A nichrome wire and an aluminum wire, each with the same initial resistance, have the same change in resistance when heated separately. (ρ_Al = 2.82 × 10−⁸ Ω ⋅ m; α_Al = 3.9 × 10−³ / °C; ρ_nichrome = 1.50 × 10−⁶ Ω ⋅ m; α_nichrome = 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 for a material due to temperature change can be described by the formula ΔR = R0αΔT, where ΔR is the change in resistance, R0 is the initial resistance, α is the temperature coefficient of resistance, and ΔT is the change in temperature. Given that both wires have the same initial resistance and experience the same change in resistance, we can set up the equation αAlΔTAl = αNichromeΔTNichrome. Rearranging to find the ratio of ΔTNichrome to ΔTAl gives ΔTNichrome / ΔTAl = αAl / αNichrome. Substituting the given values, αAl = 3.9 × 10^-3 /°C and αNichrome = 0.40 × 10^-3 /°C, we get ΔTNichrome / ΔTAl = (3.9 × 10^-3) / (0.40 × 10^-3) = 9.75, which rounds to 9.8, indicating that the temperature change in the nichrome wire is 9.8 times that of the aluminum wire for the same change in resistance.

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