A variable frequency a.c source is connected to a capacitor. How will the displacement current change with decrease in frequency?

The displacement current between the plates of a capacitor is given as,

Where, is the electric flux between the plates, which can be determined as ,

Where, E is the electric field between the plates and A is the area of of the plates of the capacitor.

For an a.c. source a variable electric field is set up between the plates. Let the field be given as,

Where is the frequency of the source. Now the electric flux will be

Therefore, the amplitude of displacement current varies, directly with frequency and hence the displacement current will decrease with decreasing frequency.