Okay, and welcome to Al's electronic classroom. And in this course, we're going to talk about resistance, capacitance and inductance, RLC circuits, and an AC circuit. All right, we're going to look at them. We're going to look at an AC circuit with resistance but no reactance. We're going to look at an AC circuit with just XML. AC circuit with XML and a resistor.

An AC circuit with capacitive reactance, an AC circuit with capacitive reactance and resistance. And then we're going to put them all together and look at an r, x sub c, x sub L and R. So that's what we're going to cover here. So, without any further ado, let's go Go to the next slide. All right on this circuit here we have 100 volts source, and two resistors in series. Now this should be somewhat of a review if you've taken my previous courses, circuit theory and advanced circuit theory, okay, even though for the most part we use DC voltages. This is an AC voltage, but everything is the same.

All right, and I just threw this in here because I, I wanted to kind of review it. We hit it pretty heavy with a battery or dc, dc current a DC voltage. So now we're adding AC but but everything that I said for DC circuits applies for this. The only thing is when we measure the voltage across the resistance says they're going to be an AC voltage, and usually they'll be an RMS voltage. Okay? And again, if you do Don't know what I mean by an RMS voltage.

Look at the course that I put up understanding voltage, current and resistance. And we explain all that actually, I think at the beginning of this, I put a review in there. So so check that out. Alright, so basically with it, we're going to what we're going to do is we're going to add the total resistances. This one and this one. Each one is 50 ohms.

I add them up, I get 100 ohms. All right. If you remember ohms law, I, whoops, let me let me stop and clear the slide off. Okay, I'm looking for I right here. And I equals V, in this case v one over it, but it would be voltage over resistance. I do my math 100 ohms over, I'm sorry, 100 volts AC over 100 ohms and I get one amp AC The reason I get one amp AC is because what's my voltage?

Right 100 volts AC. So now I want to find the voltage drop across each resistor. We know when a series circuit current is the same, I right there is the same. So v1 equals I one times R. So one amp times 50 ohms is 50 volts. And since the resistors are the same value, and I have the same current flow through them, my voltage across each resistor is going to be the same. And you know from some of the laws and our basic circuit theory class, the sum of the voltage drops have to equal the sum of the voltage sources.

So if I do a check 50 volts plus 50 volts is 100. My source volts is 100 volts AC. I've checked Now going over here on this side, we've got a parallel circuit. And we know that the voltage is the same across all my components in a parallel circuit. So we've got 100 volts AC, across this resistor, that resistor. So now I want to find the current.

So I one, which would be the current flow through this one would be I one over v one over r one right there. I do my math. And what do I get? two amps. I two is going to be the same. All right, coming up this way.

Okay, v one over r two. I do my math and I've got two amps through that. What's the total current in the circuit? Okay, well, I just Add my branch currents up, which I'm showing you here. two amps plus two amps equals four amps. That's my answer.

Now if I want to find the total resistance of the circuit, and what I mean by total resistance, that's the total resistance, that the voltage source here sees. The voltage source doesn't see 250 ohms in parallel. They see one load. So now it would be v one over RT. Ah, that should be it. I'm sorry, guys.

I'll change that. That should be it. So 100 volts AC over four amps, which is it? I do my math and I got 25 ohms. So basically what it is, is that the battery will see or I should say the AC source. We'll see 20 This will look like 125 ohm resistor right here, attached to the battery like batch to the voltage source.

That's it. All right, let me clear off the slide, we'll go to the next one Oh, before I go on. If you'll notice up here in a resistive circuit only and this is very important for this, for this section, the current and the voltage are in phase, meaning they track. So when my voltage, if I have a sine wave for my voltage, my current follows that and you'll see that because I have some slides later. I'm not going to take the time to draw that. Now what we've got upcoming slides and we'll see that Alright, so let's stop here and go to the next slide.

Okay, in this slide here, we're looking at inductive reactance And I have two inductors inductances in series and their XML or inductive reactance is 50 ohms. And if you remember, if you've taken another or my previous course, you know that x sub l equals two pi times the frequency times the value of the inductor. Alright, so the only thing that we've done here is we've given each inductor a value of 50 ohms. All right, alright. Let's clear the slide off and go on. Okay, so now, I mean, it's a series circuit.

So if you look at some of the, the the earlier courses that I I've spoken or taught or presented, all right, especially resistances. What do we do, we add up the total total resistance or in this case, since is inductive reactance. And it's only an inductive circuit, we're going to add up our total inductances. So Excel one plus XL two equals X lt, and I've given you the, the value of that here, I just add them up 50 ohms plus 50 ohms is 100 ohms. All right, so now I know the total reactance of this circuit. All right, now I want to find I, all right, right there.

That's v total or vt divided my, my total XL T. All right, in this case, it's 100 volts divided by 100 ohms. I do my math. I get one amp AC. All right, the voltage across this guy is the same across the sky because My inductive reactance is is the same, both 50 ohms. And my current is the same through that leg. So I just do my math.

One amp times 50 ohms is 50 volts, that's v1. And since v2 has the same, same parameters, it's one amp times 50 ohms equals 50 volts. That's it. Now, the only thing I want to add here is in a pure inductive circuit, I have a 90 degrees phase shift All right, voltage is here, and current is here, all right. So what we say is that voltage leads current by 90 or you probability this much, was saying the same thing, but this is more common. Current lags voltage by nature.

Degrees. So what does that mean? It means because if Remember, if you took the previous course I talk about a back emf. And so at a very at an instant, I have a back emf, that equals my source voltage. All right, that starts decay immediately. All right, but at that, that miniscule instant, where my back emf of the inductors equals my source voltage, I have no current flow.

And as my back emf starts to decay, then I my current starts to flow and that's how I get this. This 90 degree shift. Alright, it's a little bit of a delay. And when I have a sine wave, it actually looks as though I have a 90 degrees shift between my current and my voltage. All right, so we're going to stop here and go to the next slide. Okay, on this one here, we have a still have a pure inductive circuit.

But instead of the inductors being in series, we're in parallel right here. The values are the same 50 ohms and 50 ohms. And my voltage source right here is the same, it's 100 volts AC. So basically, we need to find the current in each leg right there. And if you look, again, everything's the same. So my voltage is, is constant across each leg.

So now I just do my math, v t divided by XL one, which is 100 volts AC over 50 ohms two amps. This is going to be exactly the same, because I have the same parameter. All right? I T, that's the total current that flows in and out from the generator. And the reason I write show arrows in both directions because it's an alternating waveform, alright, and current flows above and below the zero line, again, a review what I showed you at the beginning and then I also go into it a little bit deeper in understanding voltage, current resistance. All right, and when I do that, my setup my current and it's four amps total, alright?

XL T, or the amount of reactance that the generator sees. Okay, it's going to be vt over it. vt will be 100 because it's in parallel, it is a total over here are four amps. do my math. And the generator looks like it sees a 24 Ohm inductive reactance, just one. That's it, we still have a phase reversal, still 90 degrees.

But on this one here we show the voltage from the generator on the zero axis line. And here's the sum of my currents right there. Okay, and notice we still have a 90 degree phase shift. So voltage still leads, or current still lags by 90 degrees. And that That's it. That's it.

If you look at it, it's it's the same idea that I spoke about. In basic circuit theory. The only twist here is instead of using resistances, we're using inductive reactance is all right, and there's a Phase Shift, all right, in a pure resistive circuit, we have no phase shift in an inductive circuit and appeal when we have a phase shift of 90 degrees. Hang on to that clear the slide. We're going off to the next one. Okay, here we go.

Okay, we've got two capacitors. In series. Now we're talking about capacitive reactance. Okay, everything is the same that we did in the first slide when we talk about inductive reactance. Okay, find my total X sub c I'm doing here which is 100. Find my current flow my AC current flow vt over x subsea.

I do my math, I get one amp. Alright, the voltage across each component. I times x FC one i times X sub c two. Here we go. 50 ohms across each one. The math is the same Here's the difference.

Now this graphical represent representation between voltage and current may see the same. However, look at what the difference is. I have I on the plus and voltage on this one. All right, let's stop. And let me go back to the original one. The other one, previous one.

But look at here, voltages up here. All right, all right. So they're kind of equal and opposite, aren't they? That's the point I wanted to make. They're equal and opposite. All right, let's stop and go back.

Alright, so basically here are not basically what we have in a pure capacitive circuit, okay. We have current leads voltage by 90 degrees. All right, and in pure inductive circuit, current language voltage by 90 degrees. So they're opposite of each other. Just hold on to that thought. All right?

Enough. We'll see what we mean by that a little later. Just kind of stress that. All right, I mean, I don't really want to spend any more time here because basically, the way we calculate things and everything is basically the same. All right, as far as the mechanics, it's the same. It's just that in one area, we have capacitive reactance here, and two slides back when we did the inductors.

In series, we had inductance reactance in series. All right, that's the only difference and my phase angle is different. That's it. Let's stop, go to the next slide. All right, on this slide here, we're still talking about capacitive reactance. But they're in parallel right there.

And it Again, we're doing the same thing. If you look at a few slides back, we spoke about or showed you how to do inductive reactance, the same the same thing. So I'm looking for current through each branch. And here it is here. I one equals vi over x sub c one, I two equals v one over x sub c to his v one right there. Again, I do my math 100 volts AC over 50 ohms and I get two amps through each branch.

Alright, I T, I just add up the branch currents I one plus i two and my total is four amps. I want to find my total XC. Okay, that's what the source sees. So, the source or the source voltage edge sees those two capacitors in parallel as 125 Ohm capacitor that has an X subsea or capacitive reactance of 25 ohms is my phase shift. All right? My voltages here and my current is this way.

All right, 90 degrees out of phase current leads voltage by 90 degrees. All right. And let me stop here and go back to inductive reactance. And let's look at that in parallel. Notice the same phase angle, but it's the opposite. It's 180 degrees out.

We're going down where the previous one it was going up, equal. Okay? In this case equal and opposite, but the point I'm trying to make is the current isn't. The currents cancel each other out. Okay? So we'll see that as as we go on, okay, because one here, we're going this direction in the previous slide, we go up this direction, okay?

So they're opposite. All right. Okay, so we're pretty much finished here. Again, if you look at the mechanics, the mechanics are pretty much the same. The differences are the phase angle, but the steps to calculate my total current, my total reactance total is the same. The only thing that's different is the phase difference between voltage and current.

Alright, let's clear off the slides. Go to the next one.