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Exercise:
A cable used for high-voltage transmission lines is composed of NO aluminium wires with a diameter of dO twisted together. The transmission line covers a distance of LO. abcliste abc Calculate the cable's resistance and mass. abc How many copper wires with the same dimensions are required to have a cable with the same resistance? What would be its mass? abcliste

Solution:
abcliste abc The wires are arranged in parallel. The resistance of the cable is therefore given by R sscrhoelfracLN A fracsscrhoel LNd/^ pi RF fractimesretimesLNtimesd^times pi R approx resultRP The mass can be expressed as m sscrhomass V sscrhomass N L d/^ pi mF fracRAltimesNtimesLtimesd^timespi m approx resultmS abc The asption sscRAlsscRCu can be expressed as sscrhoAlfracLsscNAl A sscrhoCufracLsscNCu A Since the length and the cross section of the aluminium and copper wires are supposed to be the same this leads to: fracsscrhoAlsscNAl fracsscrhoCusscNCu Solving for the number of copper wires leads to sscNCu NCuF Ntimesfracrcre NCu approx resultNCuP The masses fulfil the following relation: fracsscmCusscmAl fracsscNCusscrhoCusscNAlsscrhoAl The mass of the copper cable is therefore sscmCu mCuF mtimesfracNCutimesRKuNtimesRAl mCu approx resultmCuS For the same resistance copper lines would be slightly thinner but about ratioS times heavier! Copper is also much more expensive than aluminium. abcliste
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Exercise:
A cable used for high-voltage transmission lines is composed of NO aluminium wires with a diameter of dO twisted together. The transmission line covers a distance of LO. abcliste abc Calculate the cable's resistance and mass. abc How many copper wires with the same dimensions are required to have a cable with the same resistance? What would be its mass? abcliste

Solution:
abcliste abc The wires are arranged in parallel. The resistance of the cable is therefore given by R sscrhoelfracLN A fracsscrhoel LNd/^ pi RF fractimesretimesLNtimesd^times pi R approx resultRP The mass can be expressed as m sscrhomass V sscrhomass N L d/^ pi mF fracRAltimesNtimesLtimesd^timespi m approx resultmS abc The asption sscRAlsscRCu can be expressed as sscrhoAlfracLsscNAl A sscrhoCufracLsscNCu A Since the length and the cross section of the aluminium and copper wires are supposed to be the same this leads to: fracsscrhoAlsscNAl fracsscrhoCusscNCu Solving for the number of copper wires leads to sscNCu NCuF Ntimesfracrcre NCu approx resultNCuP The masses fulfil the following relation: fracsscmCusscmAl fracsscNCusscrhoCusscNAlsscrhoAl The mass of the copper cable is therefore sscmCu mCuF mtimesfracNCutimesRKuNtimesRAl mCu approx resultmCuS For the same resistance copper lines would be slightly thinner but about ratioS times heavier! Copper is also much more expensive than aluminium. abcliste
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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
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Decoration
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Link