Answer :

Given,

In the figure, part a), b), and c) are same.

Capacitances are 1μF,3μF,2μF,6μF and 5μF

**Formula used**

Each parts of the figure represents a bridge circuit. A bridge circuit is the one in which, two electrical paths are branched in parallel between the same potential difference, but are bridged by a third path, from intermediate points.

Inorder to check the balancing of the bridge circuits, the following conditions must be satisfied,

For a balanced bridge with capacitance arranged as shown in figure,

If this condition is satisfied the current through the C_{5} capacitor will be zero. Hence, C_{5} will be ineffective.

In the given figures, we have to check this condition before calculating the effective capacitance.

By comparing the above figure and the question figures, we can write,

C13 μF, C26 μF, C31 μF, C42 μF, C55 μF

And,

Or,

So, the balancing condition is satisfied, and hence, the 5 μF capacitor will be ineffective.

Thus the setup will reduce to the below form.

This is a simple capacitor combination, with two series connections connected in parallel. This can be solved in parts

Effective capacitance with C_{1} and C_{3} are,

Or,

Substituting the values of C_{1} and C_{3}

Similarly on the other branch,

Or,

The above two series arrangements are arranged in parallel to each other across a potential difference. Hence their equivalent capacitance, C_{eq}, can be found by,

Or,

Hence, the equivalent capacitance in each of the arrangement will be 2.25μF.

Thus, for the case A), B) and C) the equivalent capacitance of the circuit remains constant.

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