Question

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

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

Answer 1

The correct option is D $\frac{3}{4}C{V}^2$

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