Question

A capacitor is connected across a source providing time-dependent current. Explain how the total current at an instant is the sum of conduction current and displacement current in the circuit at that instant.

Answer 1

An I_c can flow through the lines that connect the plates in a capacitor circuit, but it can’t cross the vacuum or dielectric gap between them. The electric field between the plates changes, though, as the plates charge up. The shifting field makes a displacement current Id that is the same as I_c. With Maxwell’s Ampere Law, the total current I is:

I = I_c + I_d

Outside the plates, I_d = 0, so I = I_c. Between the plates, I_c = 0, so I = I_d. This ensures the current is continuous throughout the circuit.