Question

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

Answer 1

Given, for variable frequency a.c. source, electric field between the plates,
$E=E_0\sin 2\pi vt$
Displacement current between the plates,
$I_d={ϵ}_0\frac{d{\varphi }_E}{dt}$

$I_d={ϵ}_0\frac{d}{dt}\left(EA\right)$

$I_d={ϵ}_{0}A\frac{d}{dt}\left(E_0\sin 2\pi vt\right)$

$I_d=2\pi v{ϵ}_{0}A{E}_0\cos 2\pi vt$

As frequency decreases, displacement current will also decrease.

Final answer: Decreases.