RLC Series Circuit
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 tablecolumn... 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 "inbetween" solution, i.e. no algebraic equation needed. Example exercise
Level 3  "Chaincomputations" 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 "inbetween" 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 tablecolumn... 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 "inbetween" solution, i.e. no algebraic equation needed. Example exercise
Level 3  "Chaincomputations" 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 "inbetween" results. Example exercise
Level 5 
Level 6 
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Exercise:
The impedance of a circuit with a CO capacitor and a LO inductor connected in series to a voltage signal with amplitude VO and frequency fO is measured to be ZO. Calculate the circuit's resistance and the amplitudes of the voltage signals across the capacitor and the inductor.
Solution:
The impedance of an ac series circuit is given by Z sqrtR^+leftomega Lfracomega Cright^ Solving for the resistance leads to R RF sqrtZ^leftpitimesftimesLfracpitimesftimesCright^ R approx resultRP The partial voltage across the capacitor is V_C X_C I_ fracpi f CfracV_Z VCF fracVpitimesftimesCtimesZ VC approx resultVCP The partial voltage across the inductor is V_L X_L I_ VLF pitimesftimesLfracVZ VL approx resultVLP Both partial voltages are greater than the applied voltage. This is possible since the phasors for the partial voltages are in em antiphase i.e. the phase shift between them is pi/ and they partially cancel each other.
The impedance of a circuit with a CO capacitor and a LO inductor connected in series to a voltage signal with amplitude VO and frequency fO is measured to be ZO. Calculate the circuit's resistance and the amplitudes of the voltage signals across the capacitor and the inductor.
Solution:
The impedance of an ac series circuit is given by Z sqrtR^+leftomega Lfracomega Cright^ Solving for the resistance leads to R RF sqrtZ^leftpitimesftimesLfracpitimesftimesCright^ R approx resultRP The partial voltage across the capacitor is V_C X_C I_ fracpi f CfracV_Z VCF fracVpitimesftimesCtimesZ VC approx resultVCP The partial voltage across the inductor is V_L X_L I_ VLF pitimesftimesLfracVZ VL approx resultVLP Both partial voltages are greater than the applied voltage. This is possible since the phasors for the partial voltages are in em antiphase i.e. the phase shift between them is pi/ and they partially cancel each other.
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Exercise:
The impedance of a circuit with a CO capacitor and a LO inductor connected in series to a voltage signal with amplitude VO and frequency fO is measured to be ZO. Calculate the circuit's resistance and the amplitudes of the voltage signals across the capacitor and the inductor.
Solution:
The impedance of an ac series circuit is given by Z sqrtR^+leftomega Lfracomega Cright^ Solving for the resistance leads to R RF sqrtZ^leftpitimesftimesLfracpitimesftimesCright^ R approx resultRP The partial voltage across the capacitor is V_C X_C I_ fracpi f CfracV_Z VCF fracVpitimesftimesCtimesZ VC approx resultVCP The partial voltage across the inductor is V_L X_L I_ VLF pitimesftimesLfracVZ VL approx resultVLP Both partial voltages are greater than the applied voltage. This is possible since the phasors for the partial voltages are in em antiphase i.e. the phase shift between them is pi/ and they partially cancel each other.
The impedance of a circuit with a CO capacitor and a LO inductor connected in series to a voltage signal with amplitude VO and frequency fO is measured to be ZO. Calculate the circuit's resistance and the amplitudes of the voltage signals across the capacitor and the inductor.
Solution:
The impedance of an ac series circuit is given by Z sqrtR^+leftomega Lfracomega Cright^ Solving for the resistance leads to R RF sqrtZ^leftpitimesftimesLfracpitimesftimesCright^ R approx resultRP The partial voltage across the capacitor is V_C X_C I_ fracpi f CfracV_Z VCF fracVpitimesftimesCtimesZ VC approx resultVCP The partial voltage across the inductor is V_L X_L I_ VLF pitimesftimesLfracVZ VL approx resultVLP Both partial voltages are greater than the applied voltage. This is possible since the phasors for the partial voltages are in em antiphase i.e. the phase shift between them is pi/ and they partially cancel each other.
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