Complex analysis in electrical circuits

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Discussion Overview

The discussion revolves around the application of complex analysis in electrical circuits, particularly in the context of alternating current and complex impedance. Participants explore how complex numbers and exponential functions relate to circuit analysis, especially regarding oscillations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the use of complex analysis in electrical circuits, seeking clarification on the topic.
  • Another participant mentions alternating current as a relevant concept.
  • A link is provided to a resource discussing alternating current.
  • Complex impedance is introduced as a general concept related to the discussion.
  • One participant explains that complex numbers can simplify the analysis of oscillations, referencing the relationship e^iwt = Cos(wt) + iSin(wt) and suggesting that voltage expressions can be represented as the real part of a complex number.

Areas of Agreement / Disagreement

Participants have not reached a consensus, as the initial inquiry remains open-ended and several concepts are introduced without definitive agreement on their implications or applications.

Contextual Notes

The discussion does not clarify specific assumptions about the level of understanding of complex analysis among participants, nor does it resolve the mathematical steps involved in applying complex numbers to electrical circuits.

nhmllr
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When discussing the i (the imaginary unit) in a math class, my math teacher commented that that complex analysis is used in studying electrical circuits. I know a little about resistors and what not, but never have I seen complex analysis used this way. I've tried looking it up, but it's been fruitless. Has anybody else heard of this? What was he talking about?

Thanks.
 
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Alternating current
 
clem said:
Alternating current

Ah. http://openbookproject.net/electricCircuits/AC/AC_2.html
 
In general, complex impedance.
 
This is a useful application in physics dealing with oscillations.
In analyzing complex numbers it is possible to show a relationship
e^iwt = Cos(wt) + iSin(wt)
This means that a physics expression such as V = VoCos(wt) can be written as the real part of a complex number Vo x e^iwt
Doing this means that you are dealing with exponential functions rather than Cosine and sine functions ...it is easier
 

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