Answer :
Final answer:
The temperature coefficient of resistivity for the wire is found by plugging the given values into the formula for changes in resistance with temperature: β = ΔR / (R₀ΔT) = 0.5 Ω / (39.3 Ω * 8.5°C) = 0.0015 °C⁻¹. This coefficient measures how the wire’s resistance changes per degree Celsius.
Explanation:
In this question, we are asked to determine the temperature coefficient of resistivity. The temperature coefficient of resistivity is a factor that describes how much a material's resistivity changes for each unit increase in temperature. In this case, we have a wire whose resistance changes as its temperature changes. We can use the formula for changes in resistance with temperature: ΔR = R₀(βΔT), where ΔR is the change in resistance, R₀ is the original resistance, β is the temperature coefficient of resistivity, and ΔT is the change in temperature. In this case, ΔR is 39.8 Ω - 39.3 Ω = 0.5 Ω, R₀ is 39.3 Ω, and ΔT is 28.5°C - 20°C = 8.5°C. So, the temperature coefficient of resistivity β, can be found using the rearranged formula β = ΔR / (R₀ΔT) = 0.5 Ω / (39.3 Ω * 8.5°C) = 0.0015 °C⁻¹ . Therefore, the temperature coefficient of resistivity of the wire is 0.0015 °C⁻¹.
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