Two resistances equal at $0\,^oC$ with temperature coefficient of resistance $\alpha _1$ and $\alpha _2$ joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be
AIIMS 2011, Medium
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$\mathrm{R}_{1}=\mathrm{R}_{0}\left(1+\alpha_{1} \mathrm{t}\right)+\mathrm{R}_{0}\left(1+\alpha_{2} \mathrm{t}\right)$
$=2 \mathrm{R}_{0}\left(1+\frac{\alpha_{1}+\alpha_{2}}{2} \mathrm{t}\right)$
$=\mathrm{R}_{0}^{\prime}\left(1+\frac{\alpha_{1}+\alpha_{2}}{2} \mathrm{t}\right)$
Comparing with $\mathrm{R}=\mathrm{R}_{0}(1+\alpha \mathrm{t})$
$\alpha=\frac{\alpha_{1}+\alpha_{2}}{2}$
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