|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
$(a) \frac{\alpha}{\beta} (b) \frac{\alpha+\beta}{\alpha-\beta} (c) \frac{\alpha^{2}+\beta^{2}}{\alpha\beta} (d) \frac{\beta}{\alpha}$
Text Solution
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$R_1 + R_2 = R_1 (1 + \alpha t) + R_2 (1 - \beta t)$
$\Rightarrow \mathbf{R}_1 + \mathbf{R}_2 = \mathbf{R}_1 + \mathbf{R}_2 + \mathbf{R}_1 \alpha t - \mathbf{R}_2 \beta t$
$\Rightarrow \frac{R_1}{R_2} = \frac{\beta}{\alpha}$
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