The space between the plates of a parallel-plate capacitor is filled with a dielectric of constant and resistivity . (a) Show that the time

The space between the plates of a parallel-plate capacitor is filled with a dielectric of constant κρ and resistivity ρ.

(a) Show that the time constant for the decrease of charge on the plates is τ = ε₀κρ

(b) If the dielectric is mica, for which κ = 5.0 and ρ = 9 × 10¹³ Ω · m, find the time it takes for the charge to decrease to 1/e² ≈ 14% of its initial value.