A nichrome wire and an aluminum wire, each with the same initial resistance, have the same change in resistance when heated separately.($\rho$Al = 2.82 * 10-8 $\Omega$. m; $\alpha$Al = 3.9 * 10-3 / $\degree$C; $\alpha$nichrome = 1.50 *10-6 $\Omega$. m; $\alpha$nichrome = 0.40* 10-3 / $\degree$C.) The ratio of the temperature change of the nichrome wire to the temperature change of the aluminum wire is:
A)0.019.
B)0.10.
C)0.18.
D)9.8.
E)53.

Question

A nichrome wire and an aluminum wire, each with the same initial resistance, have the same change in resistance when heated separately.($\rho$Al = 2.82 * 10-8  $\Omega$. m; $\alpha$Al = 3.9 * 10-3 / $\degree$C; $\alpha$nichrome = 1.50 *10-6  $\Omega$. m; $\alpha$nichrome = 0.40* 10-3 / $\degree$C.) The ratio of the temperature change of the nichrome wire to the temperature change of the aluminum wire is:
A)0.019.
B)0.10.
C)0.18.
D)9.8.
E)53.

Quizplus · Accepted Answer

The change in resistance is given by $\Delta R = R_0 \alpha \Delta T$. Since the initial resistances and changes in resistance are the same for both wires, $\alpha_{\text{nichrome}} \Delta T_{\text{nichrome}} = \alpha_{\text{Al}} \Delta T_{\text{Al}}$. Solving for the ratio $\frac{\Delta T_{\text{nichrome}}}{\Delta T_{\text{Al}}}$ gives $\frac{\alpha_{\text{Al}}}{\alpha_{\text{nichrome}}} = \frac{3.9 \times 10^{-3}}{0.40 \times 10^{-3}} = 9.8$.

A Nichrome Wire and an Aluminum Wire, Each with the Same