A parallel plate capacitor of plate area A and separation d is filled with two materials each of thickness `d/2` and dielectric constants `in_1` and `in_2` respectively. The equivalent capacitance will be

Options

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

Answer

C

Explanation

`1/(C_(eq))=(d//2)/(epsilon_(0)epsilon_(1)A)+(d//2)/(epsilon_(0)epsilon_(2)A) rArr C_(eq)=(2epsilon_(0)A)/D. (epsilon_(1)epsilon_(1))/((epsilon_(1)+epsilon_(1)))`