Resistance of the wire is measured as 2 Ω and 3 Ω at 10 ° C and 30 ° C respectively. Temperature coefficient of resistance of the material of the wire is

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TestHub · Accepted Answer

Resistance of a material is related to temperature by expression $R = R_{0} (1 + α Δ T)$

Here, at $10 ° C$ , we have $2 = R_{0} (1 + 10 α) . . . (i)$

And at $30 ° C$ , we have $3 = R_{0} (1 + 30 α) . . . (i i)$

From equation $(i)$ , $R_{0} = \frac{2}{(1 + 10 α)}$

Putting this value in equation $(i i)$ ,

$3 = \frac{2}{1 + 10 α} (1 + 30 α) \Rightarrow 3 + 30 α = 2 + 60 α$

$\Rightarrow 1 = 30 α$

Hence, temperature coefficient of the material of wire is $α = \frac{1}{30} = 0.033 ° C^{- 1}$

Physics - Heat & Thermo Question with Solution | TestHub

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