A regular n-sided polygon is made from a uniform wire of total resistance R. The equivalent resistance between two adjacent vertices is:
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Question

A regular n-sided polygon is made from a uniform wire of total resistance R. The equivalent resistance between two adjacent vertices is:

G1 Physics · Accepted Answer

Let the resistance of each side of the regular n-sided polygon be r. Since the total resistance of the wire is R, r = R/n Between two adjacent vertices there are two paths: Short path: R₁ = r Long path: R₂ = (n − 1)r These two paths are in parallel. Therefore, Rₑq = R₁R₂/(R₁ + R₂) = r(n − 1)r / [r + (n − 1)r] = (n − 1)r/n Using r = R/n, Rₑq = (n − 1)R/n² Hence option A.