Capacitors

JEE Main level, numerical answer, medium

123 of 180

Question 123 of 180

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 7×108 V/s7 \times 10^8 \mathrm{~V} / \mathrm{s} then the integer value of the distance between the parallel plates is (\left(\right. Take, ϵ0=9×10−12 F m,π=227)\left.\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right) ________ μm\mu \mathrm{m}.

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Answer: 1320

\begin{aligned} & Q=c V \\ & V=\frac{Q}{c}=\frac{i t}{\left(\frac{\varepsilon_0 A}{d}\right)} \\ & d=\frac{\varepsilon_0 \pi r^2}{i}\left(\frac{v}{t}\right) \end{aligned}$ Putting values $\begin{aligned} d & =\frac{9 \times 10^{-12} \times \frac{22}{7} \times(0.1)^2}{0.15} \times\left(7 \times 10^8\right) \\ & =1320 \mu \mathrm{~m} \end{aligned}

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