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}} $