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Two cylindrical wires A and B have the same resistance. The ratio of their specific resistances and diameters are 1 : 2 each, then what is the ratio of the length of B to the length of A ?

Correct answer

2

Step-by-step solution

Resistance of a wire R = ρ l π r 2 = ρ l × 4 π D 2 ∵ R A = R B ∴ 4 ρ A L A π D A 2 = 4 ρ B L B π D B 2 or L B L A = ρ A ρ B D B D A 2 = ρ A 2 ρ A 2 D A D A 2 = 4 2 = 2 1

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