Question

A coil of wire has a resistance of
25.0Ω
at
20oC
and a resistance of
25.1Ω
at 35
oC
What is its temperature coefficient of of resistance?

Answer 1

Answer on Question #46034, Physics, Electromagnetism

A coil of wire has a resistance of $25.0\Omega$ at $20{}^{\circ}C$ and a resistance of $25.1\Omega$ at $35{}^{\circ}C$ What is its temperature coefficient of resistance?

Resistance of wire depends on temperature by equation:

$$R _ {T} = R _ {T _ {0}} (1 + \alpha \Delta T)$$

Where $\alpha$ – is temperature coefficient of resistance, $\Delta T$ – temperature difference.

From this equation we can find temperature coefficient of resistance:

$$\alpha = \left(\frac {R _ {T}}{R _ {T _ {0}}} - 1\right) \frac {1}{\Delta T}$$ $$\alpha = \left(\frac {25.1\ \mathrm{Ohm}}{25.0\ \mathrm{Ohm}} - 1\right) \frac {1}{15\ K} \approx 2.7 \cdot 10 ^ {- 4}\ K ^ {- 1}$$

Answer: temperature coefficient of resistance $\alpha \approx 2.7\cdot 10^{-4}K^{-1}$

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