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 wire

Question

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 ℓ A ​ / ℓ B ​ of their respective lengths must be

TestHub · Accepted Answer

R 1 ​ = π R A 2 ​ ρ A ​ ℓ A ​ ​ R 2 ​ = π R B 2 ​ ρ B ​ ℓ B ​ ​ ℓ B ​ ℓ A ​ ​ = ρ A ​ R B 2 ​ ρ B ​ R A 2 ​ ​ = ρ A ​ ⋅ 4 R A 2 ​ 2 ρ A ​ R A 2 ​ ​ ⇒ ℓ A ​ ℓ B ​ ​ = 2

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