# The temperature dependence of resistivity

#### Question

The resistance of a wire of length $l$ and cross section area $A$ is given by $R = \rho l / A$, where $\rho$ is the resisitivity (SI units: $\mathrm{\Omega\,m}$). Over reasonably narrow temperature ranges, $R$ increases with temperature linearly: $$R(T) = R_0[1+\alpha(T-T_0)],$$ where $\alpha$ is a constant. Fit a straight line to the following data sets and determine $\rho$ for copper and iron at the reference temperature $T_0 = 300\;\mathrm{K}$. The data are measured for a wire of circular cross sectional radius $0.1\;\mathrm{mm}$ and length $100\;\mathrm{m}$.

$T\;/\mathrm{K}$$R(\mathrm{Cu})\;/\mathrm{\Omega}$$R(\mathrm{Fe})\;/\mathrm{\Omega}$
220.00.331.89
250.00.512.31
280.00.592.77
310.00.443.25
340.00.643.71
370.00.704.25
400.00.734.66

#### Solution

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