A parallel plate capacitor with vacuum between its plates has capacitance `C`. A slabe of dielectric constant `K` and having the same thickness as the separation between the plates is introduced so as to fill `1//3^(rd)` of the capacitor as shown in the figure. the new capacitance will be

Options

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

Answer

B

Explanation

`C_(1)=(2Ain_(0))/(3d),C_(2)=(Kain_(0))/(3d)`
`C_(1)` and `C_(2)` are in parallel (check polarity)
`C_(eq)=C_(1)+C_(2)=(Ain_(0))/(d)((2)/(3)+(K)/(3))=((2+K))/(3)(Ain_(0))/(d)`
`=(K+2)(c)/(3)`