For a capacitor connected in a circuit, the displacement current betw…

The correct answer is Option (3) → Both A.C. and D.C.

By Maxwell’s generalisation, the total current is the sum of the conduction current \( i_c \) and the displacement current \( i_d=\varepsilon_0\,d\Phi_E/dt \). In the wires there is only conduction current, and between the plates only displacement current.

Option (1) A.C. only — Incorrect. The equality also holds while a dc source charges the capacitor. The current in the wires then changes with time. The growing field between the plates gives a displacement current equal to it.

Option (2) D.C. only — Incorrect. With an ac source the plates are charged and discharged continuously, and at every instant the changing electric flux between them gives \( i_d=i \).

Option (3) Both A.C. and D.C. — Correct. The charge on the plates changes only through the current in the wires. So the changing electric flux between the plates always gives \( i_d=i \). With ac this holds at every instant. With dc it holds while the capacitor charges; once it is fully charged, both currents are zero.

Option (4) Neither A.C. nor D.C. — Incorrect. The displacement current makes the total current the same through every surface bounded by the same loop. So the current between the plates always matches the current in the wires.

NCERT (2026-27):
Displacement Current – “… In explicit terms, this means that outside the capacitor plates, we have only conduction current i_c = i, and no displacement current, i.e., i_d = 0. On the other hand, inside the capacitor, there is no conduction current, i.e., i_c = 0, and there is only displacement current, so that i_d = i.”