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Question

A metal plate is introduced between the plates of a charged parallel plate capacitor. what is its effect on the capacitance of the capacitor ?

Solution
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By introducing the metal plate between the plates of the charged capacitor, the capacitance of the capacitor increases.
Reason: It $$ t $$ is thickness of metal plate, then
$$ C=\frac{\varepsilon _0A}{d-t\left( 1-\frac { 1 }{ k } \right) }$$
For metal plate $$ K=\infty,C=\frac{\varepsilon_0A}{d-t} $$
Obviously, the effective separation between plates is decreased from $$ d $$ to $$ (d-t) $$

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