The expression for the capacity of the capacitor formed by compound dielectric placed between the plates of a parallel plate capacitor as shown in figure will be

Options

A. `(in_(0)A)/(d_(1)/K_(1)+d_(2)/K_(2)+d_(3)/K_(3))`
B. `(in_(0)A)/(d_(1)/K_(1)-d_(2)/K_(2)-d_(3)/K_(3))`
C. `(in_(0)A^(2))/(d_(1)/K_(1)-d_(2)/K_(2)-d_(3)/K_(3))`
D. `(in_(0)A^(2))/(1/K_(1)+1/K_(2)+1/K_(3))`

Answer

A

Explanation

The given capacitor may be supposed to be formed of three component capacitors `C_(1), C_(2) and C_(3)` connected in series.
`1/C_(s)=1/C_(1)+1/C_(2)+1/C_(3)`
`= d_(1)/(AK_(1)in_(0))+d_(2)/(AK_(2)in_(0))+d_(3)/(AK_(3)in_(0))`
`C_(s)=(in_(0)A)/(d_(1)/K_(1)+d_(2)/K_(2)+d_(3)/K_(3))`