Question

If an uncharged capacitor is charged by connecting it to a battery, then the amount of energy lost as heat is:

• A. $\frac{1}{2}QV$
• B. $QV$
• C. $\frac{1}{2}Q{V}^2$
• D. $Q{V}^2$

Answer 1

The correct option is A $\frac{1}{2}QV$

The charge stored on capacitor $=Q$

We know, if $Q$ charge has passed through battery work done by battery $=QV$

Energy stored in capacitor $=\frac{1}{2}C{V}^2=\frac{1}{2}QV$ [$\because Q=CV$]

$\therefore$ Energy lost as heat $=$ Work done by battery $-$ Energy store in capacitor

$=QV-\frac{1}{2}QV$$=\frac{1}{2}QV$

Hence, option A is correct.