Q.
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) $2CV^{2}$
B) $\frac{1}{4}\ CV^{2}$
C) $\frac{3}{4}CV^{2}$
D)
Explanation
(d) The two capacitor 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, $W = U = \frac{1}{2}C^{'}V^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1}{2}\left( \frac{3C}{2} \right)V^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{3}{4}CV^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.