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:

In AC circuits, displacement current is equal to the conduction current, which is why Kirchhoff’s current law is still applicable in circuits with capacitors.

Answer 1

In an AC circuit with a parallel plate capacitor, the conduction current \( I_c \) is the current through the resistor or conducting path, while the displacement current \( I_d \) arises due to the changing electric field between the plates of the capacitor. The displacement current is defined as: \[ I_d = \epsilon_0 A \frac{dE}{dt} \] where \( A \) is the area of the plates, and \( \frac{dE}{dt} \) is the rate of change of the electric field. In a steady AC circuit, the conduction current and the displacement current are equal, ensuring that the total current remains continuous at all points in the circuit.