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Electric Current

Problem 3.149

At the temperature 0∘C0^{\circ} \mathrm{C} the electric resistance of conductor 2 is η\eta times that of conductor 1. Their temperature coefficients of resistance are equal to α2\alpha_{2} and α1\alpha_{1} respectively. Find the temperature coefficient of resistance of a circuit segment consisting of these two conductors when they are connected (a) in series; (b) in parallel.

Reveal Answer
(a) α=(α1+ηα2)/(1+η)\alpha=\left(\alpha_{1}+\eta \alpha_{2}\right) /(1+\eta) (b) α≈(α2+ηα1)/(1+η)\alpha \approx\left(\alpha_{2}+\eta \alpha_{1}\right) /(1+\eta)
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