Question

# A regular n sided polygon is made from a uniform wire of resistance R. Given n is even, find the resistance of the polygon between any two adjacent corners.

A
Rn2
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B
n1)R2
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C
(n1)Rn2
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D
(n1)R
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Solution

## The correct option is C (n−1)Rn2 In a polygon made up of a uniform wire, each side has resistance Rn Let us consider a side AB, across which let us find out the equivalent resistance of the system of resistors. From the figure, R′AB=Rn and R′′AB=R(n−1)n Equivalent resistance across AB is given by RAB=R′ABR′′ABR′AB+R′′AB Substituting the data obtained we get, RAB=(n−1)Rn2 Hence, option (c) is the correct answer.

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