Question

The material filled between the plates of a parallel plate capacitor has a resistivity of 200Ωm. The value of the capacitance of the capacitor is 2 pF. 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 a material is 50.)

Options

• 9.0 µA

• 0.9 µA

• 9.0 mA

• 0.9 mA

Answer 1

The material filled between the plates of a parallel plate capacitor has a resistivity of 2000Ωm. The value of the capacitance of the capacitor is 2 pF. 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 0.9 mA.

Explanation:

When voltage is given to a capacitor, a tiny current leaks through the capacitor.

Given, ρ = 200 Ωm, C = 2 × 10^-12F, V = 40 V, k = 50

current leakage as a function of time,

`i(f) = i_0e^{(-t)/tau}`  .....(i)

Here, `i_0 = q_0/(rhokε_0)` for maximum current.

Add to the equation (i),

`i = (CV_0)/(rhokε_0)e^{-t"/"kε_0rho}`

`i_"leakage" = (CV_0)/(rhokε_0)` as t → ∞

= `(2 xx 10^-12 xx 40)/(200 xx 50 xx 8.85 xx 10^-12) = 903 muA` = 0.9 mA