# Dependence of resistance on temperature

1. Dec 26, 2014

### Karol

1. The problem statement, all variables and given/known data
The book says the formula is accurate as long as t and α are small. i understand about t but why also α?

2. Relevant equations
Resistance R: $R=R_0(1+\alpha t)$

3. 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

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2. Dec 26, 2014

### 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 $\alpha$.

3. Dec 27, 2014

Thanks