When an ideal capacitor is charged by dc battery, charge flows (momentarily) till the capacitor gets fully charged.
When an ac source is connected then conduction current ic = dq/dt keep on flowing 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 causes the electric flux to change and gives rise to a displacement current in the region between the plates of the capacitor.
As we know, displacement current
