What equal length of an iron wire and a copper-nickel alloy wire, each of $2 mm$ diameter connected parallel to give an equivalent resistance of $3 Ω$ ?
(Given resistivities of iron and copper-nickel alloy wire are $12 μΩ cm$ and $51 μΩ cm$ respectively)

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TestHub · Accepted Answer

R 1 R 2 R 1 + R 2 = 3 Ω ρ 1 ρ 2 ρ 1 + ρ 2 × ℓ A = 3 Ω ℓ = 3 × A × ρ 1 + ρ 2 ρ 1 ρ 2 = 3 × π 10 − 3 2 × 63 × 10 − 8 12 × 10 - 8 51 × 10 − 8 ℓ ≈ 97 m

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