Space between the plates of a parallel plate capacitor is filled with a dielectric whose dielectric constant varies with distance as per the relation: `K(X)=K_(0)+lambdaX`,
(`lambda=` constant, `K_(0)=` constant, X is perpendicular distance from one plate to a point inside dielectric). The capacitance `C_(1)` of this capacitor, would be related to its vacuum capacitance `C_(0)` per the relation (d = plate separation):

Options

A. `C=(lamda)/( d. In ( 1+k_0 lamda d))C_0`
B. `C=( lamda d )/( In ( 1 + lamda d // K_0))C_0`
C. `C=(lamda)/(d. In (1+ K_0 // lamda d)) C_0`
D. `C= (lamda d )/( In ( 1+ K-0 lamda d))C_0`

Answer

B