Two conductors have the same resistance at 0°C but their temperature coefficients of resistance are $α_{1}$ and $α_{2}$ . The respective temperature coefficients of their series and parallel combinations are nearly

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$α_{1} + α_{2}, \frac{α_{1} + α_{2}}{2}$

$\frac{α_{1} + α_{2}}{2}, \frac{α_{1} + α_{2}}{2}$

$α_{1} + α_{2}, \frac{α_{1} α_{2}}{α_{1} + α_{2}}$

$\frac{α_{1} + α_{2}}{2}, α_{1} + α_{2}$

answer is D.

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Detailed Solution

$R_{1} = R_{0} (1 + α_{1} (Δt)); R_{2} = R_{0} (1 + α_{2} (Δt))$
$Series R = R_{1} + R_{2}; Parallel \frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$

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