Question

Two condensers, one of capacity $C$ and other of capacity $\frac{C}{2}$ are connected to a $V$ volt battery, as shown in the figure. The work done in charging fully both the condensers is

• A. $\frac{1}{4}CV^{2}$
• B. $\frac{3}{4}CV^{2}$
• C. $\frac{1}{2}CV^{2}$
• D. $2 \, CV^{2}$

Answer 1

Answer: (B)

As the capacitors are connected in parallel, therefore potential difference across both the condensors remains the same
$\therefore q_{1}=CV, q_{2}=\frac{C}{2}V$
Also $q=q_{1}+q_{2}=CV+\frac{C}{2} V=\frac{3}{2}CV $
Work done in charging fully both the condensors is given by

$W=\frac{1}{2}qV=\frac{1}{2}\times\left(\frac{3}{2}CV\right)$
$V=\frac{3}{4}CV^{2}$