The material filled between the plates of a parallel plate...

The material filled between the plates of a parallel plate capacitor has resistivity $200Ωm$ . The value of capacitance of the capacitor is $2pF$ . If a potential difference of $40V$ 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 $50$ )

Options

A $0.9mA$
B $9.0mA$
C $9.0\muA$
D $0.9\muA$

Correct answer

A. $0.9mA$

Step-by-step solution

The material filled between the plates of a parallel plate capacitor has resistivity 200Ωm . The value of capacitance

$ρ = 200Ωm$

$K = 50$

$C = \dfrac{{ϵ}_{0}KA}{d} = 2 \times {10}^{- 12}\text{F}$

$R = \dfrac{ρd}{A}$

$I = \dfrac{V}{R} = \dfrac{AV}{ρd} = \dfrac{V}{ρ} ⋅ \dfrac{C}{{ϵ}_{0}K} = \dfrac{40}{200} \times \dfrac{2 \times {10}^{- 12}}{8.85 \times {10}^{- 12} \times 50} = 0.9mA$

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