A length of copper wire (α=0,004041 at 20°C) has a resistance of 5 ohms at 20°C. Calculate its resistance if the temperature were to increase to 50°C.
To calculate the resistance of the copper wire at 50°C, you can use the formula for resistance change with temperature:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R1 = Resistance at the initial temperature (20°C) = 5 ohms
α = Temperature coefficient of resistance for copper = 0.004041
T1 = Initial temperature = 20°C
T2 = Final temperature = 50°C
Substituting these values into the formula:
R2 = 5 ohms * (1 + 0.004041 * (50°C - 20°C))
R2 = 5 ohms * (1 + 0.004041 * 30°C)
R2 = 5 ohms * (1 + 0.12123)
R2 = 5 ohms * 1.12123
R2 ≈ 5.61 ohms
Therefore, the resistance of the copper wire would be approximately 5.61 ohms at 50°C.