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Current Electricity

Question
CBSEENPH12039639

A material ‘B’ has twice the specific resistance of ‘A’. A circular wire made of ‘B’ has twice the diameter of a wire made of ‘A’. Then for the two wires to have the same resistance, the ratio

  • 2

  • 1

  • 1/4

  • 1/2

Solution

A.

2

straight R subscript 1 space equals space fraction numerator straight rho subscript straight A calligraphic l subscript straight A over denominator πR subscript straight A superscript 2 end fraction
straight R subscript 2 space equals space fraction numerator straight rho subscript straight B calligraphic l subscript straight B over denominator πR subscript straight B superscript 2 end fraction
calligraphic l subscript straight A over calligraphic l subscript straight B space equals space fraction numerator straight rho subscript straight B straight R subscript straight A superscript 2 over denominator straight rho subscript straight A straight R subscript straight B superscript 2 end fraction space
equals space fraction numerator 2 straight rho subscript straight A space straight R subscript straight A superscript 2 over denominator straight rho subscript straight A 4 straight R subscript straight A superscript 2 end fraction
rightwards double arrow calligraphic l subscript straight A over calligraphic l subscript straight B space equals space 2 space space