What Determines the Resonant Frequency in a Series RLC Circuit?

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Discussion Overview

The discussion revolves around determining the resonant frequency in a series RLC circuit, specifically focusing on the equivalent circuit impedance and the behavior of passive components under different frequency conditions. The context includes homework-related inquiries and attempts to solve circuit analysis problems.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Participants discuss the need to find the equivalent circuit impedance Z formed by the components in the given configuration.
  • Some participants suggest writing KCL equations to determine the impedance, emphasizing the use of complex impedances for inductors and capacitors.
  • There is a question regarding whether any capacitors or inductors are in parallel or series with each other, indicating a need for clarification on the circuit configuration.
  • One participant proposes considering the behavior of inductors and capacitors at DC and very high frequencies as a potential approach to the problem.
  • A participant recalls a trick that may simplify the circuit analysis, which involves the impedance of the source being low.

Areas of Agreement / Disagreement

Participants generally agree on the need to analyze the circuit using KCL equations, but there is uncertainty regarding the configuration of the components and how to approach the problem effectively. Multiple views on how to simplify the circuit and analyze it remain present.

Contextual Notes

There are unresolved aspects regarding the assumptions about the circuit configuration and the specific relationships between the components, which may affect the analysis.

neiks997
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Homework Statement


I will give a circuit of 5 passive components and an AC voltage source producing a sinusoidal voltage at a fixed frequency of omega / (2*pi) Hz.
i will post a picture asking what is being looked for along with the circuit.

Homework Equations


z = R + jwL + 1 / jwc, jw0L + 1 / jw0c = 0, w0 = 1/ sqrt(LC), B = w2 - w1 = R/L = w0/Q, Q = w0L / R = 1/w0RC, w1 = w0 - B/2, w2 = w0 + B/2


The Attempt at a Solution


clueless on how to make an equivalent circuit.
 

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neiks997 said:

Homework Statement


I will give a circuit of 5 passive components and an AC voltage source producing a sinusoidal voltage at a fixed frequency of omega / (2*pi) Hz.
i will post a picture asking what is being looked for along with the circuit.

Homework Equations


z = R + jwL + 1 / jwc, jw0L + 1 / jw0c = 0, w0 = 1/ sqrt(LC), B = w2 - w1 = R/L = w0/Q, Q = w0L / R = 1/w0RC, w1 = w0 - B/2, w2 = w0 + B/2


The Attempt at a Solution


clueless on how to make an equivalent circuit.

Welcome to the PF.

It says it wants you to find the equivalent circuit impedance Z that is formed by those components in that configuration.

There are no obvious simplifications of the circuit, so you need to write the KCL equations for the circuit, to find the Z = Vin/Iin impedance. Use the complex impedances for the L and C components...
 
none of the capacitors or inductors are in parallel or series with each other?
 
neiks997 said:
none of the capacitors or inductors are in parallel or series with each other?

Nope. That's why you need to write the KCL equations to solve this.
 
I'd be tempted to do parts 2 and 3 first. What happens to L's and C's at DC and very high frequencies?

It's been many years since I did this but I half remember a trick that relies on the impedance of the source being low to simplify the circuit?
 
CWatters said:
I'd be tempted to do parts 2 and 3 first. What happens to L's and C's at DC and very high frequencies?

It's been many years since I did this but I half remember a trick that relies on the impedance of the source being low to simplify the circuit?

brilliant
 

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