AC voltage and current v = V 0 sin ( ω t − ϕ ) {\displaystyle v=V_{0}\sin(\omega t-\phi )} if i = I 0 sin ω t . {\displaystyle i=I_{0}\sin \omega t.} RMS values I r m s = I 0 2 {\displaystyle I_{rms}={\tfrac {I_{0}}{\sqrt {2}}}} and V r m s = V 0 2 {\displaystyle V_{rms}={\tfrac {V_{0}}{\sqrt {2}}}} Impedance V 0 = I 0 X {\displaystyle V_{0}=I_{0}X} Resistor V 0 = I 0 X R , ϕ = 0 , {\displaystyle V_{0}=I_{0}X_{R},\;\phi =0,} where X R = R {\displaystyle X_{R}=R} Capacitor V 0 = I 0 X C , ϕ = − π 2 , {\displaystyle V_{0}=I_{0}X_{C},\;\phi =-{\tfrac {\pi }{2}},} where X C = 1 ω C {\displaystyle X_{C}={\tfrac {1}{\omega C}}} Inductor V 0 = I 0 X L , ϕ = + π 2 , {\displaystyle V_{0}=I_{0}X_{L},\;\phi =+{\tfrac {\pi }{2}},} where X L = ω L {\displaystyle X_{L}=\omega L} RLC series circuit V 0 = I 0 Z {\displaystyle V_{0}=I_{0}Z} where Z = R 2 + ( X L − X C ) 2 {\displaystyle Z={\sqrt {R^{2}+\left(X_{L}-X_{C}\right)^{2}}}} and ϕ = tan − 1 X L − X C R {\displaystyle \phi =\tan ^{-1}{\frac {X_{L}-X_{C}}{R}}} Resonant angular frequency ω 0 = 1 L C {\displaystyle \omega _{0}={\sqrt {\tfrac {1}{LC}}}} Quality factor Q = ω 0 Δ ω = ω 0 L R {\displaystyle Q={\tfrac {\omega _{0}}{\Delta \omega }}={\tfrac {\omega _{0}L}{R}}} Average power P a v e = 1 2 I 0 V 0 cos ϕ = I r m s V r m s cos ϕ {\displaystyle P_{ave}={\frac {1}{2}}I_{0}V_{0}\cos \phi =I_{rms}V_{rms}\cos \phi } Transformer voltages and currents V S V P = N S N P = I P I S {\displaystyle {\tfrac {V_{S}}{V_{P}}}={\tfrac {N_{S}}{N_{P}}}={\tfrac {I_{P}}{I_{S}}}}
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