A parallel plate capacitor with plate area A & plate separation d is filled with a dielectric material of dielectric constant given by`K=K_(0)(1+alphax).`. Calculate capacitance of system: (given `alpha d ltlt 1)`.

Options

A. `(AK in_(0))/(d) (1 + al)`
B. `(AK in_(0))/(d) (1 + (alpha l)/(2))`
C. `(A in_(0)k)/(d) (1 + ((alphal)/(2))^(2))`
D. `(A in_(0) K)/(d) (1 + (alpha^(2)l^(2))/(2))`

Answer

B

Explanation

`dc = (K in_(0) (A)/(l)dx)/(d)`
`C_(eq) = intdc = (K in_(0) A)/(ld) dx`
` = (in_(0)A)/(l d) int_(0)^(l) (1+ax)dx`
`= (K in _(0)A)/(ld) l + (alphal^(2)/(64)) = (K in_(0) A)/(d) (1+(alphal)/(2))`