Transmission Line
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
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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 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
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