Resistance of the wire is measured as $2 Ω and 3 Ω at 10^{\circ} C and 30^{\circ} C$ respectively. Temperature co-efficient of resistance of the material of the wire is :

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$0 .033 {}^{o}C^{- 1}$

$0 .011 {}^{o}C^{- 1}$

$0 .055 {}^{o}C^{- 1}$

$- 0 .033 {}^{o}C^{- 1}$

answer is A.

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Detailed Solution

$\begin{array}{l} R = R_{0} (1 + αΔT) \\ 3 = R_{0} (1 + α (30 - 0)) \\ 2 = R_{0} (1 + α (10 - 0)) \\ \frac{3}{2} = \frac{1 + 30 α}{1 + 10 α} \\ α = \frac{1}{30} = 0 .033 {}^{o}C^{- 1} \end{array}$

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