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

Step-by-step solution

The true power dissipated in an AC circuit is P_ true = V_ rms I_ rms , where is the phase angle between voltage and current. The apparent power is defined as P_ apparent = V_ rms I_ rms . The ratio gives P_ true P_ apparent = , known as the power factor. In an LCR series circuit, the power factor equals R Z , where R is the resistance and Z is the impedance. The ratio of true power to apparent power is therefore R Z , corresponding to option D.