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

1. Dec 16, 2004

### yxgao

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

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

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

2. Dec 16, 2004

### Integral

Staff Emeritus
3. Dec 17, 2004

### rayjohn01

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. Dec 17, 2004

### yxgao

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. Dec 19, 2004

### rayjohn01

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. Dec 19, 2004

### rayjohn01

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

#### Attached Files:

• ###### SerPar.jpg
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7. Dec 20, 2004

### yxgao

Thanks! I really appreciate it!

$$\lambda$$

$$\mu$$