Find the expression for the capacitance of a parallel plate capacitor of area A and plate separation d if

i) a dielectric slab of thickness t, and

ii) a metllic slab of thicknes t

(where t<d) are introduced one by one between the platesof the capacitor. In which case would the capacitance be more and why?

Refer the following parallel plate capacitor inserted with dielectric slab in the gap.

When there is vacuum the the capacitance of the parallel plate capacitor is,

'

Due to polarization of the dielectric the electric field is reduces to E from E_{0}.

So the potential difference between the plates is,

Now if the inserted slab is conducting then electric field inside slab will be zero.

Thus,

So by inserting a conducting slab capacitance increases as the effective separation between the plates decreases.

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