Answer to Question #193035 in Electric Circuits for Marty

Question

What is the temperature coefficient of resistance of a piece of wire having a resistance of 11.56 ohms at 25°C and 10.22 ohms at 0°C? What will be its resistance at 50°C?

Answer 1

Using the two known values of resistance, we can determine the temperature coefficient of resistance for this material:

$$R_{25}=R_0(1+\alpha(T_{25}-T_0)),\\\space\\ \alpha=\frac{1}{T_{25}-T_0}\bigg(\frac{R_{25}}{R_0}-1\bigg)=5.24·10^{-3}/°\text C.$$

The resistance at 50°C:

$$R_{50}=10.22(1+5.24·10^{-3}(50-0))=12.90\space\Omega.$$