A nichrome wire and an aluminum wire, each with the same initial resistance, have the same change in resistance when heated separately. (ρAl = 2.82 × 10⁻⁸ Ω ⋅ m; αAl = 3.9 × 10⁻³ / °C; ρnichrome = 1.50 × 10−6 Ω ⋅ m; αnichrome = 0.40 × 10⁻³ / °C.) The ratio of the temperature change of the nichrome wire to the temperature change of the aluminum wire is A)0.019. B)0.10. C)0.18. D)9.8. E)53.

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Quizplus · Accepted Answer

The change in resistance is proportional to the product of the initial resistance, the temperature coefficient of resistance, and the temperature change. Since the initial resistances and changes in resistance are the same, the ratio of temperature changes is inversely proportional to the ratio of their temperature coefficients: (αAl / αnichrome) = (3.9 × 10^−3 / 0.40 × 10^−3) = 9.8.

A Nichrome Wire and an Aluminum Wire, Each with the Same