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https://texercises.com/exercise/roll-of-wire/
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Exercise:
A long copper wire with a negligibly thin insulation is stored as a roll with a mass of mO. The resistance between the s of the wire is RO. How long is the wire?

Solution:
The volume of the wire can be expressed as V fracmsscrhomassA L labeleq The cross section A can be expressed in terms of the wire's resistance R length L and the resistivity sscrhoel: A fracsscrhoel LR labeleq Be aware that the density sscrhomass and the resistivity sscrhoel are two different quantities! Combining s refeq and refeq we find V fracmsscrhomassfracsscrhoel LR L fracsscrhoel L^R Solving for the length L leads to L lengthF sqrtfracmtimesRrmtimesre length approx resultlengthP
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Exercise:
A long copper wire with a negligibly thin insulation is stored as a roll with a mass of mO. The resistance between the s of the wire is RO. How long is the wire?

Solution:
The volume of the wire can be expressed as V fracmsscrhomassA L labeleq The cross section A can be expressed in terms of the wire's resistance R length L and the resistivity sscrhoel: A fracsscrhoel LR labeleq Be aware that the density sscrhomass and the resistivity sscrhoel are two different quantities! Combining s refeq and refeq we find V fracmsscrhomassfracsscrhoel LR L fracsscrhoel L^R Solving for the length L leads to L lengthF sqrtfracmtimesRrmtimesre length approx resultlengthP
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Attributes & Decorations
Branches
Direct Current
Tags
resistance, resistivity
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Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration
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Link