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. $\frac{1}{4}C{V}^2$
• B. $\frac{3}{4}C{V}^2$
• C. $\frac{1}{2}C{V}^2$
• D. $2C{V}^2$

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

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