Exercise
https://texercises.com/exercise/partial-currents-in-parallel-circuit/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
A RO resistor and a LO inductor are connected in parallel to an ac voltage with amplitude VO. abcliste abc Calculate the total current in the circuit and the partial currents through the resistor and the inductor for a frequency of fO. Why is the total current not equal to the of the partial currents? abc Calculate the frequency for which the partial currents are equal in magnitude. What is their magnitude? abcliste

Solution:
abcliste abc The total current is given by I ItotF VtimessqrtfracR^+fracpitimesftimesL^ Itot approx resultItotP- The partial current through the resistor is I_R IRF labelcurrR fracVR IR approx resultIRP- and the partial current through the inductor I_L fracV_X_L ILF labelcurrL fracVpitimesftimesL IL approx resultILP- The partial currents are not in phase but they have a phase shift of pi/. We can verify the result for the total current as follows: I ItF sqrtIR^+IL^ ItP- abc Using s refcurrR and refcurrL we finde the following condition for the two partial currents to be equal: IRF ILF Solving for the frequency we find f fhF fracRpitimesL fh approx resultfhP abcliste
Meta Information
\(\LaTeX\)-Code
Exercise:
A RO resistor and a LO inductor are connected in parallel to an ac voltage with amplitude VO. abcliste abc Calculate the total current in the circuit and the partial currents through the resistor and the inductor for a frequency of fO. Why is the total current not equal to the of the partial currents? abc Calculate the frequency for which the partial currents are equal in magnitude. What is their magnitude? abcliste

Solution:
abcliste abc The total current is given by I ItotF VtimessqrtfracR^+fracpitimesftimesL^ Itot approx resultItotP- The partial current through the resistor is I_R IRF labelcurrR fracVR IR approx resultIRP- and the partial current through the inductor I_L fracV_X_L ILF labelcurrL fracVpitimesftimesL IL approx resultILP- The partial currents are not in phase but they have a phase shift of pi/. We can verify the result for the total current as follows: I ItF sqrtIR^+IL^ ItP- abc Using s refcurrR and refcurrL we finde the following condition for the two partial currents to be equal: IRF ILF Solving for the frequency we find f fhF fracRpitimesL fh approx resultfhP abcliste
Contained in these collections:
  1. 15 | 18

Attributes & Decorations
Branches
Circuits
Tags
ac circuit, impedance, partial current, rl parallel circuit
Content image
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration
File
Link