To establish an instantaneous current of $2 \mathrm{~A}$ through a $1 \mu \mathrm{F}$ capacitor ; the…

To establish an instantaneous current of $2 \mathrm{~A}$ through a $1 \mu \mathrm{F}$ capacitor ; the potential difference across the capacitor plates should be changed at the rate of:
  1. $2 \times 10^4 \mathrm{~V} / \mathrm{s}$
  2. $4 \times 10^6 \mathrm{~V} / \mathrm{s}$
  3. $2 \times 10^6 \mathrm{~V} / \mathrm{s}$
  4. $4 \times 10^4 \mathrm{~V} / \mathrm{s}$

Solution

As, C $=\frac{\mathrm{Q}}{\mathrm{V}}=\frac{\mathrm{It}}{\mathrm{V}}$ $ \begin{aligned} & \Rightarrow \frac{\mathrm{V}}{\mathrm{t}}=\frac{\mathrm{I}}{\mathrm{C}}=\frac{2}{1 \times 10^{-6}} \\ & =2 \times 10^6 \mathrm{~V} / \mathrm{s} \end{aligned} $

Asked in: JEE Main 2013 (22 Apr Online)

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