Series and parallel R-L-C turned circuits

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Discussion Overview

The discussion revolves around a homework problem involving a parallel R-L-C circuit. Participants are tasked with determining the resonant frequency, dynamic resistance, current resonance, and Q-factor at resonance for a circuit comprising a coil with inductance and resistance connected in parallel with a capacitor. The scope includes mathematical reasoning and technical explanations related to circuit analysis.

Discussion Character

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

Main Points Raised

  • One participant asks for help with the problem, specifically regarding the resonant frequency, dynamic resistance, current resonance, and Q-factor.
  • Another participant inquires if a schematic has been drawn and seeks clarification on the concept of resonant frequency.
  • Participants discuss the resonant frequency equation, suggesting it as fr = 1 / 2∏√(LC), while questioning the value of capacitance (C) given as 20 μF.
  • There is uncertainty about the term 'dynamic resistance,' with one participant suggesting it may refer to the real component of impedance or the derivative of voltage with respect to current.
  • One participant expresses that the problem is complex, particularly noting that the current resonance is distinct from the resonant frequency.
  • Another participant confirms the value of C as 20 μF and discusses dynamic resistance in relation to dynamic impedance.
  • There is a correction regarding the resonant frequency equation, indicating that it is an approximation for ideal circuits and that practical circuits require a more precise determination.

Areas of Agreement / Disagreement

Participants generally agree on the value of the capacitance as 20 μF and the form of the resonant frequency equation, but there is disagreement regarding the interpretation of dynamic resistance and the complexity of the problem. The discussion remains unresolved with multiple competing views on the definitions and calculations involved.

Contextual Notes

Participants express uncertainty about specific terms and calculations, particularly regarding dynamic resistance and the implications of resistance in the resonant frequency equation. The discussion highlights the need for precise definitions and careful circuit analysis.

agata78
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Homework Statement



A coil of inductance 0.20 H, resistance 60 ohms is connected in parallel with a 20 μF capacitor across a 20 V, variable frequency supply.
Determine:
1. the resonant frequency
2. the dynamic resistance
3. current resonance
4. Q- factor at resonance

Is anyone there who could help me to go through with this question please?!

Homework Equations





The Attempt at a Solution

 
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Have you drawn a schematic?

What do you understand by the resonant frequency?
 
Show some work! You can at least calculate the current for the parallel network.
 
I believe the resonant frequency equation is:

fr = 1 / 2∏√(LC)

However, I am struggling to work out the value for C (Capacitance). As in the question I have 20uF capacitor.

Is 20uF the value for C?
 
Agata 78 said:
I believe the resonant frequency equation is:

fr = 1 / 2∏√(LC)

However, I am struggling to work out the value for C (Capacitance). As in the question I have 20uF capacitor.

Is 20uF the value for C?

Yes. fr is also correct.

For par 2 I don't know what is meant by 'dynamic resistance'. Is it the real component of impedance or is it ∂V/∂I without regard to phase?

For part 3 you must solve V/I. You will find that the 'current resonance" is not the resonance of part 1.

Part 4 is messy.

In fact, this is a very messy problem altogether except for part 1.
 
Last edited:
Can you please help me work out the value of C for Part 1?

For Part 2. Dynamic resiatance is the same as dynamic impedance.
 
Agata 78 said:
Can you please help me work out the value of C for Part 1?

For Part 2. Dynamic resiatance is the same as dynamic impedance.

You just suggested C = 20 uF and I said "Yes".

So the answer is dynamic resistance = dV/dI? At resonance or anywhere?

I have to warn you, this is a bear of a problem.
 
Last edited:
Agata 78 said:
I believe the resonant frequency equation is:

fr = 1 / 2∏√(LC)
No, not precisely. That is true for an ideal resonant circuit where R=0. For any practical circuit, with non-zero R, that is only a handy approximation. This problem requires that you determine the precise resonant frequency.

However, I am struggling to work out the value for C (Capacitance). As in the question I have 20uF capacitor.

Is 20uF the value for C?
Yes. The problem specs give you R, L and C. Draw that circuit and write an expression for the impedance of each element, in Ohms.
 

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