# How to know when an LC circuit hits resonance

#### electricalguy

Gold Member
I have been having issues with a series LC circuit. I have a supply voltage of 6.96 volts, across the inductor is 7.04 volts and the capacitor voltage is 7.17 volts. The capacitor has a capacitance of 45uFarad and a supply frequency of 250 hertz. I don't know what the inductance is of the inductor. Can anyone teach me how to calculate the resonant frequency. I'm a bit stuck here on this concept. This is not a homework question.

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#### phinds

Gold Member
What has your research so far turned up? This is a VERY basic problem.

#### berkeman

Mentor
Welcome to the PF.
a supply frequency of 250 hertz.
Can you vary the drive frequency? Do you have a 2-channel oscilloscope? If yes to both, you can vary the drive frequency and watch the LC lowpass filter behavior to do a Bode plot, and find the resonance that way.

If no to either, then @phinds suggestion is your best bet.

#### electricalguy

Gold Member
My research so far tells me that resonance is reached when the supply voltage is equal to the voltage across the inductor minus the voltage across the capacitor. But I'm not sure if that is right.

#### jim hardy

Gold Member
2018 Award
I have been having issues with a series LC circuit. I have a supply voltage of 6.96 volts, across the inductor is 7.04 volts and the capacitor voltage is 7.17 volts. The capacitor has a capacitance of 45uFarad and a supply frequency of 250 hertz.
It's hard to guess from where you're starting.
Do you know what is meant by the terms "capacitive reactance' and "inductive reactance" ?

You might need to look over some very basic tutorials.

https://c03.apogee.net/contentplayer/?coursetype=foe&utilityid=wppi&id=4571

#### electricalguy

Gold Member
Okay I just did some math on it, I calculated that the capacitor had an impedance of 14.147111 ohms. So that gives me a current of 0.506817253 amps. So then I take the voltage of the inductor divided by the current and I get an impedance of 13.89060842 ohms which at 250 hertz equals 8843.03 uHenry. How can that be, because when I change the value of the capacitor the impedance ratio changes and the inductance values changing dramatically.

#### sophiecentaur

Gold Member
How can that be, because when I change the value of the capacitor the impedance ratio changes and the inductance values changing dramatically.
Do you find a different resonant frequency with a different capacitance? You have presumably read around this and know the formula for resonant frequency in terms of L and C. The way you are approaching there problem is a bit different from how I would have done it (not involving impedance at all, initially).
If you find that the capacitance does not produce the resonance at a frequency you would expect ( calculate) then there must be some parasitic capacitance.

#### electricalguy

Gold Member
Okay, so if the inductor has an insulation coating on the wires, it will experience parasitic capacitance. Is there any way to calculate the value of parasitic capacitance in the inductor?

#### jim hardy

Gold Member
2018 Award
What is the DC resistance of your inductor ? You can measure it with your multimeter. If it's less than 10% of your calculated reactance it won't grossly distort your experiment. .

Your capacitor also has series resistance but it's not so easily measured. Do you have its datasheet ? Is there a published ESR on it ?

How can that be, because when I change the value of the capacitor the impedance ratio changes and the inductance values changing dramatically.
You're asking us to evaluate your results without telling us what they are. Excruciating detail is the price of clear communication.

#### electricalguy

Gold Member
Thank you everyone for the help so far! I do have another question related to this topic. If the current passing through the circuit is too low at the applied frequency for a capacitor that is larger, would that have a negative effect on the LC circuit to be able to function.

#### jim hardy

Gold Member
2018 Award
If the current passing through the circuit is too low
By what criterion do you declare it "too low" ? It's just Ohm's Law.

would that have a negative effect on the LC circuit to be able to function.
What does that mean ?

Your questions tell me you do not yet understand the concept of "Impedance".
https://en.wikipedia.org/wiki/Electrical_impedance

That you measure nearly the same voltage across your inductor and capacitor and supply, all three within 2% of their (approximate 7 volt) average, suggests there is substantial resistance present in your circuit.
You've not made provision for that in any calculation you've shown us.

I suggest you vary frequency and make a plot with four lines
horizontal axis: frequency
vertical axis four variables :
1. supply voltage,
2. current,
3. voltage across inductor,
4. voltage across capacitor.

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#### sophiecentaur

Gold Member
If you show us the circuit diagram and tell us what voltage frequency characteristic you are expecting. Are you expecting a peak or a dip? What happens if you put a high resistor (say 10kOhms) in series?
I would feel happier if you said what book or other source you are using.
What signal source are you using?

#### electricalguy

Gold Member
Thank you everyone for the help! The suggestion from Jim Hardy has been very useful. I have started to graph the supply voltage, current, inductor voltage and capacitor voltage with different input frequencies. It has shown that I am quite a bit below resonance with this setup. Thank you to all of you again, very helpful suggestions.

#### jim hardy

Gold Member
2018 Award
It has shown that I am quite a bit below resonance with this setup. Thank you to all of you again, very helpful suggestions.
We'd be interested to see your plot. If you can scan it into a jpg and save on your computer , 'upload' button should let you insert it in a post.

Current should peak at resonance.

#### LvW

Thank you everyone for the help! The suggestion from Jim Hardy has been very useful. I have started to graph the supply voltage, current, inductor voltage and capacitor voltage with different input frequencies. It has shown that I am quite a bit below resonance with this setup. Thank you to all of you again, very helpful suggestions.
Using the technical term "resonance" one should know the definition of this term.
Some people think that it is identical to a maximum resp. minimum of some specific voltage or current - but this might be true for some simple cases only.
The basic definition is based on the phase shift caused by the circuit, which means:
We have "resonance" when the voltage measured at the output node is in phase with the input signal (zero phase shift).

#### jim hardy

Gold Member
2018 Award
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/serres.html said:
Resonance
Resonance in AC circuits implies a special frequency determined by the values of the resistance , capacitance , and inductance .
For series resonance the condition of resonance is straightforward and it is characterized by minimum impedance and zero phase.

#### jim hardy

Gold Member
2018 Award
http://eecs.vuse.vanderbilt.edu/courses/ee213/what_is_resonance.htm
What is resonance?

Resonance occurs when the reactance of an inductor equals the reactance of a capacitor at some given frequency in an RLC circuit. In series resonant circuits under resonant condition, the current will be maximum and offering minimum impedance. In parallel resonant circuits the opposite is true.
Phasor diagrams make it intuitive. OP hasn't shown us he's ready for those just yet. One step at a time.

old jim

#### LvW

Yes - of course, the above given answer to "what is resonance" is correct - however, only for a simple RLC series or parallel combination.
If the circuit is somewhat more complicated - with additional loss resistances and/or a second capacitor - the criterion "minimum/maximum" does not hold anymore.
In such a case, we have to use the phase criterion.

Moreover, even for simple RLC series or parallel circuits, it is best to use the phase criterion (zero phase shift) because the measurement of the resonance point based on application of the phase condition is much more exact if compared with an amplitude measurement (maximum).

#### jim hardy

Gold Member
2018 Award
Yes - of course, the above given answer to "what is resonance" is correct - however,
It just describing characteristics of a resonant circuit.

I didn't find an actual physics based definition with just a few minute search .

His original question was
Can anyone teach me how to calculate the resonant frequency.
I figured he'd be best served learning how to observe resonance (via frequency response plots) .
If his circuit has any Q at all he'll get the surprising result that both his capacitor and his inductor see voltage that exceeds his Vsupply.
That apparent violation of KVL should spike his curiosity and open the door for complex arithmetic.
Seeing one's voltmeter report 1 + 1 = √2 or some other non-2 result makes one a believer.

one step at a time. "What" before "Why" .

What do you think is best way to lead him to water ?

LATE EDIT This post may have come across as argumentative. Nothing was further from my mind . I just worry about flooding newbies with information overload. Last line was an honest question.

old jim

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#### sophiecentaur

Gold Member
I didn't find an actual physics based definition with just a few minute search .
One way to look at the resonant frequency is the frequency at which the most energy can be stored in the circuit but there are many alternatives. I like the Energy one because it is the least specific and, well - I like Energy.

Gold Member

#### LvW

To Jim Hardy....Sorry, I am afraid - you misunderstood something.
In no way I wanted to correct or even criticize one of your contribution.
It was my only intention to tell the questioner that - using a term like "resonance" - it is always necessary to know the meaning/definition of such a technical term.
As another example, many questioners are using the term "corner frequency" without knowing that this is not always identical to the 3-dB frequency.
It is simply a matter of definition!

#### Tom.G

using a term like "resonance" - it is always necessary to know the meaning/definition of such a technical term.
Yes. And that is the precise thing he is in the process of learning.

#### berkeman

Mentor
Thread closed briefly for Moderation...

#### berkeman

Mentor
Okay, thread is tentatively re-opened. Let's please try to stay on-point helping the OP at the level he is asking the questions. Understanding the basics of resonance can be important, but we shouldn't have to be arguing about it. Thank you.

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