A parallel - plate capacitor, filled with a dielectric of dielectric constant k, is charged to a potential `V_(0)`. It is now disconnected from the cell and the slab is removed. If it now discharges, with time constant `tau`, through a resistance, then find time after which the potential difference across it will be `V_(0)`?

Explanation

When the slab is removed , the potential difference across capacitor increases to `k V_0`
`CV_0 = kCV_0 e^(-t/tau) as q_0 = KCV_0`
`1/k = e^(-t/tau) therefore ln k = t/tau rArr t= tau ln k `