A parallel plate air capacitor has capacitance C. Now half of the space is filled with a dielectric material with dielectric constant K as shown in figure. The new capacitance is C'. Then

(1) `C'= (C )/(2) [ 1+K]` (2)` C' = C[1+K]`
(3) `C' = C[1+(K)/(2)]`
(4)` C' = C[(1)/(2) +K]`

Explanation

Answer (1)
`C_(AB)= C_(0)+C _(med.)`
`= (epsilon_(0)(A)/(2))/(d)+ (epsilon_(0)K(A)/(2))/(d)`
`= (epsilon_(0)A)/(2d) [1+K]`
`C_(AB) = (C)/(2) (1+K)`