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>>Effects of Dielectrics in Capacitors
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Question

A slab of material of dielectric constant K has the same area as the plates of a parallel plate capacitor but has thickness $3 d / 4$ , where d is the distance between plates. How is the capacitors changed when the slab is inserted between the plates?

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Solution

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$C = \frac{A ϵ _{0}}{d}$

$C^{'} = \frac{A ϵ _{0}}{d - t + \frac{t}{k}}$

Put $t = \frac{3 d}{4}$ ;

$C^{'} = \frac{4 k}{3 + k} . \frac{A ϵ _{0}}{d}$

$C^{'} = \frac{4 k}{3 + k} . C$

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