Resistance of the wire is measured as 2Ω and 3Ω at 10 ° C and 30 °...

Resistance of a material is related to temperature by expression $R = {R}_{0}\left(1 + \alpha\DeltaT\right)$

Here, at $10 ° C$, we have $2 = {R}_{0}\left(1 + 10\alpha\right) . . . \left(i\right)$

And at $30 ° C$, we have $3 = {R}_{0}\left(1 + 30\alpha\right) . . . \left(ii\right)$

From equation \left(i\right)$,${R}_{0} = \dfrac{2}{\left(1 + 10\alpha\right)}$</p><p>Putting this value in equation \left(ii\right)$,

$3 = \dfrac{2}{1 + 10\alpha}\left(1 + 30\alpha\right) ⇒ 3 + 30\alpha = 2 + 60\alpha$

$⇒ 1 = 30\alpha$

Hence, temperature coefficient of the material of wire is $\alpha = \dfrac{1}{30} = 0 . 033 ° {C}^{- 1}$