A parallel-plate capacitor is filled with a delectric meterial having resistivity`(rho)`and dielectric constant K.The capcitor 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 gepmetrical parameters like the plate area or separation between the plates. Find this time constant.

Explanation

To solve the problem, we need to derive the time constant for the discharge of a parallel-plate capacitor filled with a dielectric material. Let's go through the steps systematically.

### Step 1: Understand the Capacitor's Charge Equation
When the capacitor is charged and then disconnected from the charging source, the charge \( Q \) on the capacitor at any time \( t \) during discharge can be expressed as:
\[ Q(t) = Q_0 e^{-t/(RC)} \]
where \( Q_0 \) is the initial charge, \( R \) is the resistance through which the capacitor discharges, and \( C \) is the capacitance of the capacitor.
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