Question

(i) When an AC source is connected to an ideal capacitor, show that the average power supplied by the source over a complete cycle is zero.
(ii) A bulb is connected in series with a variable capacitor and an AC source as shown. What happens to the brightness of the bulb when the key is plugged in and capacitance of the capacitor is gradually reduced?

Answer 1

(i) Power dissipated in a circuit is given by

$P=V_{rms}{I}_{rms}cos\varphi$

where $cos\varphi =\frac{R}{Z}$

For a ideal capacitor, $R=0$

Hence $cos\varphi =0$

$⟹P=0$

(ii) When AC source is connected, the reactance of capacitor is $X_C=\frac{1}{\omega C}$.

On reducing $C$, the reactance increases, and lesser current flows through the bulb and brightness reduces.