Question

A parallel plate capacitor of plate separation $2\text{mm}$ is connected to a $DC$ source. If the plate area is $60{\text{cm}}^2$, what is the magnitude of displacement current at an instant, when the potential difference across it is varying at the rate of $4\times {10}^6\text{V/s}$

• A. $1.062\text{Amp}$
• B. $1.062\times {10}^{-2}\text{Amp}$
• C. $1.062\times {10}^{-3}\text{Amp}$
• D. $1.062\times {10}^{-4}\text{Amp}$

Answer 1

The correct option is D $1.062\times {10}^{-4}\text{Amp}$

$i_d=C\left(\frac{dV}{dt}\right)$

$=\frac{A{ϵ}_o}{d}\frac{dV}{dt}$

$=\frac{60\times {10}^{-4}\times 8.85\times {10}^{-12}}{2\times {10}^{-3}}\times 4\times {10}^6$

$=1.062\times {10}^{-4}\text{Amp}$

Hence, $\left(D\right)$ is the correct answer.