Question

A parallel plate capacitor is charged by connecting it to a battery through a resistor. If I is the current in the circuit, then in the gap between the plates :

• A. there is no current.
• B. displacement current of magnitude equal to 1 flows in the same direction as 1.
• C. displacement current of magnitude equal to 1 flows in a direction opposite to that of 1.
• D. displacement current of magnitude greater than 1 flows but can be in any direction.

Answer 1

The Correct Option is B

Step 1: Recall the Concept of Displacement Current

Displacement current is given by:

$$ I_d = \epsilon_0 \frac{d\Phi_E}{dt} $$

Where:

\( I_d \) = Displacement current

\( \epsilon_0 \) = Permittivity of free space

\( \Phi_E \) = Electric flux

\( t \) = Time

Step 2: Relate to Conduction Current

In a capacitor circuit, the displacement current in the gap is equal in magnitude to the conduction current in the connecting wires. This ensures continuity of current in the circuit.

Step 3: Conclusion

The displacement current flows in the same direction as the conduction current and has the same magnitude.