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Temperature Coefficient of Resistance
10 questions By Tony R. Kuphaldt
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Question 7 of 10
A length of copper wire (α = 0.004041 at 20o 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 50o C, and calculate what the resistance of the wire should go to if it cools back down to 20o 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!
Reveal answerR50o C = 5.606 Ω
If you got an answer of R20o C = 4.927 Ω for the second calculation, you made a common mistake that is not always warned against in textbooks! Try the math again. If you got the proper answer of 5 Ω upon doing the second calculation, try to figure out why someone may have calculated 4.927 Ω taking the temperature from 50o C down to 20o C.
Notes:One thing students need to learn is they can’t simply use the resistance-temperature formula as it is normally given if the “reference” (starting) temperature is not the same as the temperature at which α is specified at!
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Question 8 of 10
Calculate the resistance of each of these specimens, given their resistance at the reference temperature (Rr @ Tr), and their present temperatures (T):
- • Specimen 1: Copper ; Rr = 200 Ω @ Tr = 20oC ; T = 45oC ; RT =
- • Specimen 2: Copper ; Rr = 10 kΩ @ Tr = 20oC ; T = 5oC ; RT =
- • Specimen 3: Aluminum ; Rr = 1,250 Ω @ Tr = 20oC ; T = 100oC ; RT =
- • Specimen 4: Iron ; Rr = 35.4 Ω @ Tr = 20oC ; T = −40oC ; RT =
- • Specimen 5: Nickel ; Rr = 525 Ω @ Tr = 20oC ; T = 70oC ; RT =
- • Specimen 6: Gold ; Rr = 25 kΩ @ Tr = 20oC ; T = 65oC ; RT =
- • Specimen 7: Tungsten ; Rr = 2.2 kΩ @ Tr = 20oC ; T = −10oC ; RT =
- • Specimen 8: Copper ; Rr = 350 Ω @ Tr = 10oC ; T = 35oC ; RT =
- • Specimen 9: Copper ; Rr = 1.5 kΩ @ Tr = −25oC ; T = −5oC ; RT =
- • Specimen 10: Silver ; Rr = 3.5 MΩ @ Tr = 45oC ; T = 10oC ; RT =
Reveal answer- • Specimen 1: RT = 220.2 Ω
- • Specimen 2: RT = 9.394 kΩ
- • Specimen 3: RT = 1.681 kΩ
- • Specimen 4: RT = 23.35 Ω
- • Specimen 5: RT = 679 Ω
- • Specimen 6: RT = 29.18 kΩ
- • Specimen 7: RT = 1.909 kΩ
- • Specimen 8: RT = 386.8 Ω
- • Specimen 9: RT = 1.648 kΩ
- • Specimen 10: RT = 3.073 MΩ
Notes:Students may find difficulty obtaining the proper answers for the last three specimens (8, 9, and 10). The key to performing calculations correctly on these is the assumed temperature at which the α figure is given for each metal type. This reference temperature may not be the same as the reference temperature given in the question!
Here are the α values I used in my calculations, all at a reference temperature of 20o Celsius:
- • Copper = 0.004041
- • Aluminum = 0.004308
- • Iron = 0.005671
- • Nickel = 0.005866
- • Gold = 0.003715
- • Tungsten = 0.004403
- • Silver = 0.003819
Your students’ sources may vary a bit from these figures.
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Question 9 of 10
A spool of #10 AWG aluminum wire is 500 feet long. If the ambient temperature is 80o F, what is its end-to-end electrical resistance? Explain all the calculations necessary to solve this problem.
Reveal answer0.7899 Ω
Notes:Solving this problem requires several concepts be integrated: calculating the resistance of a wire given its metal type, length, and gauge; converting between different temperature units; and calculating shift in resistance due to temperature.
