If the resistance of copper wire at freezing (0°C) is 30 ohm, what is its resistance at -40°C?
The resistance of a material is known to change with temperature. The resistance of copper wire increases with decreasing temperature. Generally, the resistance of most metals approximately doubles for every 10 degrees Celsius decrease in temperature.
To find the resistance at -40°C, we can use the formula:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R2 = Resistance at -40°C
R1 = Resistance at 0°C
α = Temperature coefficient of resistance (constant for a material)
T2 = Final temperature (-40°C)
T1 = Initial temperature (0°C)
The temperature coefficient of resistance for copper is approximately 0.00404 per °C.
Plugging in the values:
R2 = 30 ohm * (1 + 0.00404 * (-40°C - 0°C))
R2 = 30 ohm * (1 + 0.00404 * (-40°C))
R2 = 30 ohm * (1 + (-0.1616))
R2 = 30 ohm * 0.8384
R2 ≈ 25.15 ohm
Therefore, the resistance of copper wire at -40°C is approximately 25.15 ohm.