If the potential difference across a capacitor is changed from 12 V to 24 V, the work done is W. How much work will be done if the potential difference is changed from 24 V to 48 V?

4 W

The correct answer is Option (1) → 4 W

Work done in charging a capacitor from 0 to V is given by

$ W = \frac{1}{2} C V^2 $

Work done in changing potential from $V_1$ to $V_2$ is

$ W' = \frac{1}{2} C (V_2^2 - V_1^2) $

Given, $ W = \frac{1}{2} C (24^2 - 12^2) = \frac{1}{2} C (576 - 144) = 216C $

For change from 24 V to 48 V,

$ W' = \frac{1}{2} C (48^2 - 24^2) = \frac{1}{2} C (2304 - 576) = 864C $

Hence, $\frac{W'}{W} = \frac{864C}{216C} = 4$

Therefore, work done = 4W.