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

  • Thread starter yxgao
  • Start date
  • #1
123
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
 

Answers and Replies

  • #2
Integral
Staff Emeritus
Science Advisor
Gold Member
7,201
56
  • #3
283
0
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
123
0
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
283
0
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
283
0
Final answer

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

Attachments

  • #7
123
0
Thanks! I really appreciate it!




[tex]\lambda[/tex]



[tex]\mu[/tex]
 

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

  • Last Post
Replies
21
Views
12K
Replies
8
Views
815
Replies
3
Views
23K
  • Last Post
Replies
13
Views
33K
Replies
10
Views
2K
Replies
12
Views
17K
  • Last Post
Replies
15
Views
1K
Replies
1
Views
17K
Replies
2
Views
5K
  • Last Post
Replies
3
Views
3K
Top