The voltage between the plates of a parallel plate capacitor of capacity 1 ~F is changing at the rate of 4 ~V / s . the displacement current in the capacitor is

Step-by-step solution

The displacement current I_d in a capacitor arises from the time-varying electric field between the plates and equals the conduction current in the connecting wires. It is defined as the derivative of charge with respect to time: I_d = dQ dt . For a parallel plate capacitor, Q = CV , where C is the capacitance and V is the voltage. Substituting gives I_d = d dt (CV) . Since C is constant, I_d = C dV dt . Given C = 1 10⁻⁶ , F and dV dt = 4 , V/s , the displacement current is I_d = (1 10⁻⁶) 4 = 4 10⁻⁶ , A = 4 , A . T