Physics - Capacitor Question with Solution | TestHub

The given capacitors having capacitance $C$ and $\frac{C}{3}$ are connected in parallel across the battery.

The equivalent capacitance $C_{eq}$ of the circuit is:

$C_{eq}=C+\frac{C}{3}=\frac{4C}{3}$

The total charge $q$ drawn from the battery to fully charge the capacitors is:

$q=C_{eq}V=\left(\frac{4C}{3}\right)V$

The work done $W$ by the battery in supplying this charge is given by the product of the total charge and the potential difference of the battery:

$W=qV$

$W=\left(\frac{4CV}{3}\right)V$

$W=\frac{4C{V}^2}{3}$