Question

Two condensers, one of capacity $C$ and the other of capacity $\frac{C}{2}$, are connected to a $V$-volt battery as shown.

• A. $\frac{1}{2}C{V}^2$
• B. $2C{V}^2$
• C. $\frac{1}{2}C{V}^2$
• D. $\frac{3}{2}C{V}^2$

Answer 1

The correct option is D $\frac{3}{2}C{V}^2$

Their equivalent capacitance,
$C_{eq}=C+\frac{C}{2}=\frac{3C}{2}$
How, total charge flown through the battery,
$Q=C_{eq}V=\frac{3VC}{2}$
$\therefore$ Work done by battery,
$W=QV$
$\therefore W=\frac{3CV}{2}V=\frac{3C{V}^2}{2}$