Question

Assertion :STATEMENT-$1$ : If the potential difference across a plane parallel plate capacitor is doubled then the potential energy of the capacitor becomes four times under all conditions. Reason: STATEMENT-$2$ : The potential energy U stored in the capacitor is $U=\frac{1}{2}C{V}^2$, where C and V have usual meaning.

• A. Statement-$1$ is True, Statement-$2$ is True; Statement-$2$ is a correct explanation for Statement-$1$
• B. Statement-$1$ is True, Statement-$2$ is True; Statement-$2$ is NOT a correct explanation for Statement-$1$
• C. Statement-$1$ is True, Statement-$2$ is False
• D. Statement-$1$ is False, Statement-$2$ is True

Answer 1

The correct option is D Statement-$1$ is False, Statement-$2$ is True

When the capacitor is isolated (disconnected from the battery), the potential remains constant. The potential difference between plates is equal to the emf of battery. So when potential difference is doubled , the energy remains constant because energy $U=\frac{1}{2}C{V}^2$.