Question

How much would you have to raise the temperature of a copper wire(originally at 20 degrees) to increase its resistance by 12%?

Answer 1

The ratio between the final and initial resistance must be

$$\frac{R_f}{R_i}=1.12.$$

In terms of temperature coefficient of copper is will be

$$\frac{R_f}{R_i}=\frac{R_{20}\cdot(1+\alpha T)}{R_{20}}=1.12,\\\space\\ T=\frac{1.12-1}{\alpha}=31°\text{C}.$$