Question

Select correct statement for a capacitor having capacitance C and connected to a source of constant emf E :

• A. Almost whole of the energy supplied by the battery will be stored in the capacitor, if resistance of connecting wire is negligibly small
• B. Energy received by the capacitor will be half of energy supplied by the battery only when the capacitor was initially uncharged
• C. Strain energy in the capacitor must increases even if the capacitor had an initial charge
• D. Energy stored depends on type of the source of emf

Answer 1

Answer: (B)

Energy received by the capacitor will be half of energy supplied by the battery only when the capacitor was initially uncharged

If capacitor was initially uncharged then whole charge $Q$ on the capacitor is supplied by the battery.

$\therefore$ When $Q$ charge flows through a battery to capacitor work done by battery = $QV$

and

Energy stored in capacitor $=\frac{1}{2}C{V}^2=\frac{1}{2}QV$ which is the the half of work done by battery.

$\therefore$ Energy received by capacitor is half of energy supplied by battery.