MCQ
The potential difference between the plates of a parallel plate capacitor is changing at the rate of $10^6\, V/s$. If the capacitance is $2\,\mu F$, the displacement current in the dielectric of the capacitor will be.....$A$
  • A
    $1$
  • $2$
  • C
    $3$
  • D
    $4$

Answer

Correct option: B.
$2$
b
Displacement current is given by

$\mathrm{i}_{\mathrm{d}}=\varepsilon_{0} \frac{\partial \phi_{\mathrm{E}}}{\partial \mathrm{t}}$

where $\phi_{\mathrm{E}}$ is the electric flux given as $\phi_{\mathrm{E}}=\mathrm{EA}$ where $A$ is area of the capacitor plates and $E$ is the electric field between the plates.

So,  $\mathrm{i}_{\mathrm{d}}=\varepsilon_{0} \frac{\partial(\mathrm{EA})}{\partial \mathrm{t}}=\varepsilon_{0} \mathrm{A} \frac{\partial \mathrm{E}}{\partial \mathrm{t}}$

But $\mathrm{E}=\mathrm{V} / \mathrm{d}$ where $\mathrm{V}$ is the potential difference between the capacitor plates separated at $d$ distant apart.

So, $i_{d}=\frac{\varepsilon_{0} A}{d} \frac{\partial V}{\partial t}=C \frac{\partial V}{\partial t}$

where $\mathrm{C}$ is the capacity of the capacitor.

$\therefore $ $\mathrm{i}_{\mathrm{d}}=2 \times 10^{-6} \times 10^{6}=2 \mathrm{A}$

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