An uncharged capacitor is connected to a battery. How much amount of energy supplied by the battery is lost as heat while charging the capacitor?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{1}{2}QV \)
Use conservation of energy. The battery of voltage V moves a charge Q through its emf, so the energy it supplies is QV. Only part of this is stored in the capacitor; the rest is lost as heat in the connecting wires.
\( E_{\text{battery}} = QV \)
\( \displaystyle E_{\text{stored}} = \frac{1}{2}CV^{2} = \frac{1}{2}QV \qquad (Q = CV) \)
\( \displaystyle E_{\text{heat}} = QV - \frac{1}{2}QV = \frac{1}{2}QV \)