Question

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

The work done by battery in charging fully both the condensers is :-

• A. $\frac{1}{2} C V^{2}$
• B. $2 CV ^{2}$
• C. $\frac{5}{2} C V^{2}$
• D. $\frac{3}{2} C V^{2}$

Answer 1

Answer: (C)

$C_{e q}=2 C+\frac{C}{2}=\frac{5 C}{2}$
$q_{\text {Battery }}=C_{e q} V=\frac{5 C V}{2}$
$W_{\text {Battery }}=\left(q_{\text {Battery }}\right) V=\frac{5 C V^{2}}{2}$