius 4.45 cm, and 568 turns. It surrounds coil of radius 6.81 meters and 9turns. If the current in the solenoid is changing at a rate of 246 A/s, what is the emf induced in the surounding coil?
a) 3.890E-02 V
b) 4.279E-02 V
c) 4.707E-02 V
d) 5.177E-02 V
e) 5.695E-02 V
6)
A cylinder of height 1.3 cm and radius 6.01 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.61 cm from point O and moves at a speed of 2.11 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.372E+01 cm3/s
b) 1.509E+01 cm3/s
c) 1.660E+01 cm3/s
d) 1.826E+01 cm3/s
e) 2.009E+01 cm3/s

7) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.83 V. The resistance, inductance, and capacitance are R =9 Ω, L= 8.50E-03H , and C=7.20E-04 F, respectively. What is the amplitude of the current?

a) 8.384E-02 A
b) 9.222E-02 A
c) 1.014E-01 A
d) 1.116E-01 A
e) 1.227E-01 A

8) A 10 F capacitor is connected in series to a 10Ω resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 4 x 100 s.
b) 1.26 x 101 s.
c) 4 x 101 s.
d) 1.26 x 102 s.
e) 4 x 102 s.

9) An ac generator produces an emf of amplitude 97 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 55 mF inductor?

a) 4.386E+00 A
b) 4.824E+00 A
c) 5.307E+00 A
d) 5.838E+00 A
e) 6.421E+00 A

10) An ac generator produces an emf of amplitude 93 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF capacitor?

a) 4.917E+00 A
b) 5.409E+00 A
c) 5.950E+00 A
d) 6.545E+00 A
e) 7.199E+00 A

### T7 W0

1)
A cylinder of height 1.69 cm and radius 4.56 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.33 cm from point O and moves at a speed of 4.9 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 3.054E+01 cm3/s
b) 3.359E+01 cm3/s
c) 3.695E+01 cm3/s
d) 4.065E+01 cm3/s
e) 4.471E+01 cm3/s

2) A long solenoid has a radius of 0.413 m and 17 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$21 s−1.What is the induced electric fied at a distance 2.25 m from the axis at time t=0.0689 s ?

a) 3.006E-06 V/m
b) 3.307E-06 V/m
c) 3.637E-06 V/m
d) 4.001E-06 V/m
e) 4.401E-06 V/m

3) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.75 T and ${\displaystyle \omega =}$1.740E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.417 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.168E+04 V
b) 1.284E+04 V
c) 1.413E+04 V
d) 1.554E+04 V
e) 1.710E+04 V

4) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.87 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.39mm}$, and ${\displaystyle n=2.55}$. What is the volume of the washer?

a) 7.754E-01 cm3
b) 8.530E-01 cm3
c) 9.383E-01 cm3
d) 1.032E+00 cm3
e) 1.135E+00 cm3

5) In an LC circuit, the self-inductance is 0.0237 H and the capacitance is 6.140E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.260E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.093E-04 s
b) 4.502E-04 s
c) 4.952E-04 s
d) 5.447E-04 s
e) 5.992E-04 s

6) An ac generator produces an emf of amplitude 53 V at a frequency of 190 Hz. What is the maximum amplitude of the current if the generator is connected to a 85 mF capacitor?

a) 4.445E+00 A
b) 4.889E+00 A
c) 5.378E+00 A
d) 5.916E+00 A
e) 6.507E+00 A

7) An ac generator produces an emf of amplitude 58 V at a frequency of 99 Hz. What is the maximum amplitude of the current if the generator is connected to a 35 mF inductor?

a) 2.422E+00 A
b) 2.664E+00 A
c) 2.930E+00 A
d) 3.224E+00 A
e) 3.546E+00 A

8) The output of an ac generator connected to an RLC series combination has a frequency of 4.30E+04 Hz and an amplitude of 6 V. If R =6 Ω, L= 5.20E-03H , and C=8.60E-06 F, what is the rms power transferred to the resistor?

a) 1.511E-03 Watts
b) 1.662E-03 Watts
c) 1.828E-03 Watts
d) 2.011E-03 Watts
e) 2.212E-03 Watts

9) Two orbiting satellites are orbiting at a speed of 70 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 30 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 4.48 x 104 volts.
b) 5.43 x 104 volts.
c) 6.58 x 104 volts.
d) 7.97 x 104 volts.
e) 9.66 x 104 volts.

10) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

#### T7 W1

1) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

2) An ac generator produces an emf of amplitude 71 V at a frequency of 68 Hz. What is the maximum amplitude of the current if the generator is connected to a 35 mF capacitor?

a) 7.252E-01 A
b) 7.977E-01 A
c) 8.775E-01 A
d) 9.652E-01 A
e) 1.062E+00 A

3) Two orbiting satellites are orbiting at a speed of 83 km/s perpendicular to a magnetic field of 57 μT. They are connected by a cable that is 23 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 8.98 x 104 volts.
b) 1.09 x 105 volts.
c) 1.32 x 105 volts.
d) 1.6 x 105 volts.
e) 1.93 x 105 volts.
4)
A cylinder of height 2.15 cm and radius 7.03 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.83 cm from point O and moves at a speed of 5.7 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 6.534E+01 cm3/s
b) 7.188E+01 cm3/s
c) 7.907E+01 cm3/s
d) 8.697E+01 cm3/s
e) 9.567E+01 cm3/s

5) In an LC circuit, the self-inductance is 0.0216 H and the capacitance is 6.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 1.240E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.846E-04 s
b) 5.330E-04 s
c) 5.863E-04 s
d) 6.449E-04 s
e) 7.094E-04 s

6) A washer has an inner diameter of 2.74 cm and an outer diamter of 4.71 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.9mm}$, and ${\displaystyle n=2.85}$. What is the volume of the washer?

a) 8.141E-01 cm3
b) 8.955E-01 cm3
c) 9.850E-01 cm3
d) 1.084E+00 cm3
e) 1.192E+00 cm3

7) A long solenoid has a radius of 0.716 m and 96 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$9 A and ${\displaystyle \alpha =}$23 s−1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?

a) 1.426E-03 V/m
b) 1.568E-03 V/m
c) 1.725E-03 V/m
d) 1.897E-03 V/m
e) 2.087E-03 V/m

8) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.75 T and ${\displaystyle \omega =}$1.740E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.417 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.168E+04 V
b) 1.284E+04 V
c) 1.413E+04 V
d) 1.554E+04 V
e) 1.710E+04 V

9) An ac generator produces an emf of amplitude 3 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a 75 mF inductor?

a) 3.679E-02 A
b) 4.047E-02 A
c) 4.452E-02 A
d) 4.897E-02 A
e) 5.387E-02 A

10) The output of an ac generator connected to an RLC series combination has a frequency of 4.00E+04 Hz and an amplitude of 8 V. If R =4 Ω, L= 7.00E-03H , and C=6.60E-06 F, what is the rms power transferred to the resistor?

a) 1.146E-03 Watts
b) 1.260E-03 Watts
c) 1.386E-03 Watts
d) 1.525E-03 Watts
e) 1.677E-03 Watts

#### T7 W2

1) A washer has an inner diameter of 2.74 cm and an outer diamter of 4.71 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.9mm}$, and ${\displaystyle n=2.85}$. What is the volume of the washer?

a) 8.141E-01 cm3
b) 8.955E-01 cm3
c) 9.850E-01 cm3
d) 1.084E+00 cm3
e) 1.192E+00 cm3

2) An ac generator produces an emf of amplitude 75 V at a frequency of 200 Hz. What is the maximum amplitude of the current if the generator is connected to a 22 mF inductor?

a) 2.466E+00 A
b) 2.713E+00 A
c) 2.984E+00 A
d) 3.283E+00 A
e) 3.611E+00 A

3) A long solenoid has a radius of 0.777 m and 67 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 2.39 m from the axis at time t=0.0399 s ?

a) 3.924E-04 V/m
b) 4.317E-04 V/m
c) 4.748E-04 V/m
d) 5.223E-04 V/m
e) 5.745E-04 V/m

4) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.34 T and ${\displaystyle \omega =}$2.670E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.646 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

a) 1.905E+04 V
b) 2.096E+04 V
c) 2.305E+04 V
d) 2.536E+04 V
e) 2.790E+04 V

5) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

6) An ac generator produces an emf of amplitude 93 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 70 mF capacitor?

a) 4.917E+00 A
b) 5.409E+00 A
c) 5.950E+00 A
d) 6.545E+00 A
e) 7.199E+00 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 4.30E+04 Hz and an amplitude of 6 V. If R =6 Ω, L= 5.20E-03H , and C=8.60E-06 F, what is the rms power transferred to the resistor?

a) 1.511E-03 Watts
b) 1.662E-03 Watts
c) 1.828E-03 Watts
d) 2.011E-03 Watts
e) 2.212E-03 Watts

8) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

9) In an LC circuit, the self-inductance is 0.0307 H and the capacitance is 5.330E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 1.840E-05 C. How long does it take for the capacitor to become completely discharged?

a) 5.251E-04 s
b) 5.776E-04 s
c) 6.354E-04 s
d) 6.989E-04 s
e) 7.688E-04 s
10)
A cylinder of height 2.91 cm and radius 8.33 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.7 cm from point O and moves at a speed of 9.14 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 2.061E+02 cm3/s
b) 2.267E+02 cm3/s
c) 2.494E+02 cm3/s
d) 2.743E+02 cm3/s
e) 3.018E+02 cm3/s

### T7 X0

1) The current through the windings of a solenoid with n= 2.760E+03 turns per meter is changing at a rate dI/dt=8 A/s. The solenoid is 74 cm long and has a cross-sectional diameter of 2.57 cm. A small coil consisting of N=32turns wraped in a circle of diameter 1.49 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.407E-04 V
b) 1.548E-04 V
c) 1.703E-04 V
d) 1.873E-04 V
e) 2.061E-04 V

2) A recangular coil with an area of 0.178 m2 and 17 turns is placed in a uniform magnetic field of 2.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.380E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 45 s?

a) 1.068E+04 V
b) 1.175E+04 V
c) 1.293E+04 V
d) 1.422E+04 V
e) 1.564E+04 V
3)
A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 7.479E+00 cm3/s
b) 8.227E+00 cm3/s
c) 9.049E+00 cm3/s
d) 9.954E+00 cm3/s
e) 1.095E+01 cm3/s

4) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?

a) 6.230E-04 s
b) 6.853E-04 s
c) 7.538E-04 s
d) 8.292E-04 s
e) 9.121E-04 s

5) A washer has an inner diameter of 2.74 cm and an outer diamter of 4.71 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.9mm}$, and ${\displaystyle n=2.85}$. What is the volume of the washer?

a) 8.141E-01 cm3
b) 8.955E-01 cm3
c) 9.850E-01 cm3
d) 1.084E+00 cm3
e) 1.192E+00 cm3

6) An ac generator produces an emf of amplitude 87 V at a frequency of 44 Hz. What is the maximum amplitude of the current if the generator is connected to a 9 mF capacitor?

a) 1.626E-01 A
b) 1.789E-01 A
c) 1.968E-01 A
d) 2.165E-01 A
e) 2.381E-01 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 890 Hz and an amplitude of 0.12 V;. If R =8 Ω, L= 8.60E-03H , and C=9.90E-04 F, what is the impedance?

a) 3.318E+01 Ω
b) 3.649E+01 Ω
c) 4.014E+01 Ω
d) 4.416E+01 Ω
e) 4.857E+01 Ω

8) An ac generator produces an emf of amplitude 7 V at a frequency of 190 Hz. What is the maximum amplitude of the current if the generator is connected to a 44 mF inductor?

a) 9.102E-02 A
b) 1.001E-01 A
c) 1.101E-01 A
d) 1.211E-01 A
e) 1.333E-01 A

9) An loop of wire with 43 turns has a radius of 0.27 meters, and is oriented with its axis parallel to a magetic field of 0.68 Tesla. What is the induced voltage if this field is reduced to 36% of its original value in 3.8 seconds?

a) 6.34 x 10-1 volts
b) 7.68 x 10-1 volts
c) 9.31 x 10-1 volts
d) 1.13 x 100 volts
e) 1.37 x 100 volts

10) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

#### T7 X1

1) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

2) The output of an ac generator connected to an RLC series combination has a frequency of 420 Hz and an amplitude of 0.73 V;. If R =2 Ω, L= 9.60E-03H , and C=7.80E-04 F, what is the impedance?

a) 2.060E+01 Ω
b) 2.266E+01 Ω
c) 2.493E+01 Ω
d) 2.742E+01 Ω
e) 3.016E+01 Ω

3) A washer has an inner diameter of 2.2 cm and an outer diamter of 4.11 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=3.23mm}$, and ${\displaystyle n=2.74}$. What is the volume of the washer?

a) 7.110E-01 cm3
b) 7.821E-01 cm3
c) 8.603E-01 cm3
d) 9.463E-01 cm3
e) 1.041E+00 cm3
4)
A cylinder of height 1.27 cm and radius 8.63 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.15 cm from point O and moves at a speed of 1.26 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.892E+01 cm3/s
b) 2.081E+01 cm3/s
c) 2.289E+01 cm3/s
d) 2.518E+01 cm3/s
e) 2.770E+01 cm3/s

5) An ac generator produces an emf of amplitude 7 V at a frequency of 95 Hz. What is the maximum amplitude of the current if the generator is connected to a 50 mF capacitor?

a) 1.427E-01 A
b) 1.570E-01 A
c) 1.727E-01 A
d) 1.899E-01 A
e) 2.089E-01 A

6) The current through the windings of a solenoid with n= 2.060E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 68 cm long and has a cross-sectional diameter of 2.96 cm. A small coil consisting of N=29turns wraped in a circle of diameter 1.74 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.463E-04 V
b) 1.609E-04 V
c) 1.770E-04 V
d) 1.947E-04 V
e) 2.142E-04 V

7) In an LC circuit, the self-inductance is 0.0307 H and the capacitance is 5.330E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 1.840E-05 C. How long does it take for the capacitor to become completely discharged?

a) 5.251E-04 s
b) 5.776E-04 s
c) 6.354E-04 s
d) 6.989E-04 s
e) 7.688E-04 s

8) An ac generator produces an emf of amplitude 97 V at a frequency of 64 Hz. What is the maximum amplitude of the current if the generator is connected to a 55 mF inductor?

a) 4.386E+00 A
b) 4.824E+00 A
c) 5.307E+00 A
d) 5.838E+00 A
e) 6.421E+00 A

9) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

10) A recangular coil with an area of 0.291 m2 and 6 turns is placed in a uniform magnetic field of 2.63 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.130E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 35 s?

a) 1.490E+04 V
b) 1.639E+04 V
c) 1.803E+04 V
d) 1.983E+04 V
e) 2.181E+04 V

#### T7 X2

1) The output of an ac generator connected to an RLC series combination has a frequency of 540 Hz and an amplitude of 0.18 V;. If R =3 Ω, L= 2.50E-03H , and C=8.20E-04 F, what is the impedance?

a) 7.872E+00 Ω
b) 8.659E+00 Ω
c) 9.525E+00 Ω
d) 1.048E+01 Ω
e) 1.153E+01 Ω

2) The current through the windings of a solenoid with n= 1.830E+03 turns per meter is changing at a rate dI/dt=14 A/s. The solenoid is 87 cm long and has a cross-sectional diameter of 2.5 cm. A small coil consisting of N=30turns wraped in a circle of diameter 1.34 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil. What is the emf induced in the coil?

a) 1.126E-04 V
b) 1.238E-04 V
c) 1.362E-04 V
d) 1.498E-04 V
e) 1.648E-04 V

3) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.
4)
A cylinder of height 1.3 cm and radius 6.01 cm is cut into a wedge as shown. Now imagine that the volume grows as θ increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.61 cm from point O and moves at a speed of 2.11 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
--(Answer & Why this question is different.)
a) 1.372E+01 cm3/s
b) 1.509E+01 cm3/s
c) 1.660E+01 cm3/s
d) 1.826E+01 cm3/s
e) 2.009E+01 cm3/s

5) In an LC circuit, the self-inductance is 0.0307 H and the capacitance is 5.330E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 1.840E-05 C. How long does it take for the capacitor to become completely discharged?

a) 5.251E-04 s
b) 5.776E-04 s
c) 6.354E-04 s
d) 6.989E-04 s
e) 7.688E-04 s

6) A washer has an inner diameter of 2.42 cm and an outer diamter of 4.53 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.47mm}$, and ${\displaystyle n=2.8}$. What is the volume of the washer?

a) 8.932E-01 cm3
b) 9.825E-01 cm3
c) 1.081E+00 cm3
d) 1.189E+00 cm3
e) 1.308E+00 cm3

7) An ac generator produces an emf of amplitude 8 V at a frequency of 80 Hz. What is the maximum amplitude of the current if the generator is connected to a 14 mF inductor?

a) 8.541E-01 A
b) 9.395E-01 A
c) 1.033E+00 A
d) 1.137E+00 A
e) 1.251E+00 A

8) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

9) A recangular coil with an area of 0.39 m2 and 16 turns is placed in a uniform magnetic field of 3.07 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.320E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 44 s?

a) 3.792E+04 V
b) 4.172E+04 V
c) 4.589E+04 V
d) 5.048E+04 V
e) 5.552E+04 V

10) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 59 mF capacitor?

a) 5.042E+00 A
b) 5.546E+00 A
c) 6.100E+00 A
d) 6.710E+00 A
e) 7.381E+00 A

### T7 Y0

1) A long solenoid has a radius of 0.777 m and 67 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 2.39 m from the axis at time t=0.0399 s ?

a) 3.924E-04 V/m
b) 4.317E-04 V/m
c) 4.748E-04 V/m
d) 5.223E-04 V/m
e) 5.745E-04 V/m

2) A square coil has sides that are L= 0.219 m long and is tightly wound with N=508 turns of wire. The resistance of the coil is R=8.42 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0619 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.791E-01 A
b) 1.970E-01 A
c) 2.167E-01 A
d) 2.384E-01 A
e) 2.622E-01 A

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.655 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (5.62)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.62 s. What is the current in the coil if the impedance of the coil is 48.9 Ω?

a) 7.890E-01 A
b) 8.679E-01 A
c) 9.547E-01 A
d) 1.050E+00 A
e) 1.155E+00 A

4) In an LC circuit, the self-inductance is 0.0689 H and the capacitance is 2.110E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.220E-05 C. How long does it take for the capacitor to become completely discharged?

a) 4.950E-04 s
b) 5.445E-04 s
c) 5.989E-04 s
d) 6.588E-04 s
e) 7.247E-04 s
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if ε = 2.64 V , R = 6.37 Ω, and L = 7.33 H?
a) -1.700E+00 s
b) -1.870E+00 s
c) -2.057E+00 s
d) -2.262E+00 s
e) -2.489E+00 s

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=4 V. The resistance, inductance, and capacitance are R =0.2 Ω, L= 4.90E-03H , and C=2.10E-06 F, respectively.

a) Q = 1.381E+02
b) Q = 1.588E+02
c) Q = 1.826E+02
d) Q = 2.100E+02
e) Q = 2.415E+02

7) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 59 mF capacitor?

a) 5.042E+00 A
b) 5.546E+00 A
c) 6.100E+00 A
d) 6.710E+00 A
e) 7.381E+00 A

8) The output of an ac generator connected to an RLC series combination has a frequency of 280 Hz and an amplitude of 0.35 V;. If R =5 Ω, L= 9.50E-03H , and C=6.90E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

9) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

10) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

#### T7 Y1

1) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

2) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.14 Ω, L= 5.20E-03H , and C=2.90E-06 F, respectively.

a) Q = 2.287E+02
b) Q = 2.630E+02
c) Q = 3.025E+02
d) Q = 3.478E+02
e) Q = 4.000E+02

3) A square coil has sides that are L= 0.436 m long and is tightly wound with N=284 turns of wire. The resistance of the coil is R=6.89 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 5.743E-01 A
b) 6.318E-01 A
c) 6.950E-01 A
d) 7.645E-01 A
e) 8.409E-01 A

4) In an LC circuit, the self-inductance is 0.025 H and the capacitance is 3.530E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.770E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.856E-04 s
b) 4.242E-04 s
c) 4.666E-04 s
d) 5.133E-04 s
e) 5.646E-04 s

5) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts
6)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.43% of its maximum value if ε = 1.64 V , R = 8.3 Ω, and L = 1.61 H?
a) -4.120E-01 s
b) -4.532E-01 s
c) -4.985E-01 s
d) -5.483E-01 s
e) -6.031E-01 s

7) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.549 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.97)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.0 s. What is the current in the coil if the impedance of the coil is 46.7 Ω?

a) 2.032E-01 A
b) 2.235E-01 A
c) 2.458E-01 A
d) 2.704E-01 A
e) 2.975E-01 A

8) An ac generator produces an emf of amplitude 17 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a 6 mF capacitor?

a) 5.253E-02 A
b) 5.778E-02 A
c) 6.356E-02 A
d) 6.991E-02 A
e) 7.691E-02 A

9) A long solenoid has a radius of 0.757 m and 90 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \alpha =}$30 s−1.What is the induced electric fied at a distance 2.08 m from the axis at time t=0.0442 s ?

a) 6.527E-04 V/m
b) 7.180E-04 V/m
c) 7.898E-04 V/m
d) 8.688E-04 V/m
e) 9.556E-04 V/m

10) The output of an ac generator connected to an RLC series combination has a frequency of 410 Hz and an amplitude of 0.82 V;. If R =7 Ω, L= 9.70E-03H , and C=9.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

#### T7 Y2

1) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

2) A square coil has sides that are L= 0.727 m long and is tightly wound with N=376 turns of wire. The resistance of the coil is R=5.59 Ω. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0485 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?

a) 1.567E+00 A
b) 1.724E+00 A
c) 1.897E+00 A
d) 2.086E+00 A
e) 2.295E+00 A

3) The output of an ac generator connected to an RLC series combination has a frequency of 970 Hz and an amplitude of 0.11 V;. If R =9 Ω, L= 8.50E-03H , and C=7.00E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?

4) A long solenoid has a radius of 0.583 m and 38 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$24 s−1.What is the induced electric fied at a distance 2.09 m from the axis at time t=0.0388 s ?

a) 1.655E-04 V/m
b) 1.821E-04 V/m
c) 2.003E-04 V/m
d) 2.203E-04 V/m
e) 2.424E-04 V/m

5) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

6) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.14 Ω, L= 5.20E-03H , and C=2.90E-06 F, respectively.

a) Q = 2.287E+02
b) Q = 2.630E+02
c) Q = 3.025E+02
d) Q = 3.478E+02
e) Q = 4.000E+02
7)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 1.53% of its maximum value if ε = 6.08 V , R = 1.88 Ω, and L = 4.67 H?
a) -5.192E+00 s
b) -5.711E+00 s
c) -6.282E+00 s
d) -6.910E+00 s
e) -7.601E+00 s

8) In an LC circuit, the self-inductance is 0.025 H and the capacitance is 3.530E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.770E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.856E-04 s
b) 4.242E-04 s
c) 4.666E-04 s
d) 5.133E-04 s
e) 5.646E-04 s

9) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.78 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.22)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.74 s. What is the current in the coil if the impedance of the coil is 32.1 Ω?

a) 1.742E+00 A
b) 1.916E+00 A
c) 2.108E+00 A
d) 2.319E+00 A
e) 2.551E+00 A

10) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a 99 mF capacitor?

a) 1.644E+00 A
b) 1.808E+00 A
c) 1.989E+00 A
d) 2.188E+00 A
e) 2.407E+00 A

### T7 Z0

1) A long solenoid has a radius of 0.306 m and 98 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$6 A and ${\displaystyle \alpha =}$22 s−1.What is the induced electric fied at a distance 2.52 m from the axis at time t=0.0246 s ?

a) 1.598E-04 V/m
b) 1.758E-04 V/m
c) 1.934E-04 V/m
d) 2.127E-04 V/m
e) 2.340E-04 V/m

2) A recangular coil with an area of 0.449 m2 and 20 turns is placed in a uniform magnetic field of 3.58 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.990E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 66 s?

a) 7.734E+04 V
b) 8.507E+04 V
c) 9.358E+04 V
d) 1.029E+05 V
e) 1.132E+05 V

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.348 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.3)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.57 s. What is the current in the coil if the impedance of the coil is 68.6 Ω?

a) 5.720E-02 A
b) 6.292E-02 A
c) 6.921E-02 A
d) 7.613E-02 A
e) 8.375E-02 A

4) In an LC circuit, the self-inductance is 0.0273 H and the capacitance is 6.440E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.620E-05 C. How long does it take for the capacitor to become completely discharged?

a) 5.443E-04 s
b) 5.988E-04 s
c) 6.586E-04 s
d) 7.245E-04 s
e) 7.969E-04 s
5)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =1.0 s if ε = 4.14 V , R = 7.92 Ω, and L = 2.26 H?
a) 3.523E-01 V
b) 4.227E-01 V
c) 5.073E-01 V
d) 6.087E-01 V
e) 7.304E-01 V

6) A step-down transformer steps 15 kV down to 250 V. The high-voltage input is provided by a 130 Ω power line that carries 4 A of currentWhat is the output current (at the 250 V side ?)

a) 1.983E+02 A
b) 2.182E+02 A
c) 2.400E+02 A
d) 2.640E+02 A
e) 2.904E+02 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 470 Hz and an amplitude of 0.67 V;. If R =4 Ω, L= 2.40E-03H , and C=5.10E-04 F, what is the impedance?

a) 6.254E+00 Ω
b) 6.879E+00 Ω
c) 7.567E+00 Ω
d) 8.324E+00 Ω
e) 9.156E+00 Ω

8) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.64 V. The resistance, inductance, and capacitance are R =2 Ω, L= 4.00E-03H , and C=8.30E-04 F, respectively. What is the amplitude of the current?

a) 3.200E-01 A
b) 3.520E-01 A
c) 3.872E-01 A
d) 4.259E-01 A
e) 4.685E-01 A

9) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

10) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

#### T7 Z1

1) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.83 V. The resistance, inductance, and capacitance are R =4 Ω, L= 4.60E-03H , and C=8.10E-04 F, respectively. What is the amplitude of the current?

a) 1.417E-01 A
b) 1.559E-01 A
c) 1.715E-01 A
d) 1.886E-01 A
e) 2.075E-01 A
2)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =5.67 s if ε = 5.58 V , R = 3.81 Ω, and L = 3.85 H?
a) 7.037E-01 V
b) 8.444E-01 V
c) 1.013E+00 V
d) 1.216E+00 V
e) 1.459E+00 V

3) A recangular coil with an area of 0.178 m2 and 17 turns is placed in a uniform magnetic field of 2.62 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.380E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 45 s?

a) 1.068E+04 V
b) 1.175E+04 V
c) 1.293E+04 V
d) 1.422E+04 V
e) 1.564E+04 V

4) A long solenoid has a radius of 0.578 m and 34 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$7 A and ${\displaystyle \alpha =}$27 s−1.What is the induced electric fied at a distance 2.63 m from the axis at time t=0.0462 s ?

a) 1.473E-04 V/m
b) 1.621E-04 V/m
c) 1.783E-04 V/m
d) 1.961E-04 V/m
e) 2.157E-04 V/m

5) Two orbiting satellites are orbiting at a speed of 83 km/s perpendicular to a magnetic field of 57 μT. They are connected by a cable that is 23 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 8.98 x 104 volts.
b) 1.09 x 105 volts.
c) 1.32 x 105 volts.
d) 1.6 x 105 volts.
e) 1.93 x 105 volts.

6) A step-down transformer steps 18 kV down to 170 V. The high-voltage input is provided by a 240 Ω power line that carries 5 A of currentWhat is the output current (at the 170 V side ?)

a) 5.294E+02 A
b) 5.824E+02 A
c) 6.406E+02 A
d) 7.046E+02 A
e) 7.751E+02 A

7) The output of an ac generator connected to an RLC series combination has a frequency of 810 Hz and an amplitude of 0.64 V;. If R =6 Ω, L= 8.70E-03H , and C=8.20E-04 F, what is the impedance?

a) 4.444E+01 Ω
b) 4.889E+01 Ω
c) 5.378E+01 Ω
d) 5.916E+01 Ω
e) 6.507E+01 Ω

8) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

9) In an LC circuit, the self-inductance is 0.0795 H and the capacitance is 7.930E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 2.420E-05 C. How long does it take for the capacitor to become completely discharged?

a) 9.370E-04 s
b) 1.031E-03 s
c) 1.134E-03 s
d) 1.247E-03 s
e) 1.372E-03 s

10) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.348 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.3)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.57 s. What is the current in the coil if the impedance of the coil is 68.6 Ω?

a) 5.720E-02 A
b) 6.292E-02 A
c) 6.921E-02 A
d) 7.613E-02 A
e) 8.375E-02 A

#### T7 Z2

1)
Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.47 s if ε = 7.04 V , R = 7.69 Ω, and L = 5.78 H?
a) 4.249E-01 V
b) 5.099E-01 V
c) 6.118E-01 V
d) 7.342E-01 V
e) 8.810E-01 V

2) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$2 A and ${\displaystyle \alpha =}$21 s−1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?

a) 1.605E-04 V/m
b) 1.766E-04 V/m
c) 1.942E-04 V/m
d) 2.136E-04 V/m
e) 2.350E-04 V/m

3) A step-down transformer steps 18 kV down to 260 V. The high-voltage input is provided by a 290 Ω power line that carries 3 A of currentWhat is the output current (at the 260 V side ?)

a) 1.888E+02 A
b) 2.077E+02 A
c) 2.285E+02 A
d) 2.513E+02 A
e) 2.764E+02 A

4) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

5) An RLC series combination is driven with an applied voltage of of V=V0sin(ωt), where V0=0.44 V. The resistance, inductance, and capacitance are R =7 Ω, L= 5.40E-03H , and C=5.70E-04 F, respectively. What is the amplitude of the current?

a) 4.723E-02 A
b) 5.195E-02 A
c) 5.714E-02 A
d) 6.286E-02 A
e) 6.914E-02 A

6) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.18 V;. If R =6 Ω, L= 7.50E-03H , and C=7.50E-04 F, what is the impedance?

a) 2.708E+01 Ω
b) 2.978E+01 Ω
c) 3.276E+01 Ω
d) 3.604E+01 Ω
e) 3.964E+01 Ω

7) A recangular coil with an area of 0.182 m2 and 5 turns is placed in a uniform magnetic field of 2.74 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 2.390E+03 s−1. What is the magnitude (absolute value) of the induced emf at t = 79 s?

a) 1.656E+03 V
b) 1.821E+03 V
c) 2.003E+03 V
d) 2.204E+03 V
e) 2.424E+03 V

8) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.348 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (2.3)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$7.57 s. What is the current in the coil if the impedance of the coil is 68.6 Ω?

a) 5.720E-02 A
b) 6.292E-02 A
c) 6.921E-02 A
d) 7.613E-02 A
e) 8.375E-02 A

9) In an LC circuit, the self-inductance is 0.025 H and the capacitance is 3.530E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.770E-05 C. How long does it take for the capacitor to become completely discharged?

a) 3.856E-04 s
b) 4.242E-04 s
c) 4.666E-04 s
d) 5.133E-04 s
e) 5.646E-04 s

10) Two orbiting satellites are orbiting at a speed of 70 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 30 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 4.48 x 104 volts.
b) 5.43 x 104 volts.
c) 6.58 x 104 volts.
d) 7.97 x 104 volts.
e) 9.66 x 104 volts.
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### Key: A0

1) A long solenoid has a radius of 0.845 m and 78 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$3 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 0.214 m from the axis at time t=0.0655 s ?

-a) 1.160E-04 V/m
-b) 1.276E-04 V/m
-c) 1.403E-04 V/m
-d) 1.544E-04 V/m
+e) 1.698E-04 V/m

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.54 T and ${\displaystyle \omega =}$1.860E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.642 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

-a) 2.415E+04 V
+b) 2.656E+04 V
-c) 2.922E+04 V
-d) 3.214E+04 V
-e) 3.535E+04 V

3) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.78 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.22)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$9.74 s. What is the current in the coil if the impedance of the coil is 32.1 Ω?

+a) 1.742E+00 A
-b) 1.916E+00 A
-c) 2.108E+00 A
-d) 2.319E+00 A
-e) 2.551E+00 A

4) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.14mm}$, and ${\displaystyle n=2.86}$. What is the volume of the washer?

+a) 1.071E+00 cm3
-b) 1.178E+00 cm3
-c) 1.296E+00 cm3
-d) 1.425E+00 cm3
-e) 1.568E+00 cm3
5)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.69% of its maximum value if ε = 4.79 V , R = 4.18 Ω, and L = 2.7 H?
-a) -8.773E-01 s
-b) -9.651E-01 s
-c) -1.062E+00 s
+d) -1.168E+00 s
-e) -1.284E+00 s

6) An ac generator produces an emf of amplitude 4 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a 19 mF capacitor?

-a) 6.946E-02 A
+b) 7.640E-02 A
-c) 8.404E-02 A
-d) 9.245E-02 A
-e) 1.017E-01 A

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=5 V. The resistance, inductance, and capacitance are R =0.17 Ω, L= 4.40E-03H , and C=3.40E-06 F, respectively.

-a) Q = 1.391E+02
-b) Q = 1.600E+02
-c) Q = 1.840E+02
+d) Q = 2.116E+02
-e) Q = 2.434E+02

8) The output of an ac generator connected to an RLC series combination has a frequency of 1.00E+03 Hz and an amplitude of 0.6 V;. If R =3 Ω, L= 1.70E-03H , and C=5.40E-04 F, what is the impedance?

-a) 8.123E+00 Ω
-b) 8.935E+00 Ω
-c) 9.828E+00 Ω
+d) 1.081E+01 Ω
-e) 1.189E+01 Ω

9) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

-a) 5.43 x 100 volts
+b) 6.58 x 100 volts
-c) 7.97 x 100 volts
-d) 9.65 x 100 volts
-e) 1.17 x 101 volts

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

+a) 1.88 x 109 s.
-b) 5.93 x 109 s.
-c) 1.88 x 1010 s.
-d) 5.93 x 1010 s.
-e) 1.88 x 1011 s.

#### Key: A1

1) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved, Q=≡ω0L/R is definedso that Q is large if the resistance is low. Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(ωt), where V0=3 V. The resistance, inductance, and capacitance are R =0.14 Ω, L= 5.20E-03H , and C=2.90E-06 F, respectively.

-a) Q = 2.287E+02
-b) Q = 2.630E+02
+c) Q = 3.025E+02
-d) Q = 3.478E+02
-e) Q = 4.000E+02

2) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.305 m. The magnetic field is spatially uniform but decays in time according to ${\displaystyle (4.59)e^{-\alpha t}}$, where ${\displaystyle \alpha =}$5.58 s. What is the current in the coil if the impedance of the coil is 13.3 Ω?

-a) 4.141E-01 A
+b) 4.555E-01 A
-c) 5.011E-01 A
-d) 5.512E-01 A
-e) 6.063E-01 A

3) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

-a) 5.43 x 100 volts
+b) 6.58 x 100 volts
-c) 7.97 x 100 volts
-d) 9.65 x 100 volts
-e) 1.17 x 101 volts

4) A long solenoid has a radius of 0.861 m and 28 turns per meter; its current decreases with time according to ${\displaystyle I_{0}e^{-\alpha t}}$, where ${\displaystyle I_{0}=}$1 A and ${\displaystyle \alpha =}$20 s−1.What is the induced electric fied at a distance 0.106 m from the axis at time t=0.055 s ?

-a) 1.026E-05 V/m
-b) 1.129E-05 V/m
+c) 1.242E-05 V/m
-d) 1.366E-05 V/m
-e) 1.502E-05 V/m

5) A washer has an inner diameter of 2.42 cm and an outer diamter of 4.53 cm. The thickness is ${\displaystyle h=Cr^{-n}}$ where ${\displaystyle r}$ is measured in cm, ${\displaystyle C=4.47mm}$, and ${\displaystyle n=2.8}$. What is the volume of the washer?

-a) 8.932E-01 cm3
-b) 9.825E-01 cm3
-c) 1.081E+00 cm3
+d) 1.189E+00 cm3
-e) 1.308E+00 cm3

6) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$3.71 T and ${\displaystyle \omega =}$6.600E+03 s−1. Suppose the electric field is always zero at point ${\displaystyle {\mathcal {O}}}$, and consider a circle of radius 0.31 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral ${\displaystyle \oint {\vec {B}}\cdot d{\vec {s}}}$ around the circle.

+a) 4.769E+04 V
-b) 5.246E+04 V
-c) 5.771E+04 V
-d) 6.348E+04 V
-e) 6.983E+04 V

7) The output of an ac generator connected to an RLC series combination has a frequency of 910 Hz and an amplitude of 0.88 V;. If R =7 Ω, L= 6.80E-03H , and C=9.60E-04 F, what is the impedance?

-a) 3.575E+01 Ω
+b) 3.933E+01 Ω
-c) 4.326E+01 Ω
-d) 4.758E+01 Ω
-e) 5.234E+01 Ω

8) An ac generator produces an emf of amplitude 53 V at a frequency of 190 Hz. What is the maximum amplitude of the current if the generator is connected to a 85 mF capacitor?

-a) 4.445E+00 A
-b) 4.889E+00 A
+c) 5.378E+00 A
-d) 5.916E+00 A
-e) 6.507E+00 A
9)
Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is opened as as S2 is closed. How long will it take for the energy stored in the inductor to be reduced to 2.63% of its maximum value if ε = 8.7 V , R = 8.35 Ω, and L = 1.44 H?
+a) -3.137E-01 s
-b) -3.451E-01 s
-c) -3.796E-01 s
-d) -4.176E-01 s
-e) -4.593E-01 s

10) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

+a) 1.88 x 109 s.
-b) 5.93 x 109 s.
-c) 1.88 x 1010 s.
-d) 5.93 x 1010 s.
-e) 1.88 x 1011 s.

#### Key: A2

1) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

+a) 1.88 x 109 s.
-b) 5.93 x 109 s.
-c) 1.88 x 1010 s.
-d) 5.93 x 1010 s.
-e) 1.88 x 1011 s.

2) A spatially uniform magnetic points in the z-direction and oscilates with time as ${\displaystyle {\vec {B}}(t)=B_{0}\sin \omega t}$ where ${\displaystyle B_{0}=}$2.34 T and ${\displaystyle \omega =}$2.670E+03 s−1. Suppose the electric field is always zero at point