The resistance of a conductor is 6 $\Omega$ at 50°C and 7 $\Omega$ ...

Question

The resistance of a conductor is 6 $\Omega$ at 50°C and 7 $\Omega$ at 100°C. Calculate the mean temperature coefficient $\alpha$ and resistance at 0°C.

Accepted Answer

Using $R_T = R_0(1 + \alpha T)$:
$$\frac{R_{100}}{R_{50}} = \frac{1 + 100\alpha}{1 + 50\alpha} = \frac{7}{6}$$
$$6 + 600\alpha = 7 + 350\alpha \Rightarrow 250\alpha = 1$$
$$\alpha = 4 	imes 10^{-3} 	ext{ °C}^{-1}$$

Resistance at 0°C:
$$R_0 = \frac{R_{50}}{1 + 50\alpha} = \frac{6}{1 + 0.2} = \frac{6}{1.2} = 5\ \Omega$$

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