The resistances of an iron wire and a copper wire at 20 ∘ are 3.9 Ω and 4.1 Ω respectively. At what temperature will the resistances be equal ? Temperature coefficient of resistivity for iron is 5.0 ×−3K−1 and for copper it is 4.0 ×10−3K−1. Neglect any thermal expansion.
R′Fe=RFe×(1+αFe×△θ)
R′Cu=RCu(1+αcu×△θ)
R′Fe=R′Cu
⇒RFe×(1+αFe×△θ)
⇒3.9[1+5×10−3(20−θ)]
=⇒3.9+3.9×5×10−3(20−θ)
⇒4.1×4×10−3(20−θ)−3.9×5×10−3(20−θ)
= 4.1−3.9 ⇒16.4(20−θ)−19.5(20−θ)
=0.2×103
⇒(20−θ)(−3.1)=0.2×103
⇒θ−20=64.5
⇒θ=84.5∘C