Question

Explain why current flows through an ideal capacitor when it is connected to an a.c. source but not when it is connected to a d.c. source in a steady state.

Answer 1

When an ideal capacitor is charged by dc battery, charge flows momentarily till the capacitor gets fully charged .Ideal capacitor means infinte resistance for dc.

When an ac source is connected to the capacitor, conduction current, $i_c=\frac{dq}{dt}$ continuously flows in the connecting wire. Due to changing current, charge deposited on the plates of the capacitor changes with time.This causes change in electric field between the plates of the capacitor which cause the electric flux to change and gives rise to the displacement current in the region between the plates of the capacitor.

Displacement current is given by,

$i_d={ϵ}_o\frac{d{\varphi }_E}{dt}$ and $i_d=i_c$ at all instant.