What is the resonance frequency expression for a parallel RLC circuit?

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Discussion Overview

The discussion revolves around the resonance frequency expression for a parallel RLC circuit, comparing it to the expression for a series RLC circuit. Participants explore whether the resonance frequencies are the same or differ, and under what conditions this might occur.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant states the resonance frequency for a series RLC circuit is given by w = 1/√(LC) and questions if the same applies to a parallel RLC circuit.
  • Another participant suggests that the resonance frequencies are generally the same because the reactances of L and C must cancel in both configurations.
  • Contrarily, a different participant argues that the resonance frequency should not be the same and references a source that provides a different expression for the parallel circuit.
  • One participant introduces the idea that the circuit can be viewed as both series and parallel under certain conditions, leading to different expressions for resonance depending on the perspective taken.
  • A participant mentions a specific equation involving component resistances that could lead to a different resonance condition.

Areas of Agreement / Disagreement

Participants express differing views on whether the resonance frequency expressions for series and parallel RLC circuits are the same. There is no consensus, and multiple competing perspectives remain in the discussion.

Contextual Notes

Participants reference specific conditions and assumptions regarding component resistances and circuit configurations, but these are not fully resolved within the discussion.

yxgao
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What is the resonance frequency expression for a parallel RLC circuit?

I know that for a series RLC circuit, it is:
<br /> w=\frac{1}{\sqrt{LC}}<br />

Is it the same for a parallel RLC circuit? I remember reading somewhere that it was not exactly the same, although it approaches the series RLC expression in a certain limit. What is this limit?

Thanks!
YG
 
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In general it will be precisely the same because in both instances the reactances of the L and the C must cancel -- in the series circuit jwL + 1/(jwC) = 0
( sum of reactive impedances )
in the parallel circuit 1/(jwL) + jwC = 1/infinity = 0 ( sum of admittances )
they result in the same thing.
If for an instant you put R=0 (series ), or r=infin ( parallel ) then you can see that such a circuit is BOTH series and parallel.
My guess is that Integral got out the wrong side of the bed this morning, but has invested in Google.
Ray.
 
It shouldn't be the same, I don't think. If you read through the site Integral provided, it gives the form for the parallel circuit, which is slightly different, right?
 
For the circuit given with individual component resistances ( I was thinking of a simpler circuit) there is difference depending on your view. The circuit is both series and parallel at the same time ( the source impedance is infinite ). The impedance is minimal and of zero rectance as per your equation looking around the series loop.
However from the source viewpoint that is not the case except for r's very small
The expression for resonance ( meaning infinite parallel reactance is
w^2 .L . C = r1/r2 so if r1=r2 the equation is the same.
Ps I may have the r1,r2 reversed but you get the idea.
Ray
 
Final answer

attached is the simple analysis showing the error or ratio of resonances.
Ray
 

Attachments

  • SerPar.jpg
    SerPar.jpg
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Thanks! I really appreciate it!




\lambda



\mu
 

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