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)

Step-by-step solution

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