In the figure a capacitor id filled with dielectric. The resultant capacitance is

Options

A. `(2epsilon_(0)A)/(d) [(1)/(k_(1)) + (1)/(k_(2)) + (1)/(k_(3))]`
B. `(epsilon_(0)A)/(d) [(1)/(k_(1)) + (1)/(k_(2)) + (1)/(k_(3))]`
C. `(2epsilon_(0)A)/(d) [k_(1) + k_(2) + k_(3)]`
D. None of these

Answer

D

Explanation

`C_(1) = (K_(1)epsilon_(0)(A)/(2))/(((d)/(2))) = (K_(1)epsilon_(0)A)/(d)`
`C_(2) = (K_(2)epsilon_(0)((A)/(2)))/(((d)/(2))) = (K_(2)epsilon_(0)A)/(d)` and `C_(3) = (K_(3)epsilon_(0)A)/(2d) = (K_(3)epsilon_(0)A)/(2d)`
Now, `C_(eq) = C_(3) + (C_(1)C_(2))/(C_(1) + C_(2)) = ((K_(3))/(2) + (K_(1)K_(2))/(K_(1) + K_(2))).(epsilon_(0)A)/(d)`