Temperature Coefficient of Resistance
Basic Electricity
An electronics instructor wants to demonstrate to his students the effect of electrical resistance changing with temperature. To do this, he selects a carbon resistor about 3 centimeters in length and 5 millimeters in diameter, black in color, with a wire at each end, and connects it to an ohmmeter. Whenever he grasps the resistor between his fingers, the ohmmeter instantly responds by showing a greatly reduced resistance.
What is wrong with this experiment?
If we were to plug an electric saw into a very long extension cord, and then plug the other end of the cord into a power receptacle, we would notice a decreased level of performance from the saw, as compared with how it performs when directly plugged into the same receptacle (with no extension cord).
Determine if the saw’s performance becomes better or worse as the ambient temperature increases, and explain your answer.
The electrical resistance of a conductor at any temperature may be calculated by the following equation:

Where,
R_{T} = Resistance of conductor at temperature T
R_{r} = Resistance of conductor at reference temperature T_{r}
α = Temperature coefficient of resistance at reference temperature T_{r}
Simplify this equation by means of factoring.
A length of copper wire (α = 0.004041 at 20^{o} C) has a resistance of 5 ohms at 20 degrees Celsius. Calculate its resistance if the temperature were to increase to 50 degrees Celsius.
Now, take that calculated resistance, and that new temperature of 50^{o} C, and calculate what the resistance of the wire should go to if it cools back down to 20^{o} C. Treat this as a separate problem, working through all the calculations, and don’t just say “5 ohms” because you know the original conditions!
Calculate the resistance of each of these specimens, given their resistance at the reference temperature (R_{r} @ T_{r}), and their present temperatures (T):
 • Specimen 1: Copper ; R_{r} = 200 Ω @ T_{r} = 20^{o}C ; T = 45^{o}C ; R_{T} =
 • Specimen 2: Copper ; R_{r} = 10 kΩ @ T_{r} = 20^{o}C ; T = 5^{o}C ; R_{T} =
 • Specimen 3: Aluminum ; R_{r} = 1,250 Ω @ T_{r} = 20^{o}C ; T = 100^{o}C ; R_{T} =
 • Specimen 4: Iron ; R_{r} = 35.4 Ω @ T_{r} = 20^{o}C ; T = −40^{o}C ; R_{T} =
 • Specimen 5: Nickel ; R_{r} = 525 Ω @ T_{r} = 20^{o}C ; T = 70^{o}C ; R_{T} =
 • Specimen 6: Gold ; R_{r} = 25 kΩ @ T_{r} = 20^{o}C ; T = 65^{o}C ; R_{T} =
 • Specimen 7: Tungsten ; R_{r} = 2.2 kΩ @ T_{r} = 20^{o}C ; T = −10^{o}C ; R_{T} =
 • Specimen 8: Copper ; R_{r} = 350 Ω @ T_{r} = 10^{o}C ; T = 35^{o}C ; R_{T} =
 • Specimen 9: Copper ; R_{r} = 1.5 kΩ @ T_{r} = −25^{o}C ; T = −5^{o}C ; R_{T} =
 • Specimen 10: Silver ; R_{r} = 3.5 MΩ @ T_{r} = 45^{o}C ; T = 10^{o}C ; R_{T} =
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