A parallel plate air capacitor has capacitance C. Half of space between the plates is filled with dielectric of dielectric constant K as shown in figure. The new capacitance is C' . Then

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

Explanation

Answer (2)
`(1)/(C_(AB))= (1)/(((epsilon_(0)KA)/(d/2)))+ (1)/((epsilon_(0)A)/(d/2))`
`implies (1)/(C_(AB))= (d)/( 2epsilon_(0)A) [(1)/(K) +1]`
`implies (1)/(C_(AB))= (d)/(2 epsilon_(0)A) [ (1+K)/(K)]`

`implies C_(AB) =(2epsilon_(0)A)/(d) [(K)/(1+K)]`
`= 2C [ (K)/(1+K)]`
`C_(AB) = C((2K)/(1+K))`