Question

Capacity of a parallel plate air condenser is 2 μF and voltage between the plates is changing at the rate of 3 V/s. The displacement current in the capacitor is

• A. 8 μA
• B. 2 μA
• C. 6 μA
• D. 4 μA

Hint:

The displacement current in a capacitor is given by \( I_d = C \frac{dV}{dt} \), where \( C \) is the capacitance and \( \frac{dV}{dt} \) is the rate of change of voltage.

Answer 1

The Correct Option is C

Step 1: Understanding displacement current.
The displacement current \( I_d \) in a capacitor is given by the formula: \[ I_d = C \frac{dV}{dt} \] where \( C \) is the capacitance and \( \frac{dV}{dt} \) is the rate of change of voltage across the plates. Step 2: Given values.
We are given: - Capacitance \( C = 2 \, \mu F = 2 \times 10^{-6} \, F \) - Rate of change of voltage \( \frac{dV}{dt} = 3 \, V/s \) Step 3: Calculating the displacement current.
Substitute the given values into the formula for displacement current: \[ I_d = (2 \times 10^{-6}) \times 3 = 6 \times 10^{-6} \, A = 6 \, \mu A \] Step 4: Conclusion.
The displacement current in the capacitor is 6 μA, which corresponds to option (C).