Answer to Question #231904 in Physics for Aypeter

Question

The resistance of a coil of a copper wire at the beginning of a heat test is 173Ω, the temperature being 160C. At end of the test, the resistance is 212Ω. Calculate the temperature raise of the coil. Assuming the temperature coefficient of resistance of copper to be 0.00426/0C at 00C.

Answer 1

At 16°C and another temperature:

$$R_1=R_0(1+\alpha T_1),\\ R_2=R_0(1+\alpha T_2).$$

Express T₂:

$$T_2=\frac 1\alpha\bigg(\frac{R_2}{R_0}-1\bigg),$$

from the first expression we have

$$R_0=\frac{R_1}{1+\alpha T_1}.\\\space\\ T_2=\frac 1\alpha\bigg(\frac{R_2}{\frac{R_1}{1+\alpha T_1}}-1\bigg)=73°\text{C}.$$