The conduction current is same as displacement current in a circuit when the source is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → either a.c. or d.c.
The displacement current in a gap, \( i_d = \varepsilon_0\,d\phi_E/dt \), is what keeps the current continuous where no charge flows, for example between the plates of a capacitor. For a capacitor of plate area A,
\( \displaystyle i_d = \varepsilon_0 \frac{d}{dt}\left(\frac{q}{\varepsilon_0 A}\,A\right) = \frac{dq}{dt} = i_c \)
This result uses only the fact that charge is building up on the plates; it does not depend on the kind of source. With a.c. the capacitor charges and discharges continuously, and with d.c. the same equality holds while the capacitor is charging. In both cases the displacement current in the gap equals the conduction current in the wires.
Why the other options are incorrect
Option (1) a.c. only — Incorrect. The equality \( i_d = i_c \) is not limited to a.c.; it holds during the charging of a capacitor by a d.c. source as well.
Option (2) d.c. only — Incorrect. It holds for a.c. too, where it applies at every instant.
Option (4) neither d.c nor a.c. — Incorrect. The two currents are equal in both cases; this is the reason Maxwell introduced the displacement current.