A parallel plate capacitor with air as the dielectric has capacitance C.A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure.The new capacitance will be

Options

A. `(K + 3)(C)/(4)`
B. `(K + 2) (C)/(4)`
C. `(K + 1)(C)/(4)`
D. `(KC)/(4)`

Answer

A

Explanation

The two condensers with K and with air are in parallel.With air, `C_(1) = (epsilon_(0))/(d)((3A)/(4)) = (3epsilon_(0)A)/(4d)`
With medium, `C_(2) = (epsilon_(0)K)/(d)((A)/(4)) = (epsilon_(0)AK)/(4d)`
`therefore C' = C_(1) + C_(2)`
or `C' = (3epsilon_(0)A)/(4d)+ (epsilon_(0)AK)/(4d) = (epsilon_(0)A)/(d) [3/4+K/4] = (C)/(4)(K+ 3)`
or `C' = C/4 (K + 3)`