A parallel plate capacitor is charged by a battery and then the battery is disconnected. If the plat

Question

A parallel plate capacitor is charged by a battery and then the battery is disconnected. If the plates of the capacitor are moved further apart, then: A. the charge stored in it decreases. B. the energy stored in it increases. C. its capacitance increases. D. the potential difference across it increases. E. the electric field between the plates decreases. Choose the correct answer.

Professor PC Thomas Classes · Answer

(a) : When the battery is disconnected, the charge $Q$ on the plates remains constant. As the distance $d$ increases, the capacitance $C = \frac{\varepsilon_0 A}{d}$ decreases. Since $V = \frac{Q}{C}$, a decrease in $C$ leads to an increase in potential difference $V$ (Statement D is correct). The energy stored $U = \frac{Q^2}{2C}$ increases because $C$ decreases (Statement B is correct). The electric field $E = \frac{V}{d} = \frac{Q}{C d} = \frac{Q}{\varepsilon_0 A}$ remains constant. Therefore, only statements B and D are correct.