By what factor is the resistance of a copper wire changing when its temperature is increased from 20 degrees Celsius to 120 degrees Celsius? The temperature coefficient of resistivity for copper = 3.9 x 10^-3 (C)^-1.
To find the factor by which the resistance of a copper wire changes when its temperature is increased, we can use the temperature coefficient of resistivity. The formula for calculating the change in resistance due to temperature is:
ΔR = R0 * α * ΔT
Where:
ΔR is the change in resistance
R0 is the initial resistance
α is the temperature coefficient of resistivity
ΔT is the change in temperature.
In this case, the initial temperature is 20 degrees Celsius, the final temperature is 120 degrees Celsius, and the temperature coefficient of resistivity for copper is 3.9 x 10^(-3) (C)^(-1).
First, we need to calculate the change in temperature:
ΔT = T2 - T1
= 120 - 20
= 100 degrees Celsius
Next, we can plug the values into the formula:
ΔR = R0 * α * ΔT
To find the factor by which the resistance changes, we divide the change in resistance by the initial resistance:
Factor = (R0 + ΔR) / R0
= (R0 + (R0 * α * ΔT)) / R0
= 1 + α * ΔT
Now, we can substitute the values to calculate the factor:
Factor = 1 + (3.9 x 10^(-3)) * 100
By calculating this, we get:
Factor ≈ 1 + 0.0039 * 100
≈ 1 + 0.39
≈ 1.39
Therefore, the factor by which the resistance of the copper wire changes when its temperature is increased from 20 degrees Celsius to 120 degrees Celsius is approximately 1.39.