The resistance of a wire increases by $3.9 \%$ when the temperature of the wire is raised $100^{\circ} \mathrm{C}$. What is the temperature coefficient of resistivity of the wire material?
A) $0.00039^{\circ} \mathrm{C}^{-1}$
B) $0.039^{\circ} \mathrm{C}^{-1}$
C) $3.9^{\circ} \mathrm{C}^{-1}$
D) $0.0039^{\circ} \mathrm{C}^{-1}$
E) $0.39^{\circ} \mathrm{C}^{-1}$

Question

Quizplus · Accepted Answer

The temperature coefficient of resistivity ($\alpha$) is calculated using the formula $\alpha = \frac{\Delta R / R_0}{\Delta T}$, where $\Delta R / R_0$ is the relative change in resistance and $\Delta T$ is the change in temperature. Given a $3.9\%$ increase in resistance over a $100^{\circ}C$ temperature change, $\alpha = \frac{0.039}{100} = 0.00039^{\circ}C^{-1}$.

The Resistance of a Wire Increases By 3.9%3.9 \%3.9% When the Temperature of the Wire Is Raised

The Resistance of a Wire Increases By $3.9 \%$ When the Temperature of the Wire Is Raised