Question

The space between the plates of a parallel plate capacitor is completely
filled in two ways. In the first case, it is filled with a slab of dielectric
constant K. In the second case, it is filled with two slabs of equal
dimensions but dielectric constants Kį and K2, respectively as shown in
the figure. The capacitance of the capacitor is same in the two cases.
Obtain the relationship between K, K, and K2.
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Answer 1

The capacitance of the capacitors in series and parallel combination is given below.

Explanation:

This combination can be assumed to be a combination of two parallel plates capacitors connected in series with capacity  

2K1 ϵ o A / d   and   K 2 ϵ 0 A /d 2

• In series, the resultant capacitance is 2 K1 K2 ϵ 0 A  / ( K1 + K2) d
• Thus resultant dielectric constant is 2 K1 K2 / K1 + K2