Q. Two resistance $R_{1}$ and $R_{2}$ are made of different materials. The temperature coefficient of the material of $R_{1}$ is $\alpha$ and of the material of $R_{2}$ is $- \beta.$ The resistance of the series combination of $R_{1}$ and $R_{2}$ will not change with temperature, if $R_{1}/R_{2}$ equals
A) $\frac{\alpha}{\beta}$
B) $\frac{\alpha + \beta}{\alpha - \beta}$
C) $\frac{\alpha^{2} + \beta^{2}}{\alpha\beta}$
D) $\frac{\beta}{\alpha}$
Explanation
(d) $R_{1} + R_{2} = R_{1}(1 + \alpha t) + R_{2}(1 - \beta t)$
$\Rightarrow R_{1} + R_{2} = R_{1} + R_{2} + R_{1}\alpha t - R_{2}\beta t \Rightarrow \frac{R_{1}}{R_{2}} = \frac{\beta}{\alpha}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.