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

In summary, the resonance frequency expression for a parallel RLC circuit is different than for a series circuit. However, if you change the view of the circuit so that the source impedance is infinite, the resonance frequency expression is the same.
  • #1
yxgao
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0
What is the resonance frequency expression for a parallel RLC circuit?

I know that for a series RLC circuit, it is:
[tex]
w=\frac{1}{\sqrt{LC}}
[/tex]

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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  • #2
  • #3
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.
 
  • #4
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?
 
  • #5
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
 
  • #6
Final answer

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

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  • #7
Thanks! I really appreciate it!




[tex]\lambda[/tex]



[tex]\mu[/tex]
 

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

The resonance frequency expression for a parallel RLC circuit is given by the formula: f0 = 1 / (2π √(LC)), where f0 is the resonance frequency in Hertz, L is the inductance in Henrys, and C is the capacitance in Farads.

2. How is the resonance frequency of a parallel RLC circuit calculated?

The resonance frequency of a parallel RLC circuit is calculated by using the formula: f0 = 1 / (2π √(LC)). This formula takes into account the inductance and capacitance values of the circuit to determine the frequency at which resonance occurs.

3. What does resonance frequency mean in a parallel RLC circuit?

Resonance frequency in a parallel RLC circuit refers to the frequency at which the reactive components (inductance and capacitance) of the circuit cancel each other out, resulting in a purely resistive circuit. This causes the circuit to have a maximum current and minimum impedance, making it ideal for certain applications.

4. How does the resonance frequency affect the behavior of a parallel RLC circuit?

The resonance frequency greatly affects the behavior of a parallel RLC circuit. At resonance frequency, the circuit becomes purely resistive and experiences a maximum current, resulting in a peak in the voltage across the circuit. This can be useful in applications such as filtering and tuning circuits.

5. Can the resonance frequency of a parallel RLC circuit be adjusted?

Yes, the resonance frequency of a parallel RLC circuit can be adjusted by changing the values of the inductance and capacitance components. This can be done using various techniques such as adjusting the physical size or material of the components or using external tuning circuits.

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