Question

The space between the plates orf a parallel plate capacitor is completely filled with a meterail of resistaivity `2xx10^(11) Omegam` and dielectric constant 6. Capacity of the capacitor with the given dielectric medium between the paltes is 20uF. Find the leakage current if a potential difference 2500 V is applied across the capacitor.

Answer 1

Charge on the capacitor,
`Q = CV = 20xx10^(-19) xx2500 = 5xx10^(-5)C`
Surface charge density is `sigma_s = (A)/(Q)` [A is the plate area.]
Electric field strength between the plates is `E = (sigma_(s))/(K epsilon_0) = (Q)/(Kaepsilon_0)`
Using `J = simgaE = (E )/(rho)`
[Here `simga` is the conducitivity and `rho` is the resistivity.]
Current density is `J = Q//KA epsion_0rho` and current is
`JA = (Q)/(Kepsilonrho) =(5xx10^(-5))/(6xx(8.85xx10^(-22))xx(2xx10^(11))`
`=4.7xx10^(-6) A = 4.7muA`