The material filled between the plates of a parallel plate capacitor… | JEE Main 2021 (26 Aug, Shift 1)

Q29JEE Main 2021 · 26 AUG · SHIFT 1Medium

Capacitors in DC Circuits & RC

The material filled between the plates of a parallel plate capacitor has resistivity 200 $\Omega$ m. The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permittivity of material is 50)

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Answer: (c)

For a filled capacitor $RC = \rho\varepsilon = \rho K\varepsilon_0$ .
$RC = 200\times50\times8.85\times10^{-12} = 8.85\times10^{-8}\text{ s}$ , so $R = \dfrac{8.85\times10^{-8}}{2\times10^{-12}} = 4.4\times10^{4}\ \Omega$ .
$I = \dfrac{V}{R} = \dfrac{40}{4.4\times10^{4}} \approx 0.9\times10^{-3}\text{ A}$
So the answer is (c) 0.9 mA.

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