Engineering What Determines the Resonant Frequency in a Series RLC Circuit?

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SUMMARY

The resonant frequency in a series RLC circuit is determined by the formula w0 = 1/sqrt(LC), where L is the inductance and C is the capacitance. To analyze the circuit, one must calculate the equivalent impedance Z using the equations z = R + jwL + 1/jwC and apply Kirchhoff's Current Law (KCL) to derive the necessary relationships. The discussion emphasizes the importance of understanding the behavior of inductors and capacitors at DC and high frequencies to simplify the analysis. Additionally, the quality factor Q is defined as Q = w0L/R, which plays a crucial role in determining the bandwidth of the circuit.

PREREQUISITES
  • Understanding of series RLC circuit theory
  • Familiarity with complex impedance calculations
  • Knowledge of Kirchhoff's Current Law (KCL)
  • Basic concepts of resonant frequency and quality factor (Q)
NEXT STEPS
  • Study the derivation of the resonant frequency in RLC circuits
  • Learn how to apply Kirchhoff's Current Law (KCL) in circuit analysis
  • Explore the effects of varying frequency on the impedance of inductors and capacitors
  • Investigate the concept of quality factor (Q) and its implications in circuit design
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing or designing RLC circuits will benefit from this discussion.

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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