Finding values of RLC circuit given resonance frequency

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Discussion Overview

The discussion revolves around solving for the values of resistance (R), inductance (L), and capacitance (C) in a series RLC circuit given the resonance frequency, power absorbed by the resistor, and quality factor (Q). The context includes homework-related problem-solving and mathematical reasoning.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant mentions encountering an imaginary number when solving for L and questions whether to use the real part as the answer.
  • Another participant suggests that the phasor angle of the source voltage is irrelevant and emphasizes defining the source phasor for calculations.
  • A participant points out that at resonance, the net reactance seen by the source should be considered and questions the phase angle between voltage and current.
  • There is a clarification that average power is calculated using the RMS value of the current, which does not involve an angle, implying that the inductance calculated should not have an angle either.
  • One participant expresses uncertainty about the communication of ideas and seeks clarification on their interpretation of the discussion.
  • Another participant suggests a methodical approach to determining R, L, and C, indicating that the initial assumption about R may be incorrect.
  • There is a suggestion to provide an explanation for reducing the total impedance to just R.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of the phasor angle and the approach to solving for the circuit parameters. There is no consensus on the correct method or interpretation of the calculations.

Contextual Notes

Participants have not resolved the assumptions regarding the calculations, particularly concerning the treatment of imaginary numbers and the implications of resonance on the circuit parameters.

gfd43tg
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Homework Statement


A series RLC circuit is driven by an ac source with a phasor voltage Vs = 10∠30◦ V. If the circuit resonates at 103 rad/s and the average power absorbed by the resistor at resonance is 2.5 W, determine the values of R, L, and C, given that Q = 5.

Homework Equations





The Attempt at a Solution


Hello,

As I am solving this, I am substituting into the equation for the power of the resistor using some of the parameters given in the problem statement. However, when I finally solve for L, then I end up getting an imaginary number part, 0.2∠60. Do I just use the real part as my answer, or am I doing this incorrectly?
 
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Here is my attempt

ImageUploadedByPhysics Forums1397617891.477692.jpg
 
The phasor angle attributed to the source voltage should be irrelevant; You can always define the source phasor to be the reference phasor for your calculations (unless other current or voltage phasors elsewhere in the circuit are also given so that the true reference phasor is something or somewhere else that you can't "get at" directly). So just take your source to be 10V @ 103 rad/sec.

At resonance the net reactance seen by the source is what? What does that tell you about the phase angle between the voltage and current at resonance?
 
when I finally solve for L, then I end up getting an imaginary number part, 0.2∠60.
Average power is (magnitude of current)2 * R
where you use the RMS value of the current
So current in this formula has no angle, and the inductance you calculate will not have an angle.
 
I'm not entirely sure if this is what you guys are trying to communicate to me, so here is my interpretation of what you guys are telling me in my next attempt

ImageUploadedByPhysics Forums1397719614.429544.jpg
 
Your method looks better, though I haven't checked your arithmetic.

You should give a few words' explanation why you reduced ZL + ZC + R to just R.
 
So w_0 is 10^3 rad/s, not 103 rad/s?

Anyway, start with determining R, which is already wrong.
Then L.
Then C.

Don't use current at all.
 

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