Parallel Resonance

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Transcript

Okay, on this section of the course, we're going to talk about parallel resonance circuits right there. All right. And in an LC circuit, which is an inductor and a capacitor in parallel, at resonance, the currents are equal, but if you remember, they're also 180 degrees out, meaning they're the opposite of each other. All right? Oh I put are equal and opposite. So and resonance, an LC circuit currents are equal and opposite, okay?

The Z of the circuit is at its highest point, meaning we have minimum current flow. And there's one of the slides where we show you that, okay, we're also called a resonant tank circuit or some people will cut out the resident and say, 10 circuit. All right, so those are the characteristics of a resonant circuit. And we're going to go into the next couple of slides and we're going to look at this and and look at some other one or two other properties of it. So let's go on to the next slide and continue. Okay, here we have a graphical representation or a schematic drawing of a resonant circuit right there.

And you'll notice we got a capacitor and an inductor in parallel, this Rs which is 10 ohms in this example, right there, okay, that actually is is stating the resistance in the coil, all right, because that is an inductor. And an inductor is a coil of wire around some type of form. All right, and one of the properties of a parallel resonant circuit as we stated It is we have a minimum amount of current flow. During resonance, our resonant frequency is 1000 kilohertz. So we have minimum current. And my impedance is also at its highest level, because if I have minimum current that means that my impedance is that maximum, which I'm showing you here.

And we're showing you at resonance that the impedance or the Z of this circuit is 2020 225,000 ohms. Alright, and again, is my resonant frequency 1000 kilohertz. And, again, this is how I determine my resonant frequency one over two pi the square root of LC and there's going to be some there's a two slides coming up where where I do one and we go through the math and get the resonant frequency. So that's here. So, so far, all right, remember, at a parallel resonant circuit, my current is minimum at my resonant frequency, and my impedance Z is maximum at my resonant frequency. All right, I just put this up, added this little chart on the slide right here.

And I just thought it was a good idea to do that. Some of these things we already know basically, this shows you X sub c and XML. And if you look X sub c goes down as frequency increases. And x sub l goes up as frequency increases. And we I mean, you can check the numbers if you want. It gives you the the ohmic value of XML and XML at each one of these frequencies.

And then what he does is he calculates the value of IC and i L. And we know that they we can take the difference. So he's showing you the difference here. The point the point I'm trying to make is at at resonance, which is right there, my current is zero, right? Because my current is equal in both legs 20 over here, and 20 over there, if I subtract them the zero, all right, so we have a small current flow right there. But that current flow is determined by the winding. Primarily the winding and the coil it's it's actually the resistance in the circuit as a whole, but, but most of that most of that would be the winding and the coil.

All right, and On the next slide, I'm going to show you how we got that 225 K. And you probably saying, Well, how do we get that, that'll that'll become clear on the next slide. So, just wanted to show you that we're going to stop here, I'm going to clear the slide off and go to the next one. Alright, so here we're going to look at at how we got this say this z here. And this is done by Q, meaning the quality, Houston's for quality of this, this coil right here, all right, and define the quality of the coil. It is XML, at at resonance, whatever that value of XML is at resonant divided by the resistance of the coil. In this example, it's 10.

And when you buy a coil, you'll find you'll get a manufacturer's specs. And and he'll state that or if you wind your own coils, you just put an ohm meter on there and you measure, right and then you you know what it is. All right. So if I go through the math, we know that XML at residence is 1500 ohms. Right there, we're gonna divide, divide that by 10, which is the value of Rs, which is the resistance of the coil, and I do my math and I get 150. All right, it's just, it's just a number.

Okay? It's just a number. It's a ratio. And to find my total impedance, which is z t, it's going to be the value of of Q times the value of x sub l. And in this case, 150 times 1500 ohms. And there's z right there. So z is at resonance.

This circuit is 2220 5000 ohms at resonance at resonance, so therefore, if I want to find the current, it would be 300 micro volts because that's my generate a voltage there divided by the impedance of the circuit at residence and I go through the math and I get zero dot 00133. Micro hampers, okay? And for those of you who don't say, well, gee, what's a micro ampere? a micro ampere is 1,000,000th of an amp. And that's less than that. It's it's zero dot it's, it's a very small number zero dot 0013. micro amperes are this number times 1,000,000th of an ampere.

And you can see that it's it's, it's really a trickle really a trickle. Alright, so that's it. What going to talk about cue a little bit more in the next coming slides. Okay, well, I'll leave that when we get there. We're finished here. Okay, on on basically I just put this up here.

We've talked about this up here. But this is really how current splits. In this circuit. If you'll notice I have i L, and I see right there, and they're opposite ones going up, the other is going down. So what we're trying to tell you there is because they're equal and opposite, I've actually got zero current flow. The only current flow I get is through IR, which we calculated on the last slide, which is zero dot 00133, micro amperes.

And that at resonant that's the only current that that's supplied by my generator. There. Now, I haven't added this and I've saved I should add that even though we're showing a, this is a generator, I mean, this could be a tune circuit. Right? And this could be, even though we didn't talk about it, that could be an antenna, right? and amplify stage.

And what do I want to do? I want to for whatever reason, maybe it's a radio broadcast of some sorts. I want to hear what what's broadcasting on 1000 kilohertz. So I tuned my resonance circuit, I get maximum gain. And now I can hear what's going on. There's some other things we got to do.

We got to demodulate it and that and, and quite honestly, that's in phase two of my course, that right now, this this course this section of courses, is really just we're building the foundation. All right, we're going to get into circuits and that's in phase two. We talk about amplifiers, oscillators, tuners and so forth, transistors, that type of thing, but Just tip just to let you know, okay, that could be an antenna. And what we're doing is we're selecting that frequency. All right. So we can work on it or do something with it.

Maybe there's some intelligent information like music or or language. And we can pull that off of that somehow there's a procedure to do that. All right, but the first thing I need to do is I need to select that frequency. So when I have a resonant tune circuit, again, one of the properties is if we select a frequency or you'll see later slides a group of frequencies, and we reject all others, so we can do whatever we want demodulated and qualify it, whatever. All right, that's the point I want to make. And that with this chart again, the only thing I wanted to show you is right here, at resonance, the only voltage or the only current, that supply is a very small current.

Alright. And with that, we'll end it, we're going to go to the next slide. All right, we've got one more section on resonance. I'm going to end it here and on the next section, we're going to talk about cue a little bit more. I am going to do a a problem on how to find the resonant frequency and a couple of things here that I mentioned earlier. We'll we'll do that the next section.

So I'm going to wrap it up here and just put a synopsis or a summary of what we talked about. So far. line current IP is minimum at the resonant frequency, we showed you that I is in phase with the generator voltage or the phase angle of the circuit. zero degrees at resonance. And the impedance Z t equals q times X sub l is maximum at resonant frequency because of minimum, I T. And that's it. And I put that up here earlier.

If you want to check your calculations, in other words, you, I really would like you to put the parameters in the circuit. There are one over two pi frequency of residence equals one over two pi square root of LC and you can check yourself by using that calculator. All right. Okay, we're going to stop here. We're going to go to the next section.

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