Question

Explain why the reactance provided by a capacitor to an alternating current decreases with increasing frequency?

Answer 1

A capacitor does not allow flow of direct current through it as the resistance across the gap is infinite.
The current is zero in a DC capacitive circuit, which corresponds to infinite reactance. Since $X_C$ is inversely proportional to frequency, when an alternating voltage is applied across the capacitor plates, the plates are alternately charged and discharged. The current through the capacitor is a result of this charging voltage (or charge).

Thus, a capacitor will pass more current through it if the voltage is changing at a faster rate, i.e., if the frequency of supply is higher.
This implies that the reactance offered by a capacitor is less with increasing frequency.
Capacitors tend to pass high-frequency current and block low-frequency currents and DC.