A parallel- plate capacitor, fileld with a dielectric of dielectric consatnt `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 slab is removed, the potential difference across capacitor increases to `kV_(0)`
`CV_(0) = kCV_(0) e^((t)/(tau))` as `q_(0) = KCV_(0)`
`(1)/(k) = e^((t)/(tau)) rArr k= e^((t)/(tau))`, `:. ln = (t)/(tau) rArr = tau l nk`