A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is $7 \times 10^{8}$ V/s then the integer value of the distance between the parallel plates is –
$(Take, ϵ_{0} = 9 \times 10^{- 12} \frac{F}{m}, π = \frac{22}{7})________μ m .$

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answer is 1320.

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Detailed Solution

$\begin{aligned} Q = V C = \frac{i t}{(\frac{ϵ_{0} A}{d})} = \frac{i t d}{ϵ_{0} (π r^{2})} \\ i = \frac{d Q}{d t} = C \frac{d V}{d t} = \frac{A ε_{0}}{d} \frac{d V}{d t} \\ \Rightarrow d = \frac{ϵ_{0} (π r^{2})}{i} (\frac{d V}{d t}) \\ = \frac{(9 \times 10^{- 12}) (\frac{22}{7}) (0.1)^{2}}{0.15} (7 \times 10^{8}) m \\ d = 1320 μ m \end{aligned}$

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