When the space between the plates of a parallel plate condenser is completely filled with two slabs of dielectric constants `K_(1)` and `K_(2)` and each slab having area `A` and thickness equal to `(d)/(2)` as shown in the figure

Fig. The equivalent circuit is as shown.
.

Explanation

(a) Capacity of the upper half `C_(1)=(2K_(1) in_(0) A)/(d)`
(b) Capacity of the lower half `C_(2)=(2K_(2) in_(0)A)/(d)`
( c) `C_(1)` and `C_(2)` may be supposed to be connected in series.
(d) Effective capacity
`C=(C_(1)C_(2))/(C_(1)+C_(2))=(epsilon_(0)A)/(d) ((2K_(1)K_(2))/(K_(1)+K_(2)))=C_(0) ((2K_(1)K_(2))/(K_(1)+K_(2)))`
Here `C_(0)` is the capacity of the condenser with air medium.
( e) Effective dielectric constant `K=((2K_(1)K_(2))/(K_(1)+K_(2)))`.