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

Explanation

Total potential difference between the plates
`V = E_(0)(d-t)+Et" "(t=(d)/(2))`
`V = E_(0)(d-(d)/(2))+E(d)/(2)" "E_(0)(d)/(2)+(E_(0))/(K).(d)/(2)=E_(0)(d)/(2)(1+(1)/(K))=E_(0)(q)/(A epsilon_(0))(d)/(2)(1+(1)/(K))`
As, `C = (q)/(V)=(q)/((q)/(A epsilon_(0))(d)/(2)(1+(1)/(K)))=(2 A epsilon_(0))/(d(1+(1)/(K))) rArr C = (2 K epsilon_(0)A)/(d(K+1))`.