A parallel-plate capacitor is filled with a dielectric material...

The capacitance of a parallel-plate capacitor filled with a dielectric of constant $K$ is given by:

$C = \dfrac{K \varepsilon_0 A}{d}$

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:

$R = \dfrac{\rho d}{A}$

where $\rho$ is the resistivity of the material.

The time constant $\tau$ for the discharge of the capacitor through the dielectric is the product of its resistance and capacitance:

$\tau = R C$

Substituting the expressions for $R$ and $C$, we get:

\tau = \left( \dfrac{\rho d}{A} \right) \left(\dfrac{K \varepsilon_0 A}{d} \right)

$\tau = \varepsilon_0 \rho K$

The time constant is independent of the geometrical parameters $A$ and $d$.