MCQ
Two resistances $R_1$ arid $\kappa_2$ 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
    $\frac{\alpha^2+\beta^2}{\alpha \beta}$
  • $\frac{\beta}{\alpha}$

Answer

Correct option: D.
$\frac{\beta}{\alpha}$
$ 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}$

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