Question

A variable frequency AC source is connected to a capacitor. Will the displacement current increases or decreases with increase in frequency.

Answer 1

the resistance of a capacitor (capacitive reactance ) varies inversely with frequency. so if frequency increases , resistance decreases and so the current increases. and vice versa.
Xc= 1 /2πfC
f is the frequency and C is the capacitance of the capacitor

Answer 2

Xc = capacitive or reactive impedance (resistance ) = 1/jωC = -j/ωC
| Z | = | Xc| = (ωC)⁻¹

Current i (rms) = V_rms / Z = V_rms * (ωC) = V_rms * 2πC  * f

So as frequency increases, current increases.  Capacitor is an open circuit for DC (0 frequency) and near short circuit for a large frequency.  So its impedance reduces as frequency increases.