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When an ideal capacitor is charged by a ...

When an ideal capacitor is charged by a d.c. battery, no current flows. However, when an ac source is used, the current flows continously. How does one explain this, based on the concept of displacement current ?

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When an ideal capacitor is charged by a d.c. battery, charge flows (momentarily) till the capacitor gets fully charged. When an a.c. source is connected then conduction current `i_c =(dq)/(dt)` keeps on flowing dt 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 i, is given by
`i_d = epsi_0 = (dq_E)/(dt)`
and is equal to the conduction current at all instants.
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