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 $3Ω$ ?
(Given resistivities of iron and copper-nickel alloy wire are $12 μ Ω c m$ and $51 μ Ω c m$ respectively)

Question

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 $3Ω$ ?

(Given resistivities of iron and copper-nickel alloy wire are $12 μ Ω c m$ and $51 μ Ω c m$ respectively)

TestHub · Accepted Answer

R 1 ​ + R 2 ​ R 1 ​ R 2 ​ ​ = 3Ω ρ 1 ​ + ρ 2 ​ ρ 1 ​ ρ 2 ​ ​ × A ℓ ​ = 3Ω ℓ = 3 × A × ρ 1 ​ ρ 2 ​ ( ρ 1 ​ + ρ 2 ​ ) ​ = ( 12 × 1 0 − 8 ) ( 51 × 1 0 − 8 ) 3 × [ π ( 1 0 − 3 ) 2 ] × ( 63 × 1 0 − 8 ) ​ ℓ ≈ 97 m

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