Two material having the dielectric constans `K_(1)` and `K_(2)` are filled between two parallel plates of a capacitor.
where area of each plate is `A` and the distance between the plates is `d`.
The capacitor of the capacitor is:

Options

A. `(A epsilon_(0)(K_(1) xx K_(2)))/(d(K_(1) + K_(2)))`
B. `(A epsilon_(0)(K_(1) - K_(2)))/(d)`
C. `(A epsilon_(0)(K_(1)K_(2)))/((K_(1) + K_(2)))`
D. `(A epsilon_(0)(K_(1) +K_(2)))/(d)`

Answer

D

Explanation

In each capacitor the area of the plate will br `(A)/(2)`.
In the given combination the arrengment is equivalent to two capacitor connected in parallel. Also in each capacitor the area of the plate will be `(A)/(2)`.
`:.` Equivalent capacitor `C'' = C_(1) + C_(2)`
`= (K_(1)epsilon_(0)A//2)/(d) + (K_(2)epsilon_(0)A//2)/(d) = ((K_(1) + K_(2))epsilon_(0)A)/(d)`