Question

The resistance of a wire is 126.48ohms at 100°C and 100ohms at 30°C.

Determine the temperature coefficient of copper at 0°C.

Answer 1

Given:

$R_1=126.48\:\Omega$

$t_1=100\:\rm {^\circ C}$

$R_2=100\:\Omega$

$t_2=30\:\rm {^\circ C}$

In general

$$R(t)=R_0(1+\alpha t)$$ $$\alpha=\frac{R_1-R_2}{R_2t_1-R_1t_2}$$ $$R_0=\frac{R_1}{1+\alpha t_1}=\frac{R_1}{1+\frac{R_1-R_2}{R_2t_1-R_1t_2} t_1}$$

$$R_0=\frac{126.48}{1+\frac{126.48-100}{100*100-126.48*30}*100}=88.7\:\Omega$$