Question

A parallel-plate capacitor is filled with a dielectric material of resistivity rho and dielectric constant K. The capacitor is charged and disconnected from the charging source. The capacitor is slowly discharged through the dielectric. Show that the time constant of the discharge is independent of all geometrical parameters like the plate area or separation between the plates. Find this time constant.

Answer 1

A parallel-plate capacitor is filled with a dielectric material of resistivity rho and dielectric constant K. The capacitor is charged and disconnected from the charging source. The capacitor is slowly discharged through the dielectric. Show that the time constant of the discharge is independent of all geometrical parameters like the plate area or separation between the plates.

Answer 2

As mentioned in the question, the discharge’s time constant is independent of all geometrical parameters like the separation between the plates and the plate area. The time constant is ρKε0.

Explanation:

• A parallel plate capacitor’s capacitance is C = Kε0Ad.
• The dielectric material’s resistance is denoted as R. So, R = ρdA
• The time constant is denoted as τ. So, τ = RC = ρKε0.
• The time constant is not dependent on the plate area or separation among the plates.