An uncharged capacitor is connected to a battery. If the energy supplied by the battery is E, then the energy stored in the capacitor in charging is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → E/2
While the capacitor charges, a total charge Q = CV passes through the battery at its constant emf V, so the work done by the battery is QV. The capacitor, however, stores only half of this, because the potential difference across it rises gradually from 0 to V.
\( \displaystyle E = QV = CV^{2} \)
\( \displaystyle U = \frac{1}{2}QV = \frac{1}{2}CV^{2} \)
\( \displaystyle U = \frac{E}{2} \)
The other half is dissipated as heat in the resistance of the connecting wires, whatever the value of that resistance.