Question

Two resistances $R_{1}$ 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. $\frac{\beta}{\alpha}$

Answer 1

Answer: (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 $
$\Rightarrow \frac{R_{1}}{R_{2}}=\frac{\beta}{\alpha}$