Phasor circuit solving for current

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Discussion Overview

The discussion revolves around solving a phasor circuit problem for current, focusing on the interaction of multiple sources and the treatment of components at different frequencies. Participants explore methods for calculating the current in a linear circuit using phasor analysis and source transformations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant converts a current source to e^(j30°) but expresses uncertainty about the next steps and questions the frequency dependency of the components.
  • Another participant suggests determining the current Ix by analyzing the circuit with one source at a time, implying that the contributions from each source can be summed directly.
  • A different viewpoint emphasizes the necessity of solving for each frequency separately and converting solutions to the time domain before combining them.
  • One participant acknowledges the cleverness of noticing resonances in the circuit and confirms the correctness of a previous answer, though it is unclear if this is universally accepted.

Areas of Agreement / Disagreement

There are multiple competing views regarding the approach to solving the circuit, particularly concerning the treatment of different frequencies and the method of combining results. The discussion remains unresolved as participants express differing strategies without reaching consensus.

Contextual Notes

Participants have not fully clarified the assumptions regarding frequency dependencies and the implications of source transformations on the overall circuit analysis.

gfd43tg
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As I am trying this problem, I convert the current source to e^(j30°). I am not sure what I should do with that. I added it to the other current source that I did a source transformation on. By the way, all the components should have the same frequency as the voltage source, right? The frequency of the current source doesn't affect the impedance of the capacitors and inductors?
 

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Here is my attempt

ImageUploadedByPhysics Forums1399361454.312838.jpg


ImageUploadedByPhysics Forums1399361474.282759.jpg
 
It's a linear circuit, so you can determine Ix due to one source (with the other source "disabled"), and then determine Ix due to the second source (after "disabling" the first).

The circuit's Ix will be the sum of those two components, which you express by simply writing a "+" sign between the two above components because they are not of the same frequency.
 
You need to solve for each frequency separately. Convert each solution into the time domain, then add in the time domain. You can't avoid converting to the time domain separately for w1 and w2 before the final addition.
 
Here is my attempt, I think he had a little trick going

ImageUploadedByPhysics Forums1399689409.371969.jpg
 
You were clever to notice the resonances of the two L-C circuits & that there is a short circuit at each frequency. And your final answer is 100% correct! Nice work.
 

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