Question

To establish an instantaneous displacement current of / ampere in the space between the plates of a parallel plate capacitor of $\frac{1}{2}$ farad , the value of $\frac{dV}{dt}$ is:

Answer 1

Given, $Current=1A,distance=\frac{1}{2}frad$

So, $I_D={\epsilon }_{0}d\frac{{\varphi }_E}{dt}=\frac{{\epsilon }_{0}d\left(EA\right)}{dt}={\epsilon }_{0}A\frac{d}{dt}={\epsilon }_{0}A\frac{d\left(\frac{v}{d}\right)}{dt}={\epsilon }_0\frac{A}{d}\times \frac{dv}{dt}=\frac{cdv}{dt}$

$\Rightarrow \frac{dv}{dt}=\frac{I_D}{2C}$