Question

Potential difference across plates of a capacitor $6\mu F$ is changing at the rate of $72V{s}^{-1}$. Displacement current at that instant will be

• A. $1.2A$
• B. 12 x ${10}^{-6}$A
• C. 7.2 x ${10}^{-6}$A
• D. none

Answer 1

The correct option is D none

Given,

$C=\frac{A{\epsilon }_0}{d}=6\mu C$

$\frac{dV}{dt}=72V/s$

Displacement current, $I_D={\epsilon }_0\frac{d{\varphi }_E}{dt}$

$I_D={\epsilon }_0\frac{d\left(EA\right)}{dt}$

$I_D={\epsilon }_{0}A\frac{d\left(V/d\right)}{dt}$

$I_D=\frac{{\epsilon }_{0}A}{d}.\frac{dV}{dt}$

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

$I_D=6\times {10}^{-6}\times 72$

$I_D=432\times {10}^{-6}A$

The correct option is D.