By what factor is the resistance of a copper wire changed when its temperature is increased from 20¢ªC to 120¢ªC? (the temperature coefficient of resistivity for copper = 3.9 ¢¥ 10‑3/C¢ª)
To calculate the change in resistance of a copper wire when its temperature is increased, we can use the formula:
ΔR = R_initial * α * ΔT
Where:
ΔR is the change in resistance,
R_initial is the initial resistance,
α is the temperature coefficient of resistivity, and
ΔT is the change in temperature.
In this case, we want to find the factor by which the resistance changes, so we can rewrite the formula as:
Resistance factor = (R_final - R_initial) / R_initial
We are given that the initial temperature is 20°C and the final temperature is 120°C. The temperature coefficient of resistivity for copper is 3.9 × 10^-3/°C.
Step 1: Calculate the change in temperature (ΔT):
ΔT = T_final - T_initial
ΔT = 120°C - 20°C
ΔT = 100°C
Step 2: Calculate the change in resistance (ΔR):
ΔR = R_initial * α * ΔT
ΔR = R_initial * (3.9 × 10^-3/°C) * 100°C
Step 3: Calculate the final resistance (R_final):
R_final = R_initial + ΔR
Step 4: Calculate the resistance factor:
Resistance factor = (R_final - R_initial) / R_initial
By following these steps with the given values, you can find the factor by which the resistance of the copper wire changes when its temperature increases from 20°C to 120°C.