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 μ Ω cm and 51 μ Ω cm 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 3 Ω ? (Given resistivities of iron and copper-nickel alloy wire are 12 μ Ω cm and 51 μ Ω cm respectively) (A) 82 m (B) 97 m (C) 110 m (D) 90 m

Tardigrade Admin · Accepted Answer

( R 1 R 2/ R 1+ R 2)=3 (((12 × 10-6 × 10-2) ℓ × 4/π(2)2 × 10-6) × ((51 × 10-6 × 10-2) ℓ × 4/π(2)2 × 10-6)/(63 × 10-6 × 10-2 × ℓ × 4)π(2)2 × 10-6) ⇒ ℓ=97 m

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

82 m

97 m

110 m

90 m

R1​+R2​R1​R2​​=3 π(2)2×10−663×10−6×10−2×ℓ×4​π(2)2×10−6(12×10−6×10−2)ℓ×4​×π(2)2×10−6(51×10−6×10−2)ℓ×4​​ ⇒ℓ=97m

Q. 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 $12 μ Ω c m$ and $51 μ Ω c m$ respectively)