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
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(d) ${R_1} + {R_2} = {R_1}(1 + \alpha t) + {R_2}(1 - \beta \,t)$
$==>$ ${R_1} + {R_2} = {R_1} + {R_2} + {R_1}\alpha t - {R_2}\beta t$
$==>$ ${R_1} + {R_2} = {R_1} + {R_2} + {R_1}\alpha t - {R_2}\beta t$
$==>$ $\frac{{{R_1}}}{{{R_2}}} = \frac{\beta }{\alpha }$
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