A wire has a resistance of   $3.1\mathrm{\Omega }$  at 30°C and a resistance   $4.5\mathrm{\Omega }$  at 100°C. The temperature coefficient of resistance of the wire  

$\begin{array}{l}{R}_1=3.1\mathrm{\Omega }\text{ at }t={30}^{\circ }\mathrm{C}\\ R_2=4.5\mathrm{\Omega }\text{ at }t={100}^{\circ }\mathrm{C}\\ \text{ We have, }R=R_0(1+\alpha t)\\ \therefore R_1=R_e[1+\alpha (30\left)\right]\\ R_2=R_0[1+\alpha (100\left)\right]\\ \Rightarrow \frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}=\frac{1+30\alpha }{1+100\alpha }\end{array}$

$\Rightarrow \frac{3.1}{4.5}=\frac{1+30\alpha }{1+100\alpha }\Rightarrow \alpha ={0.0064}^{\circ }{\mathrm{C}}^{-1}$