A parallel plate capacitor is connected to a battery and charged to voltage V. Leah says that the charge on the plates will decrease if the distance between the plates is increased while they are still connected to the battery. Gertie says that the charge will remain the same. Which one, if either, is correct, and why?
A) Gertie, because the maximum voltage is determined by the battery.
B) Gertie, because the capacitance of the capacitor does not change.
C) Leah, because the capacitance decreases when the plate separation is increased.
D) Leah, because the capacitance increases when the plate separation is increased.
E) Neither, because the charge increases when the plate separation is increased.

Question

Quizplus · Accepted Answer

C) Leah is correct because the capacitance of a parallel plate capacitor is given by $C = \frac{\varepsilon_0 A}{d}$, where $C$ is the capacitance, $\varepsilon_0$ is the permittivity of free space, $A$ is the area of the plates, and $d$ is the distance between the plates. Increasing the distance ($d$) between the plates decreases the capacitance. Since the capacitor is connected to a battery, the voltage ($V$) across the capacitor remains constant. The charge ($Q$) on the capacitor is given by $Q = CV$. Therefore, if the capacitance ($C$) decreases and the voltage ($V$) remains constant, the charge ($Q$) on the plates must decrease.

A Parallel Plate Capacitor Is Connected to a Battery and Charged