Dependence of resistance on temperature

[Karol]

Homework Statement

The book says the formula is accurate as long as t and α are small. i understand about t but why also α?

Homework Equations

Resistance R: $R=R_0(1+\alpha t)$

The Attempt at a Solution

According to the graph (see picture) α is the slope and is suited for every material, so only t makes a difference, because of the limited linear approximation

 

[haruspex]

I agree with you. We could expand the approximation to more terms to make it more accurate: $R=R_0(1+\alpha t + \beta t^2 + ...)$. The approximation $R=R_0(1+\alpha t)$ is reasonable if t is small and $\beta$ not large; it has nothing to do with $\alpha$.

 

[Karol]

Thanks