A DC current does not go through the capacitor after the initial charging. Check the equation that describes the impedance in RC circuits when the frequency f decreases to zero (which is the case of any DC current). Explain qualitatively why an AC current can go through a capacitor, but a DC current cannot.

Explanation:

The equation for the impedance of and RC circuit is given as

Where frequency, capacitance

At ,  the impedance of the circuit becomes infinite and hence no current flows.

In the case of D.C. the Voltage across the capacitance does not change after full charging and remains equal and opposite to the D.C. Voltage across it and hence no current can flow through it. On the other hand, the Polarity of Voltage in Ac voltage keeps reversing per cycle and thereby makes the capacitor to discharge and charge again.

That's why AC current can go through a capacitor, but a DC current can't