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

Answer 1

Answer: (C)

The two condensers in the circuit are in parallel order, hence $C=C+\frac{C}{2}=\frac{3C}{2}$ The work done in charging the equivalent capacitor is stored in the form of potential energy. Hence, $W=U=\frac{1}{2}C{V}^2$ $=\frac{1}{2}\left(\frac{3C}{2}\right)V^2$ $=\frac{3}{4}C{V}^2$