Question

(i) When an AC source is connected to an ideal inductor, show that the average power supplied by the source over a complete cycle is zero.

(ii) A lamp is connected in series with an inductor and an AC source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the inductor ? Explain.

Answer 1

(i) The average power supplied by the source over a complete cycle is

$P_{av}=E_{rms}.I_{rms}.cos\varphi$

When the circuit contains an ideal inductor, then the phase difference between the current and voltage is $\frac{\pi }{2}$.

$So,\varphi =\frac{\pi }{2}.So,cos\varphi =cos\frac{\pi }{2}=0.$

Hence $P_{av}=0.$

So, when an ac source is connected to an ideal inductor, the average power supplied by the source over a complete cycle is zero.

(ii) The brightness of the lamp will decrease. When the key is plugged in and the iron rod is inserted inside the inductor, it increases the inductance. Hence, the reactance of the inductor $(X_L=\omega L)$increases. So, the impedance of the circuit $(Z=R+j\omega L)$ increases, which decreases the current in the circuit.