Question

A copper wire has a resistance of 2.0 ohm at 0C and 2.26 ohm at 30C. What is the resistance at 50C?

Answer 1

Question #55653, Physics / Electric Circuits |

A copper wire has a resistance of 2.0 ohm at 0C and 2.26 ohm at 30C. What is the resistance at 50C?

Answer:

The resistance of the copper wire is defined by the equation:

$R_{1} = R_{0}(1 + \alpha [T_{1} - T_{0}])$ , where $R_{1}, T_{1}$ – the final resistance and temperature, $R_{0}, T_{0}$ – the initial resistance and temperature and $\alpha$ – the temperature coefficient for copper.

Using data for the resistances at $0\mathrm{C}^0$ and $30\mathrm{C}^0$ , the temperature coefficient of resistance for copper can be found:

2.26 ohm = 2.0 ohm(1 + $\alpha [30\mathrm{C}^0 -0\mathrm{C}^0 ]$

2.26 ohm = 2.0 ohm + 30α

$\alpha = 0.26 / (30 C^{0}) = 8.7 \times 10^{-3} (C^{0})^{-1}$

Thus, the resistance at $50\mathrm{C}^0$ is:

(The initial temperature and resistance are $30\mathrm{C}^0$ and 2.26 ohm, respectively.)

$R_{1} = 2.26$ ohm $\times (1 + 8.7 \times 10^{-3} (C^{0})^{-1} [50 C^{0} - 30 C^{0}]) = 2.65$ omh

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