Question

If a wire of resistance R is cut into 'n' equal parts. All the parts are first
connected in series and then in parallel. Calculate the ratio of series and
parallel combination of the resistors​

Answer 1

Wire is cut into n equal parts. Since all dimensions are same for pieces, Resistance of each wire is equal and has a value = R/n.

Resistance is proportional to length of wire and inversely proportional to area of cross-section.

IF length is 1/nth, then Resistance is also 1/n th of original value.When these five are connected in parallel combination, then net resistance becomes 1/nth again. So R1 = R/n * 1/n = R/n^2

Answer 2

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