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

Explanation

To show that the displacement current inside a capacitor is the same as the current charging the capacitor, we can follow these steps:

### Step 1: Understand the Circuit
We have a capacitor made of two parallel plates, each with an area \( A \) and separated by a distance \( d \). The capacitor is connected to an alternating current (AC) source, which can be represented as \( E(t) = E_0 \sin(\omega t) \).

### Step 2: Relate Charge to Voltage
The charge \( q \) on the capacitor is related to the voltage \( V \) across it by the equation:
\[
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