Two condensers, one of capacity C and the other of capacity C/2, are connected to a V- volt battery, as shown.
The work done in charging fully both the condensers is

CV²

$\frac{1}{4} {CV}^{2}$

$\frac{3}{4} {CV}^{2}$

$\frac{1}{2} {CV}^{2}$

Solution

$\frac{3}{4} {CV}^{2}$

The two condensers in the circuit are in parallel order, hence

$C' = C + \frac{C}{2} = \frac{3 C}{2}$

The work done in charging the equivalent capacitor is stored in the form of potential energy.

Hence,

$W = U = \frac{1}{2} C' V^{2} = \frac{1}{2} (\frac{3 C}{2}) V^{2} = \frac{3}{4} {CV}^{2}$

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