parallel plate capacitor has capacitance `C` when no dielectric between thw plates. Now a slab of dielectric constant `K`, having 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

`C_(0) = (in_(0) A)/(d)`
When one fourth of capacitors is filled with dielectric fo constant `K`. Fig, then
`C_(1) = (K in_(0) A//4)/(d)`
and `C_(2) = (in_(0) 3A//4)/(d)` ,
which are in parallel
`:. C_(p) = C_(1) + C_(2) = (K in_(0) A)/(4d) + (3 in_(0) A)/(4d)`
`= (K +3) (in_(0)A)/(4d) = (K + 3) (C )/(4)`