Question
When an ideal capacitor is charged by a dc battery, no current flows. However, when an ac source is used, the current flows continuously. How does one explain this, based on the concept of displacement current?
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Answer
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 $\text{i}_{c} =\frac{\text{dq}}{\text{dt}}$ keep on flowing in the connecting wires.
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. Displacement current id is given by id $ = \in_{0}\frac{\text{dq}_{E}}{\text{dt}}$ and is equal to the conduction current at all instants.
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. Displacement current id is given by id $ = \in_{0}\frac{\text{dq}_{E}}{\text{dt}}$ and is equal to the conduction current at all instants.
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