Four identical metal plates are arranged in air at equal distance d from each other. The area of each plate is `A`. A batery of emf V is connected across plates 1 distribution and find the capacitance of the system between points `1` and `2` if the other two plates are connected by a conducting wire as shown in.
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Explanation

Let us give numbers to the four plates. Here `X` and `Y` are connected to the positive and negative terminals of the battery (say), then the charge distribution will be as shown.

Here the arrangement can be represented as the grouping of three identcial capacitors each of capacity `(in_(0)A)/(d)`. The arrangement will be as shown

Now the equivalent capacitance between `X` and `Y` is `C_(XY)=((C+C)C)/(C+C+C)=(2C)/(2)=(2 in_(0)A)/(3d)`.