Hello,
the problem is associated to the fact that when resistance in RLC is not zero, then capacitor's voltage and inductor's voltage reach resonance at different frequency(right around the area of current's resonance frequency).
I know the equations for calculating them:
Volatage resonance for inductor at:
ω=1/(LC-(R^2*C^2)/2)
Voltage resonance for capacitor at:
ω=sqrt( 1/(LC) - R^2/(2*L^2) )
It is easy to see that if R>0, then voltage resonance for inductor comes into being at higher resonance, for capacitor at lower.
What I need is an explanation, not a mathematical proof, but a physical explanation of it. WHY?
Thanks!
It is a series RLC circuit.
There are three frequencies discussed:
1)ωr - resonance frequency for the current (obviously the same for the whole series)
2)ωL - resonance frequency for the inductor's voltage
3)ωC - resonance frequency for the capacitor's voltage
The first one doesn't change, the two latter do as R goes up.
lammas,
I have no idea what those three terms listed mean. Could you provide some link or other material that discusses what they are? You see, resistance has no resonant frequency. Neither does L or C unless they are considered together.
Ratch
Mr Al. understands the problem best. I am not familiar with the terminology in english so sorry about that.
If it is really about analysis with formulas then I am back where I started - have to do math to get there. But that doesn't actully explain it, it just describes when things happen. The formulas in my first post are the result of analysis, but they don't tell us a clear story which we could put into words and visualize clearly. At least I'm not able to...
To the Ineffable All,
Only in parallel resonant circuits are there three resonance points. They are the frequency where the inductive and capacitive reactance are equal, the frequency where the impedance is the greatest, and the frequency where the voltage and current are in phase with each other. If the Q of the parallel resonant circuit is greater than 10, then those three frequency points are quite close together. Series resonant circuits, as the OP has said he is inquiring about, have only one resonant point. Unless the OP can produce some documentation that shows multifrequency resonance for series circuits, everyone is spinning their wheels postulating about it.
Ratch
You're kidding right?
Both the OP and myself have calculated the three resonant peaks and that's exactly what the OP wanted. We've come up with formulas (similar to the OP original post) and calculated three frequencies that are different from each other. I've also included a numerical example which helps to illustrate this. If you took the time to do the calculations you'd have to find the same thing too.
You are stating here that there is only one resonant point in a series circuit yet you are willing to accept further documentation that shows multi-frequency resonance for series circuits, so apparently you are not completely sure to begin with.
To be sure, simply do a circuit analysis and compute the voltage across all three elements excited by an AC voltage source. You'll definitely see the voltages across each element peak at three different frequencies. We've done this already so that's where we get the result (note one of the OP's original formulations is not correct however and needs adjustment, but then it definitely works).
...knowing the terms and definitions can always help to avoid misunderstandings and misinterpretations.
Therefore - what is the thing called "resonance"?
I must confess that I still think that any RLC circuitry (series oder parallel) can have only ONE point of resonance - based on the common definition of resonance ("hopelessly pedantic").
As my example shows (opamp amplifier with amplitude peaking in the vicinity of loop gain 0 dB) a local maximum is not always identical to a resonant point.
...... so we could say that there can be two resonance frequencies, using these two common definitions of resonance.
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