Unendliche Kette
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
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\(\LaTeX\)
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Exercise:
Der Beginn einer unlich ausgedehnten Kette von Widerständen ist in der untenstehen Abbildung gezeigt.Bestimme den Ersatzwiderstand zwischen den Punkten a und b. Hinweis: Der Widerstand R_ab ist genauso gross wie R_a'b' also wie der Ersatzwiderstand wenn die Schaltung links von a' und b' entfernt wird. Die unliche Kette behält dabei die gleiche Struktur. centernoindent tikzpicturescale. draw to european resistor ; draw to european resistor ; draw to european resistor ; draw to european resistor ; draw - to european resistor -; draw - to european resistor -; draw - to european resistor -; draw - to european resistor -; draw to european resistor -; draw to european resistor -; draw to european resistor -; drawdashed - stealth --; drawdashed - stealth ----; filldraw circle .cm; filldraw - circle .cm; node at -. a; node at -.- b; node at . a'; node at -. b'; tikzpicture center
Solution:
Der Ersatzwiderstand von der Teil-Kette rechts von a' und b' nennen wir Rers'. Dann kann man die unliche Widerstandskette wie folgt betrachten: centernoindent tikzpicturescale. nodeabove at a; nodebelow at - b; nodeabove at a'; nodebelow at - b'; nodebelow at - Rers'; drawthick --; drawthick ----; drawthick ---; drawthick ---; tikzpicture center Der Abbildung entsprech ist der Ersatzwiderstand der ganzen Kette Rers R + underbracefracR + fracRers'_mathrmParallelschaltung + R R + fracRRers'R+Rers'. Weil die Widerstandskette unlich lang ist spielt es keine Rolle ob sie bei a/b oder a'/b' nt. Also ist RersRers'. Die obige Beziehung wird dadurch zu Rers^ -RRers - R^. Diese quadratische Gleichung hat nur eine positive Lösung negative Widerstände machen physikalisch keinen Sinn. Sie ist Rers+sqrtR.
Der Beginn einer unlich ausgedehnten Kette von Widerständen ist in der untenstehen Abbildung gezeigt.Bestimme den Ersatzwiderstand zwischen den Punkten a und b. Hinweis: Der Widerstand R_ab ist genauso gross wie R_a'b' also wie der Ersatzwiderstand wenn die Schaltung links von a' und b' entfernt wird. Die unliche Kette behält dabei die gleiche Struktur. centernoindent tikzpicturescale. draw to european resistor ; draw to european resistor ; draw to european resistor ; draw to european resistor ; draw - to european resistor -; draw - to european resistor -; draw - to european resistor -; draw - to european resistor -; draw to european resistor -; draw to european resistor -; draw to european resistor -; drawdashed - stealth --; drawdashed - stealth ----; filldraw circle .cm; filldraw - circle .cm; node at -. a; node at -.- b; node at . a'; node at -. b'; tikzpicture center
Solution:
Der Ersatzwiderstand von der Teil-Kette rechts von a' und b' nennen wir Rers'. Dann kann man die unliche Widerstandskette wie folgt betrachten: centernoindent tikzpicturescale. nodeabove at a; nodebelow at - b; nodeabove at a'; nodebelow at - b'; nodebelow at - Rers'; drawthick --; drawthick ----; drawthick ---; drawthick ---; tikzpicture center Der Abbildung entsprech ist der Ersatzwiderstand der ganzen Kette Rers R + underbracefracR + fracRers'_mathrmParallelschaltung + R R + fracRRers'R+Rers'. Weil die Widerstandskette unlich lang ist spielt es keine Rolle ob sie bei a/b oder a'/b' nt. Also ist RersRers'. Die obige Beziehung wird dadurch zu Rers^ -RRers - R^. Diese quadratische Gleichung hat nur eine positive Lösung negative Widerstände machen physikalisch keinen Sinn. Sie ist Rers+sqrtR.
Meta Information
Exercise:
Der Beginn einer unlich ausgedehnten Kette von Widerständen ist in der untenstehen Abbildung gezeigt.Bestimme den Ersatzwiderstand zwischen den Punkten a und b. Hinweis: Der Widerstand R_ab ist genauso gross wie R_a'b' also wie der Ersatzwiderstand wenn die Schaltung links von a' und b' entfernt wird. Die unliche Kette behält dabei die gleiche Struktur. centernoindent tikzpicturescale. draw to european resistor ; draw to european resistor ; draw to european resistor ; draw to european resistor ; draw - to european resistor -; draw - to european resistor -; draw - to european resistor -; draw - to european resistor -; draw to european resistor -; draw to european resistor -; draw to european resistor -; drawdashed - stealth --; drawdashed - stealth ----; filldraw circle .cm; filldraw - circle .cm; node at -. a; node at -.- b; node at . a'; node at -. b'; tikzpicture center
Solution:
Der Ersatzwiderstand von der Teil-Kette rechts von a' und b' nennen wir Rers'. Dann kann man die unliche Widerstandskette wie folgt betrachten: centernoindent tikzpicturescale. nodeabove at a; nodebelow at - b; nodeabove at a'; nodebelow at - b'; nodebelow at - Rers'; drawthick --; drawthick ----; drawthick ---; drawthick ---; tikzpicture center Der Abbildung entsprech ist der Ersatzwiderstand der ganzen Kette Rers R + underbracefracR + fracRers'_mathrmParallelschaltung + R R + fracRRers'R+Rers'. Weil die Widerstandskette unlich lang ist spielt es keine Rolle ob sie bei a/b oder a'/b' nt. Also ist RersRers'. Die obige Beziehung wird dadurch zu Rers^ -RRers - R^. Diese quadratische Gleichung hat nur eine positive Lösung negative Widerstände machen physikalisch keinen Sinn. Sie ist Rers+sqrtR.
Der Beginn einer unlich ausgedehnten Kette von Widerständen ist in der untenstehen Abbildung gezeigt.Bestimme den Ersatzwiderstand zwischen den Punkten a und b. Hinweis: Der Widerstand R_ab ist genauso gross wie R_a'b' also wie der Ersatzwiderstand wenn die Schaltung links von a' und b' entfernt wird. Die unliche Kette behält dabei die gleiche Struktur. centernoindent tikzpicturescale. draw to european resistor ; draw to european resistor ; draw to european resistor ; draw to european resistor ; draw - to european resistor -; draw - to european resistor -; draw - to european resistor -; draw - to european resistor -; draw to european resistor -; draw to european resistor -; draw to european resistor -; drawdashed - stealth --; drawdashed - stealth ----; filldraw circle .cm; filldraw - circle .cm; node at -. a; node at -.- b; node at . a'; node at -. b'; tikzpicture center
Solution:
Der Ersatzwiderstand von der Teil-Kette rechts von a' und b' nennen wir Rers'. Dann kann man die unliche Widerstandskette wie folgt betrachten: centernoindent tikzpicturescale. nodeabove at a; nodebelow at - b; nodeabove at a'; nodebelow at - b'; nodebelow at - Rers'; drawthick --; drawthick ----; drawthick ---; drawthick ---; tikzpicture center Der Abbildung entsprech ist der Ersatzwiderstand der ganzen Kette Rers R + underbracefracR + fracRers'_mathrmParallelschaltung + R R + fracRRers'R+Rers'. Weil die Widerstandskette unlich lang ist spielt es keine Rolle ob sie bei a/b oder a'/b' nt. Also ist RersRers'. Die obige Beziehung wird dadurch zu Rers^ -RRers - R^. Diese quadratische Gleichung hat nur eine positive Lösung negative Widerstände machen physikalisch keinen Sinn. Sie ist Rers+sqrtR.
Contained in these collections:
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Ersatzwiderstand 2 by uz
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Kette von Widerständen by TeXercises