A metal wire has a resistance of 15.50 Ω at a temperature of 25.0°C.If the same wire has a resistance of 15.9 Ω at 90.0°C,what is the resistance when its temperature is −32.0°C?

Question

Quizplus · Accepted Answer

Using the formula R=R₀(1 + αΔT), where R₀ is the resistance at 25.0°C, α is the temperature coefficient of resistance, and ΔT is the change in temperature in °C, we can solve for α:
α = (R - R₀) / (R₀ ΔT)
α = (15.9 Ω - 15.50 Ω) / (15.50 Ω (90.0°C - 25.0°C))
α = 0.00420 / °C
Using this value of α and the same formula, we can solve for the resistance at -32.0°C:
R = R₀(1 + αΔT)
R = 15.50 Ω (1 + 0.00420 / °C (-32.0°C - 25.0°C))
R = 15.1 Ω.

A Metal Wire Has a Resistance of 15