To establish an instantaneous displacement current of 2 ,A in the… - Vidyadip

MCQ

To establish an instantaneous displacement current of $2\,A$ in the space between two parallel plates of $1\,\mu F$ capacitor, the potential difference across the capacitor plates will have to be changed at the rate of

A
$4\,\times 10^4\,\,V/s$
B
$4\,\times 10^6\,\,V/s$
C
$2\,\times 10^4\,\,V/s$
✓
$2\,\times 10^6\,\,V/s$

✓

Answer

Correct option: D.

$2\,\times 10^6\,\,V/s$

d
$\mathrm{I}_{\mathrm{D}}=\varepsilon_{\circ} \frac{\mathrm{d} \phi_{\mathrm{E}}}{\mathrm{dt}}=\varepsilon_{\circ} \frac{\mathrm{d}}{\mathrm{dt}}(\mathrm{EA})=\varepsilon_{\mathrm{o}} \mathrm{A} \frac{\mathrm{d}}{\mathrm{dt}}\left(\frac{\mathrm{V}}{\mathrm{d}}\right)$

or $\mathrm{I}_{\mathrm{D}}=\frac{\varepsilon_{\mathrm{o}} \mathrm{A}}{\mathrm{d}} \frac{\mathrm{dV}}{\mathrm{dt}}=\mathrm{C} \frac{\mathrm{d} \mathrm{V}}{\mathrm{dt}}$

$\therefore \quad \frac{\mathrm{d} \mathrm{V}}{\mathrm{dt}}=\frac{\mathrm{I}_{\mathrm{D}}}{\mathrm{C}}=\frac{2}{10^{-6}}=2 \times 10^{6} \mathrm{V} / \mathrm{s}$

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