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  4. The material filled between the plates of a parallel plate capacitor has resistivity 200 Ω 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 permitivity of material is 50 )

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Q. 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 permitivity of material is $50$ )

JEE MainJEE Main 2021Electrostatic Potential and Capacitance

Solution:

$\rho=200 \,\Omega m$
$C =2 \times 10^{-12} F$
$V =40 \,V$
$K =56$
$i =\frac{ q }{\rho k \varepsilon_{0}}=\frac{ q _{0}}{\rho k \varepsilon_{0}} e ^{-\frac{ t }{\rho k \varepsilon_{0}}}$
$i _{\max }=\frac{2 \times 10^{-12} \times 40}{200 \times 50 \times 8.85 \times 10^{-12}}$
$=\frac{80}{10^{4} \times 8.85}=903 \,\mu A =0.9\, mA$