Find the capacitance in shown figure

Options

A. `(2KAepsilon_(0))/((K+1)d)`
B. `(2KAepsilon_(0))/d`
C. `((K+1)Aepsilon_(0))/(2d)`
D. `(2KAepsilon_(0))/((K^(2)+1)d)`

Answer

A

Explanation

The combination is same as the two capacitors are connected in series and distance between plates of each capacitor is `d//2`.
So, `C_(1) = (Kepsilon_(0)A)/(d//2)` and `C_(2) = (epsilon_(0)A)/(d//2)`
Hence, `C_("net") = (C_(1)C_(2))/(C_(1)+C_(2))=(((2Kepsilon_(0)A)/(d))((2epsilon_(0)A)/d))/(((2Kepsilon_(0)A)/(d))+((2epsilon_(0)A)/d))=(2KAepsilon_(0))/((K+1))d`