A parallel-plate capacitor is filled with a dielectric material having resistivity and dielectric constant K . The capacitor is charged and disconnected from the charging source. It is then slowly discharged through the dielectric. Determine the time constant of the discharge, noting that it is independent of geometrical parameters such as the separation between the plates or the plate area.

Step-by-step solution

The capacitance of a parallel-plate capacitor filled with a dielectric of constant K is given by: C = K ₀ A d where A is the area of the plates and d is the separation between them. The resistance of the dielectric material between the plates is given by: R = d A where is the resistivity of the material. The time constant for the discharge of the capacitor through the dielectric is the product of its resistance and capacitance: = R C Substituting the expressions for R and C , we get: = ( d A ) ( K ₀ A d ) = ₀ K The