Question

Find the capacitance between A and B if three dielectric slabs of dielectric constants `K_(1) area `A _(2)` and thickness `d_(2)`) are inserted between the plates of a parallel late capacitor of plate area A. (Given that the distance between the two plates is `d_(1)=d_(2)+d_(2)`.)
.

Answer 1

.
It is equivalent to
`C=C_(1)+(C_(2)C_(3))/(C_(2)+C_(3))`
`=(A_(1)K_(1)epsilon_(0))/(d_(1)+d_(2))+((A_(1)K_(2)epsilon_(0))/d_(1).(A_(2)K_(3)epsilon_(0))/d_(2))/((A_(2)K_(2)epsilon_(0))/d_(1)+(A_(2)K_(3)epsilon_(0))/d_(2))`
`=(A_(1)K_(1)epsilon_(0))/(A_(2)+d_(2))+(A_(2)^(2)K_(2)K_(3)epsilon_(0)^(2))/(A_(1)K_(2)epsilond_(2)+A_(2)K_(2)epsilond_(1))`
`=(A_(1)K_(1)epsilon)/(d_(1)+d_(2))+(A_(2)K_(2)K_(3)epsilon_(0))/(K_(2)d_(2)+K_(3)d_(1))`