Electricity/Principles

Basic formulas calculating resistance, current, voltage, and power-
where:

• V= voltage (Measured in Volts)
• I= current (Measured in Amperes)
• R= resistance (Measured in Ohms)
• P= power (Measured in Watts)

Symbols and Abbreviations

The symbols used for quantities in electrical engineering can be confusing, since the symbol for a quantity may be different from the symbol for the units in which it is measured. We list the common symbols here, even though we have not yet defined all of the concepts involved.

Electrical charge

is typically denoted $Q$, measured in coulombs, abbreviated $C$.

Current

is typically denoted $I$, measured in amperes, abbreviated $A$.

An ampere is, among other things, a coulomb per second.

Example: $V=IR\,$   Ohm's law; voltage equals current times resistance.

Example: "$I=28mA\,$"   "The current is 28 milliamperes."

Voltage

is typically denoted $V$ (or sometimes $E$), and measured in volts, abbreviated $V$. The use of "$E$" stands for "emf" (electro-motive force.)

A volt is, among other things, a joule per coulomb.

Example: "$V=28mV\,$"   "The voltage is 28 millivolts."

Resistance

is typically denoted $R$, measured in ohms, abbreviated with the capital Greek omega: $\Omega$.

An ohm is, among other things, a volt per ampere.

Example: "$R=2.7K\Omega \,$"   "The resistance is 2.7 kilohms."

Conductance

It is sometimes useful to speak of the reciprocal of resistance. This is called conductance, and is typically denoted $G$, traditionally measured in "mhos" ("mho" is "ohm" spelled backwards), abbreviated with an upside-down omega: $\mho$. A less flippant term than "mho" has been adopted: the siemens, abbreviated $S$.

A mho/siemens is, among other things, an ampere per volt.

Example: $I=VG\,$   Ohm's law rewritten in terms of conductance.

Example: "$G=65m\mho \,$"   "The conductance is 65 millimhos."

Example: "$G=65mS\,$"   "The conductance is 65 millisiemens."

Capacitance

is typically denoted $C$, measured in farads, abbreviated $f$.

A farad is, among other things, a second per ohm, or a coulomb per volt.

Example: $t=RC\,$   The time constant is the resistance times the capacitance.

Example: "$C=75pf\,$"   "The capacitance is 75 picofarads."

Inductance

is typically denoted $L$, measured in henries, abbreviated $h$.

A henry is, among other things, an ohm-second.

Example: $f={\frac {1}{2\ \pi \ {\sqrt {L\ C}}}}$   is the formula for the frequency of a resonant circuit.

Example: "$L=120nh\,$"   "The inductance is 120 nanohenries."

Power

is typically denoted $P$, measured in watts, abbreviated $W$.

A watt is, among other things, a joule per second, or a volt-ampere.

Example: $P=VI\,$   The power is the voltage times the current.

Example: "$P=75W\,$"   "The power is 75 watts."

The frequency

of an oscillation or signal is typically denoted $f$, measured in hertz, abbreviated $Hz$.

A hertz is really just a reciprocal second. In fact, the unit of frequency used to be just "cycles per second" or simply "cycles".

Example: "$f=102.5Mc\,$"   "102.5 megacycles on the FM dial" (old way.)

Example: "$f=102.5MHz\,$"   "102.5 megahertz on the FM dial" (new way.)

It happens that, in a lot of the mathematical formulas the unit of radians per second is superior. A frequency in radians per second is $2\ \pi$ times the frequency in hertz. When measured this way, the symbol $f$ is replaced with the lower-case Greek omega: $\omega$. Many occurrences of $2\ \pi$ disappear from various formulas when radians are used.

Example: $\omega ={\frac {1}{\sqrt {L\ C}}}$   is the formula for the frequency of a resonant circuit, in radians per second.

Example: $X_{C}={\frac {1}{2\ \pi \ f\ C}}$   is the formula for capacitive reactance, calibrated in hertz.

Example: $X_{C}={\frac {1}{\omega \ C}}$   is the formula for capacitive reactance, calibrated in radians per second.

Example: "$\omega =644.0265mrad/s\,$"   "644.0265 megaradians per second on the FM dial" (not known to have ever been announced.)