A parallel-plate capacitor is filled half-and half with two dielectrics of dielectric constants `epsilon_(1)` and `epsilon_(2)`, respectively. In the first case, one dielectric is placed over the other. In the second case, one dielectric fills half the space and the other the second half. Calculate their capacitances in the two cases. The distance between the plates is d and area of each plate is A.

[Hint:(i) In fact there are two capacitors, each of area equal to the area of a plate and thickness equal to half the plate separation. The are in series. (ii) There are two capacitors, each of thickness equal to the plate separation and area equal to half of the area of a plate. They in parallel.]

Answer

(i) `(2epsilon_(0)A)/(d).(epsilon_(1)epsilon_(2))/(epsilon_(1)+epsilon_(2))`(ii) `(epsilon_(0)A)/(d)(epsilon_(1)+epsilon_(2))/(2)`