In an a.c. circuit containing L, C and R in series, the ratio of apparent power to the true power is (Z and R are the impedance and resistance respectively, = phase angle)

Step-by-step solution

Apparent power S in an a.C. circuit is S = V_ rms I_ rms , or equivalently S = I_ rms ^2 Z , where Z is the circuit's impedance. True power P represents the actual power dissipated and is given by P = V_ rms I_ rms , where is the phase angle between voltage and current, or P = I_ rms ^2 R , with R being the resistance. The ratio of apparent to true power is S P = V_ rms I_ rms V_ rms I_ rms = 1 . Given that the power factor is = R Z , then 1 = Z R . Alternatively, starting from the current-based expressions: S P =