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Exercise:
A long copper wire with a negligibly thin insulation is stored as a reel 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 Remark: The air gaps between neighbouring strands of wire are neglected.
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Exercise:
A long copper wire with a negligibly thin insulation is stored as a reel 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 Remark: The air gaps between neighbouring strands of wire are neglected.
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Tags
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Difficulty
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Points
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Language
ENG (English)
Type
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Decoration
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