Question

You are given a $2\mu F$ parallel plate capacitor. How would you establish an instantaneous displacement current of
1 mA in the space between its plates?

Answer 1

Given,

$C=2\mu F=2\times {10}^{-6}F$
Displacement current, $i_D=1mA=1\times {10}^{-3}A$
Inside capacitor $i_C=0$
Charge at any time t on the capacitor plate

$q=CV$

$\Rightarrow \frac{dq}{dt}=C\frac{dV}{dt}$

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

Putting value
$1\times {10}^{-3}=2\times {10}^{-6}\frac{dV}{dt}$

$\frac{dV}{dt}=5\times {10}^2\frac{V}{s}$

Hence, applying a varying potential difference of $5\times {10}^2\frac{V}{s}$ would produce a displacement current of desired value.


Final Answer: Hence, applying a varying potential difference of $5\times {10}^2\frac{V}{s}$ would produce a displacement current of desired value.