Two wires of resistance R1 and R2 at 0°C have temperature coefficient of resistance a1 and a2, respectively. These are joined in series. The effective temperature coefficient of resistance is

R 1 R 2 α 1 α 2 R 1 2 + R 2 2

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Two wires of resistance R₁ and R₂at 0°C have temperature coefficient of resistance a₁ and a₂, respectively. These are joined in series. The effective temperature coefficient of resistance is

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$\frac{α_{1} + α_{2}}{2}$

$\sqrt{α_{1} α_{2}}$

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

$\frac{\sqrt{R_{1} R_{2} α_{1} α_{2}}}{\sqrt{R_{1}^{2} + R_{2}^{2}}}$

answer is C.

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We know, temperature coefficient is

$α = \frac{1}{R} \frac{dR}{dT}$

and effective resistance in the above arrangement will be

$R_{eff} = R_{1} + R_{2}$

$\frac{{dR}_{eff}}{dt} = \frac{{dR}_{1}}{dt} + \frac{{dR}_{2}}{dt} = R_{1} α_{1} + R_{2} α_{2}$

$α_{eff} = \frac{R_{1} α_{1} + R_{2} α_{2}}{R_{1} + R_{2}}$

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