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. $2CV^{2}$

Answer 1

Answer: (B)

$\frac{3}{4}CV^{2}$

Answer 2

:

As the capacitors are connected in parallel, therefore potential difference across both the condensers 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 condensers is given by

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