Question: 42. 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 :
(1) there is no current.
(2) displacement current of magnitude equal to I flows in the same direction as I.
(3) displacement current of magnitude equal to I flows in a direction opposite to that of I.
(4) displacement current of magnitude greater than I flows but can be in any direction.
Answer: Option (2)
Explanation:
When a capacitor is being charged, conduction current I flows through the connecting wires and the resistor.
Inside the gap between the capacitor plates, there is no flow of free charges.
However, the electric field between the plates changes with time during charging.
According to Maxwell’s theory, a time-varying electric field gives rise to a displacement current.
The displacement current is given by
I_d = \varepsilon_0 \frac{d\Phi_E}{dt},
where \Phi_E is the electric flux between the plates.
For a charging capacitor, the rate of change of electric flux is such that the displacement current between the plates is equal in magnitude to the conduction current in the external circuit.
The direction of displacement current is the same as the direction of the conduction current in the circuit.
Thus, in the gap between the plates, a displacement current of magnitude equal to I flows in the same direction as I,
which corresponds to option (2).