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1) Theoretical approach

In the case of AC voltage

1. When AC voltage is connected with a capacitor, one plate of the capacitor gets charged positively and the other gets negatively charged.
2. Later when the direction of AC current changes, the capacitor will change its direction, and thus will get discharged.
3. This process continues in the case of AC voltage.

In the case of DC voltage

1. When DC voltage is connected with the capacitor, one plate of the capacitor gets charged positively and the other gets negatively charged.
2. When one plate is completely positive charged and the other is negatively charged, the process stops. The capacitor is saturated and the current flow stops.
3. Further, if DC voltage is increased, the capacitor will get damaged.

2) Mathematical approach

The reactance of the capacitor is given by the formula, X_C = 1/2πfC. Where X_C is the reactance, f is the frequency and C is the capacitance value.

The reactance of capacitor during DC

Since f = 0 in the case of a DC supply. X_C = 1/0 = infinity. The reactance is infinite hence no current passes through the circuit. That’s how a capacitor blocks DC.