Two identical parallel plate (air) capacitors `c_(1) and c_(2)` have capacitances C each. The space between their plates is now filled with dielectrics as shown. If two capacitors still have equal capacitance, obtain the relation betweenn dielectric constants `k,k_(1) and k_(2)`.

Explanation

Let `A to` area of each plate.
After inserting respective dielectric slabs:
`C_(1)'=KC . . . (i)`
& `C_(2)'=K_(1)(in_(0)(A//2))/(d),(K_(2)in_(0)(A//2))/(d)=(in_(0)A)/(2d)(K_(1)+K_(2)),C_(2)'=(C)/(2)(K_(1)+K_(2))` . . (ii)
From (i) and (ii) `C_(1)'=C_(2)', KC=(C)/(2)(K_(1)+K_(2)),K=(1)/(2)(K_(1)+K_(2))`