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# A silver wire has a resistance of 2.1 Ω at 27.5 °C, and a resistance of 2.7 Ω at 100 °C. Determine the temperature coefficient of resistivity of silver.

3.7 A silver wire has a resistance of 2.1 Ω at 27.5 °C, and a resistance of 2.7 Ω at 100 °C. Determine the temperature coefficient of resistivity of silver.

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Given,

$\dpi{100} T_1= 27.5 \degree C$ ;  $\dpi{100} R_1 = 2.1\Omega$

$\dpi{100} T_2= 100\degree C$ ;  $\dpi{100} R_2= 2.7\Omega$

We know,

$\dpi{100} R_2 = R_1[1 + \alpha \Delta T]$

2.7 = 2.1[1 + $\alpha$ (100 -  27.5) ]

$\alpha$  = (2.7 - 2.1) / 2.1(100 -27.5)

$\alpha$ = 0.0039 $\dpi{80} \degree C^{-1}$

Hence, Temperature Coefficient of silver wire is 0.0039 $\dpi{80} \degree C^{-1}$

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