When a battery is connected to a capacitor, why do the two plates acquire charges of the same magnitude? Will this be true if the two plates are different sizes or shapes?

A parallel plate capacitor is a device used to store electric charge and energy.

The expression for the capacitance of the parallel plate capacitor is as follows:

\(C = \frac{{{\varepsilon _0}A}}{d}\)

Here, \({\varepsilon _0}\) is the permittivity of free space, A is the cross-sectional area, and d is the separation between the plates.

From the law of conservation of charge, when a battery is joined to a capacitor, it becomes charged; one plate gets a negative charge and the other an equivalent amount of positive charge. Since they are neutral before they are connected, they must be neutral after they are connected. The charge removed from one plate appears as the excess on the other plate.

Suppose the two conductors are of different sizes and shapes. In that case, it will not affect the number of positive and negative charges as the capacitance is independent of the nature of the conductors. It depends only on the area of cross-section and the distance between them.