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A parallel- plate capacitor, fileld with...

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)` ?

Text Solution

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When slab is removed , the potential difference across capatitor increases to `kV_0`
`CV_0-kCV_0e^(t/tau) as q_0=KCV_0`
`1/k=e^(t/tau) rArr =e^(t/tau), therefore ln =t/tau rArr t=taulnk`
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