Chapter 27, Problem 27.78AP

The dielectric material between the plates of a parallel-plate capacitor always has some nonzero conductivity σ. Let A represent the area of each plate and d the distance between them. Let κ represent the dielectric constant of the material. (a) Show that the resistance R and the capacitance C of the capacitor are related by

$RC=\frac{\kappa {ϵ}_0}{\sigma }$

(b) Find the resistance between the plates of a 14.0-nF capacitor with a fused quartz dielectric.