Question

The conduction current is same as displacement current in a circuit when the source is

• A. a.c. only
• B. d.c. only
• C. either a.c. or d.c.
• D. neither d.c nor a.c.

Hint:

Displacement current equals the rate of charge build-up on the plates, whatever the source.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Maxwell added the displacement current \(I_d = \varepsilon_0 \frac{d\Phi_E}{dt}\) so that the total current stays continuous across a capacitor gap.

Step 2: Key Idea:
Between the plates there is no conduction current, but the electric field changes. Whenever charge flows in the wires, the field between the plates changes at the matching rate, so \(I_d = I_c\).

Step 3: Apply to an a.c. source:
With an a.c. source the capacitor charges and discharges all the time. The conduction current in the wires equals the displacement current in the gap at every instant.

Step 4: Apply to a d.c. source:
With a d.c. source the capacitor charges while the current flows in the wires. During this time the conduction current again equals the displacement current. After full charge both are zero, so they are still equal.

Step 5: Check the options:
The equality does not depend on the type of source, so it holds for a.c. and for d.c. Options 1 and 2 wrongly restrict it to one type. Option 4 is false because they are equal in both cases.

Final Answer:
The two currents match for either kind of source. \[ \boxed{\text{Option 3: either a.c. or d.c.}} \]