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Specific Resistance of Conductors
15 questions By Tony R. Kuphaldt
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Question 4 of 15
Write a single equation relating the resistance, specific resistance, length, and cross-sectional area of an electrical conductor together.
Reveal answerR = ρ l AWhere,
R = Resistance, measured along the conductor’s length
ρ = Specific resistance of the substance
l = Length of the conductor
A = Cross-sectional area of the conductor
Follow-up question: algebraically manipulate this equation to solve for length (l) instead of solving for resistance (R) as shown.
Notes:A beneficial exercise to do with your students is to analyze this equation (and in fact, any equation) qualitatively instead of just quantitatively. Ask students what will happen to R if ρ increases, or if l decreases, or if A decreases. Many students find this a more challenging problem than working with real numbers, because they cannot use their calculators to give them qualitative answers (unless they enter random numbers into the equation, then change one of those numbers and re-calculate - but that is twice the work of solving the equation with one set of numbers, once!).
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Question 5 of 15
Examine the following specific resistance table for various metals:
Metal type ρ in Ω · cmil / ft @ 32oF ρ in Ω · cmil / ft @ 75oF
Zinc (very pure) 34.595 37.957
Tin (pure) 78.489 86.748
Copper (pure annealed) 9.390 10.351
Copper (hard-drawn) 9.810 10.745
Copper (annealed) 9.590 10.505
Platinum (pure) 65.670 71.418
Silver (pure annealed) 8.831 9.674
Nickel 74.128 85.138
Steel (wire) 81.179 90.150
Iron (approx. pure) 54.529 62.643
Gold (99.9 % pure) 13.216 14.404
Aluminum (99.5 % pure) 15.219 16.758
Of the metals shown, which is the best conductor of electricity? Which is the worst? What do you notice about the resistivity of these metals as temperature is increased from 32oF to 75 oF?Reveal answerHere is the same table, the order re-arranged to show resistivity from least to greatest:
Metal type ρ in Ω · cmil / ft @ 32oF ρ in Ω · cmil / ft @ 75oF
Silver (pure annealed) 8.831 9.674
Copper (pure annealed) 9.390 10.351
Copper (annealed) 9.590 10.505
Copper (hard-drawn) 9.810 10.745
Gold (99.9 % pure) 13.216 14.404
Aluminum (99.5 % pure) 15.219 16.758
Zinc (very pure) 34.595 37.957
Iron (approx. pure) 54.529 62.643
Platinum (pure) 65.670 71.418
Nickel 74.128 85.138
Tin (pure) 78.489 86.748
Steel (wire) 81.179 90.150
Notes:The data for this table was taken from table 1-97 of the American Electrician’s Handbook (eleventh edition) by Terrell Croft and Wilford Summers.
It may come as a surprise to some students to find that gold is actually a worse conductor of electricity than copper, but the data doesn’t lie! Silver is actually the best, but gold is chosen for a lot of microelectronic applications because of its resistance to oxidation.
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Question 6 of 15
What is the electrical resistance of a 12-gauge copper wire, 500 feet long, at room temperature?
Reveal answerWire resistance = 0.7726 Ω
Notes:Ask your students to share their sources for data: values of ρ, cross-sectional area, etc.
