Solve the above problem when a thin metal sheet is inserted, separating dielectric`1` and `2` from `3`.

Explanation

Let `C=(in_(0)A)/(d) ,C_(1)=K_(1)(in_(0)(A)/(2))/((d)/(2))=K_(1)C`
`C_(2)=K_(2)(in_(0)(A)/(2))/((d)/(2))=K_(2)C, C_(3) =(K_(3)in_(0)A)/((d)/(2)),= 2K_(3) C`

The equivalent circuit as shown

`(1)/(C)=(1)/(C_(3))+(1)/(C_(1)+C_(2)),(1)/(KC)=(1)/(2K_(3)C)+(1)/((K_(1)+K_(2))C)`
`(1)/(K)=(1)/(K_(1)+K_(2))+(1)/(2K_(3))`.