Question

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance 2.5µ F. The dielectric constant of the medium between the capacitor plates is 1. It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _______ Vs$^{-1}$.

Answer 1

100 Vs$^{-1}$

Answer 2

Given the capacitor current relation:

$$I_d = C \frac{dV}{dt}$$

Rearranging for $\frac{dV}{dt}$:

$$\frac{dV}{dt} = \frac{I_d}{C}$$

Substitute:

$$\frac{dV}{dt} = \frac{0.25 \times 10^{-3}\, \text{A}}{2.5 \times 10^{-6}\, \text{F}} = 100\, \text{V/s}$$