Question

A parallel plate capacitor is charged by an ac source. Show that the sum of conduction current \( I_c \) and the displacement current \( I_d \) has the same value at all points of the circuit.

Hint:

The displacement current in a capacitor is analogous to the conduction current, and both are equal in magnitude in an ac circuit.

Answer 1

The conduction current \( I_c \) in a parallel plate capacitor flows through the plates. The displacement current \( I_d \) is associated with the changing electric field between the plates. The total current \( I \) is the sum of these two: \[ I = I_c + I_d \]. For a capacitor, the conduction current is defined as \( I_c = \frac{Q}{t} \), where \( Q \) is the charge. The displacement current is proportional to the rate of change of the electric field \( E \) between the plates: \( I_d = \epsilon_0 A \frac{dE}{dt} \), with \( A \) being the plate area. Given that the displacement current is electrically equivalent to the conduction current, \( I_c = I_d \). Consequently, the total current, formed by the sum of conduction and displacement currents, remains constant throughout the circuit.