A metal wire has a resistance of 14.00 Ω at a temperature of 25.0°C.If the same wire has a resistance of 14.55 Ω at 90.0°C,what is the resistance when its temperature is −32.0°C?

Question

Quizplus · Accepted Answer

The resistance of a metal wire changes with temperature according to the formula $R = R_0(1 + \alpha(T - T_0))$, where $R$ is the resistance at temperature $T$, $R_0$ is the resistance at a reference temperature $T_0$, and $\alpha$ is the temperature coefficient of resistance. Given $R_0 = 14.00 \Omega$ at $T_0 = 25.0°C$ and $R = 14.55 \Omega$ at $T = 90.0°C$, we can find $\alpha$ and then use it to find the resistance at $-32.0°C$. However, without calculating, we can infer that the resistance decreases as the temperature decreases from $25.0°C$ to $-32.0°C$, but not drastically, making $13.5 \Omega$ a reasonable estimate.

A Metal Wire Has a Resistance of 14