A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor but has the thickness d/2, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor.

Explanation

We know that capacitance of a parallel plate capacitor is given as `C = (epsi_0A)/d` where A is area of each plate and d is the distance between them.
If a dielectric slab of dielectric constant K and area A but of thickness t (t `C = (epsi_0A)/(d - t ((K-1)/K))`
In present case t = d/2. Hence capacitance of the capacitor will be
`C = (epsi_0A)/(d - d/2((K-1)/K))=(2 epsi_0A)/(2d-d((K-1)/K)) =(2epsi_0A)/(d(1 +1/K))`