22.7 Power

The power supplied to or dissipated by a resistor is
P = I2R

just as for DC circuits.

No power is dissipated by a capacitor or an inductor. That is, no power is dissipated by a pure inductor; if the inductor also has resistance, its resistance dissipates power. Only the resistor dissipates energy or power.

From the phasor diagram here, we can see that the resistance R is related to the total impedance Z by

R = Z cos

so we can write the power as

P = I2 Z cos


P = I V cos

This term cos is known as the power factor of the circuit. For a circuit with only a capacitor or only an inductor the current and voltage are out of phase by ± 90° so the power factor is zero. This is another way of understanding that capacitors and inductors do not dissipate power. Remember, I or V without a subscript means the rms value of the current or voltage, I = Irms and V = Vrms.

RCL Circuits

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(c) Doug Davis, 2002; all rights reserved