Question

A leaky parallel plate capacitor is filled completely with a material having dielectric constant `K = 5` and electrical conductivity `sigma= 7.4 xx 10^-12 Omega^-1 m^-1`. If the charge on the capacitor at the instant `t = 0` is `q_0 = 8.55 muC`, then calculate the leakage current at the instant `t = 12 s`.

Answer 1

Correct Answer - A::C
`tau_C=CR=((Kepsilon_0A)/d)((rhod)/A)=Kepsilon_0rho`
`5xx8.86xx10^-12/(7.4xx10^-12)~~6s`
Initial current
`i_0=(q_0/C)/r=q_0/(CR)=q_0/tau_C=8.55/6=1.425muA`
now, current as function ofi the `i=i_0e^(-t/tau_C)`
or `i=(1.425)e^(-12/6)=0.193muA`