Exercise
https://mathematikaufgaben.ch/exercise/transmission-line
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video for this exercise has yet been created.

Visit our YouTube-Channel to see solutions for other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
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 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
Report An Error
You are on mathematikaufgaben.ch.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
Meta Information
\(\LaTeX\)-Code
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 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
Contained in these collections:
  1. 10 | 10

Attributes & Decorations
Branches Direct Current
Tags resistance, resistivity
Content image
Difficulty
(2, default)
Points
0 (default)
Language ENG (English)
Type Calculative / Quantity
Creator by
Decoration