From the figure find the capacitance of the capacitor ?

Options

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

Answer

B

Explanation

The given capacitor can be viewed as a series combination of two capacitors `C_(1) and C_(2)` where
`C_(1)=((epsi_(0)K_(1)A//2))/(d)," "C_(2)=((epsi_(0)K_(2)A//2))/(d)`
where d is the separation between the plates, `therefore ` The effective capacitance
`C=(C_(1)C_(2))/(C_(1)+C_(2))`
`((epsi_(0)K_(1)A//2)/(d)xx(epsi_(0)K_(2)A//2)/(d))/((epsi_(0)K_(1)A//2)/(d)+(epsi_(0)K_(2)A//2)/(d))=(((epsi_(0)A)/(2d))^(2)K_(1)K_(2))/(((epsi_(0)A)/(2d))(K_(1)+K_(2)))`
`=(epsi_(0)A)/(2d)((K_(2)K_(2))/(K_(2)+K_(2)))`