Question

A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor. 

Answer 1

In Fig. conduction current is flowing in the wires, causes charge on the plates

So I_C = dq/dt .....(1)

Using Gauss’s Theorem, if one of the plate is inside the tiffin type Gaussian surface

 

Using Gauss’s Theorem, if one of the plate is inside the tiffin type Gaussian surface

ϕE = q/ε₀

From equation (2) and (3),
Both conduction current and displacement currents are equal.