Question

The charge on a parallel plate capacitor varies as $q=q_0\cos \left(2\pi \nu t\right)$. The plates are very large and close to each other (area $=A$, separation $=d$). The displacement current through the capacitor is

• A. $2q_0\pi \nu \sin \left(\pi \nu t\right)$
• B. $-2q_0\pi \nu \sin \left(2\pi \nu t\right)$
• C. $2q_0\pi \sin \left(\pi \nu t\right)$
• D. $q_0\pi \nu \sin \left(2\pi \nu t\right)$

Answer 1

The correct option is B $-2q_0\pi \nu \sin \left(2\pi \nu t\right)$

We know that the displacement current $I_D$ and conduction current $I_C$ are related as,

$I_D=I_C$

$\Rightarrow I_D=\frac{dq}{dt}$

$\Rightarrow I_D=\frac{d}{dt}\left(q_0\cos 2\pi \nu t\right)=-2\pi q_0\nu \sin 2\pi \nu t$

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