Variable Resistor
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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Exercise:
A fixed resistor R and a variable resistor R_v are connected in series to a voltage supply Delta V. abcliste abc Derive a formal expression for the power dissipated in the variable resistor. abc Show that the power dissipated in the variable resistor is greatest for R_v R. abcliste
Solution:
abcliste abc The power dissipated in the varialbe resistor can be expressed as P_v R_v I^ R_vleftfracDelta VR+R_vright^ abc In order to find the maximum we can derive P_v with respect to R_v using the product rule: fracddP_vddR_v leftfracDelta VR+R_vright^ - R_vfracleftDelta Vright^leftR+R_vright^ At the maximum this expression has to be equal to zero: fracleftDelta Vright^leftR+R_vright^ - R_vfracleftDelta Vright^leftR+R_vright^ Rearranging the terms multiplying by R+R_v^ and dividing by Delta V^ leads to R_v R+R_v The solution R_vR easily follows from this. abcliste
A fixed resistor R and a variable resistor R_v are connected in series to a voltage supply Delta V. abcliste abc Derive a formal expression for the power dissipated in the variable resistor. abc Show that the power dissipated in the variable resistor is greatest for R_v R. abcliste
Solution:
abcliste abc The power dissipated in the varialbe resistor can be expressed as P_v R_v I^ R_vleftfracDelta VR+R_vright^ abc In order to find the maximum we can derive P_v with respect to R_v using the product rule: fracddP_vddR_v leftfracDelta VR+R_vright^ - R_vfracleftDelta Vright^leftR+R_vright^ At the maximum this expression has to be equal to zero: fracleftDelta Vright^leftR+R_vright^ - R_vfracleftDelta Vright^leftR+R_vright^ Rearranging the terms multiplying by R+R_v^ and dividing by Delta V^ leads to R_v R+R_v The solution R_vR easily follows from this. abcliste
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Exercise:
A fixed resistor R and a variable resistor R_v are connected in series to a voltage supply Delta V. abcliste abc Derive a formal expression for the power dissipated in the variable resistor. abc Show that the power dissipated in the variable resistor is greatest for R_v R. abcliste
Solution:
abcliste abc The power dissipated in the varialbe resistor can be expressed as P_v R_v I^ R_vleftfracDelta VR+R_vright^ abc In order to find the maximum we can derive P_v with respect to R_v using the product rule: fracddP_vddR_v leftfracDelta VR+R_vright^ - R_vfracleftDelta Vright^leftR+R_vright^ At the maximum this expression has to be equal to zero: fracleftDelta Vright^leftR+R_vright^ - R_vfracleftDelta Vright^leftR+R_vright^ Rearranging the terms multiplying by R+R_v^ and dividing by Delta V^ leads to R_v R+R_v The solution R_vR easily follows from this. abcliste
A fixed resistor R and a variable resistor R_v are connected in series to a voltage supply Delta V. abcliste abc Derive a formal expression for the power dissipated in the variable resistor. abc Show that the power dissipated in the variable resistor is greatest for R_v R. abcliste
Solution:
abcliste abc The power dissipated in the varialbe resistor can be expressed as P_v R_v I^ R_vleftfracDelta VR+R_vright^ abc In order to find the maximum we can derive P_v with respect to R_v using the product rule: fracddP_vddR_v leftfracDelta VR+R_vright^ - R_vfracleftDelta Vright^leftR+R_vright^ At the maximum this expression has to be equal to zero: fracleftDelta Vright^leftR+R_vright^ - R_vfracleftDelta Vright^leftR+R_vright^ Rearranging the terms multiplying by R+R_v^ and dividing by Delta V^ leads to R_v R+R_v The solution R_vR easily follows from this. abcliste
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| Internal Resistance | tags |
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| Ammeter | tags |
| Variable Resistor | title |
| Range Extension | tags |
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