Question

review the temperature vs resistance graph below. resistance vs. temperature part a part b find the temperature coefficient of resistance.

Explanation:

Step1: Recall the formula for temperature - coefficient of resistance

The resistance - temperature relationship is given by $R = R_0(1+\alpha\Delta T)$. For a linear graph of $R$ vs $T$, the slope of the line $m=-R_0\alpha$. First, we need to find the slope of the $R - T$ graph.

Step2: Select two points on the graph

Let's take two well - defined points on the graph. Suppose the first point $(T_1,R_1)=(0, 5)$ and the second point $(T_2,R_2)=(100,85)$. The slope $m$ of the line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $m=\frac{R_2 - R_1}{T_2 - T_1}=\frac{85 - 5}{100-0}=\frac{80}{100}=0.8$.

Step3: Relate slope to temperature - coefficient of resistance

We know that $m=-R_0\alpha$. Assuming $R_0 = 5\Omega$ (resistance at $T = 0^{\circ}C$), then $\alpha=-\frac{m}{R_0}$. Substituting $m = 0.8$ and $R_0 = 5$, we get $\alpha=-\frac{0.8}{5}=- 0.16\Omega/^{\circ}C$.

Answer:

$-0.16\Omega/^{\circ}C$