Question

A parallel plate condenser of capacity $10\mu F$ is connected to an A.C. supply voltage $e=4\sin \left(100\pi t\right)$. The maximum displacement current:

• A. $4\pi \mu A$
• B. $4\pi mA$
• C. $2.8\pi \mu A$
• D. $2\pi \mu A$

Answer 1

Answer: (B)

$4\pi mA$

Displacement current, $i_d={\epsilon }_{\circ }A\frac{dE}{dt}$
where, $A$ is area and $E$ is electric field
$\begin{array}{c}E=\frac{e}{d}=\frac{4\sin \left(100\pi t\right)}{d}\\ i_d={\epsilon }_{\circ }A\times \frac{1}{d}\left[\frac{d}{dt}\left(4\sin 100\pi t\right)\right]\\ =\frac{{\epsilon }_{\circ }A}{d}.4\left(cos100\pi t\right)\times 100\pi \\ =C.400\pi .cos100\pi t\\ {\left(i_d\right)}_{max}=\left(10\times {10}^{-6}\right)\times 400\pi A\\ =4\pi \times {10}^{-3}A=4\pi mA\end{array}$