Answer to Question #317099 in Physics for Stephen

Question

A platinum coil has a resistance of 3.146ohms at 40°C and 3.767 ohms at 100°C. Find the resistance at 0°C and the temperature coefficient of resistance at 40°C

Answer 1

$$R(t_1)=R_0(1+\alpha t_1)\\ R(t_2)=R_0(1+\alpha t_2)$$

$$\alpha=\frac{R(t_2)-R(t_1)}{R(t_1)t_2-R(t_2)t_1}$$

$$\alpha=\frac{3.767-3.146}{3.146*100-3.767*40}=3.788*10^{-3}\:\rm K^{-1}$$

$$R_0=\frac{R_1}{1+\alpha t_1}=\frac{3.146}{1+3.788*10^{-3}*40}=2.732\:\Omega$$