A parallel plate capacitor is filled with dielectrics. What is capacitance?

Options

A. `(2K_(1)K_(2))/(K_(1) + K_(2))`
B. `(K_(1) K_(2))/(K_(1) + K_(2))`
C. `(2epsi_(0)A)/(d) ((K_(1) K_(2))/(K_(1) + K_(2)))`
D. `(2epsi_(0)A)/(d) ((2K_(1) + K_(2))/(2K_(1) K_(2)))`

Answer

C

Explanation

`C_(1)= (K_(1) epsi_(0)A)/(d//2), C_(2)= (K_(2)epsi_(0)A)/(d//2)`
`C_(1)= (2K_(1) epsi_(0)A)/(d), C_(2)= (2K_(2) epsi_(0)A)/(d)`
`(1)/(C_(eq))= (1)/(C_(1)) + (1)/(C_(2))`
`(1)/(C_(eq)) = (1)/((2K_(1) epsi_(0)A)/(d)) + (1)/((2K_(2) epsi_(0)A)/(d))`
`(1)/(C_(eq))= (d)/(2K_(1) epsi_(0)A) + (d)/(2K_(2) epsi_(0)A)`
`therefore (1)/(C_(eq)) = (d)/(2 epsi_(0)A) ((K_(1) + K_(2))/(K_(1) K_(2)))`
`C_(eq)= (2 epsi_(0)A)/(d) ((K_(1) K_(2))/(K_(1) + K_(2)))`