Well, welcome. Okay, um, we're going to talk about in this particular course, we're going to talk about reactance, capacitive reactance, inductive reactance resistors in a circuit where we have an AC voltage. And even though I did a course called electronic basic fundamentals where we covered a lot of AC voltage, I wanted to redo a little bit of it here, just in case you forgot, or maybe you didn't take the course. So this if you've taken this, this may be somewhat of a review for you. It's not as long as that I do give you enough to understand the following material, but let's just go through this. And again, you may find that this is a repeat If not, then just dive in and you're going to learn something new, okay.

So, understanding voltage, AC voltage or AC voltage current flows in both directions. The voltage that is brought into your home is 120 volts RMS volts AC, and the frequency is 60 hertz. One of the reasons that we use AC voltage is because it's easier to transport over long distances than DC. Alright, so let's go on to the next slide. Okay, what I'm trying to show here is, if I had a graphical representation of voltage, this would be DC voltage. Alright, notice I've got zero volts here.

Let's say this red line represents plus five volts All right, I mean current flow current flow is in one direction right. Now, if I put a battery in here, what I show you right there, current flow goes from the negative terminal of the battery up through the load down into the positive terminal of the battery. So current flows in one direction, DC direct current, okay, if I swapped the polarity on that then it would go the other way. But right now for our purposes, AC voltage stands for alternating current. DC current stands for direct current and it only flows in one direction. Now, this is a sine wave That's one word by the way.

And notice I represent zero volts there. Okay? Now notice that a sine wave goes above and below the 00 volt line. Okay? So from here to here, all right, I have a plus voltage, and from here to here, it goes below zero, I have a negative voltage, all right, and it keeps repeating that, okay. So from here to here is one cycle, and then I repeat that.

Okay. So what does that mean? That means from here to there, a, let's say a to b. current is flowing in one direction, and I'll pick this direction here. And then from this story, Right, Shane, I'm gonna kind of call that BTC where it's negative, then current is flowing in the opposite direction. So that's why we call this AC voltage, alternating current. All right, one half of the cycle, it's, and I'm just going to pick it, it's going clockwise.

And the other half of the cycle and the negative portion of the cycle here, it's going counterclockwise. So it reversed the current flow reverses direction, twice in one cycle. Okay, so I wanted to find some terms here. One of it is the Hertz. And it's derived as the unit of frequency. So one hertz is one cycle per second.

Okay, that's what we mean. All right. It is The name of Henrik Rolf hertz or Rudolf hertz, and he was the first person provide conclusive proof of the existence of electromagnetic waves. So, he studied this about the electromagnetic waves in the the atmosphere and how they radiate and so forth. All right. So hertz, a commonly expressed in multipliers, kilohertz 1000 hertz, megahertz, a million hertz gigahertz and terahertz.

Mega means a million. Giga means 100 million and terahertz means a million billion, okay. I'm not sure if we, we have anything that that can generate a terahertz right now. So, quite honestly, I really haven't heard of it. Up until when I started teaching this. They had mentioned that when I started reading Searching this course.

But the point I want to make here is, when I say hurts, hurts is means frequency. So one hertz is one cycle. And if you remember from the previous slide, one slyke cycle is from where it starts to where it ends. So this is one cycle here. And then if I continue, this would be another cycle there. So, cycle and hertz are the same.

So when I say 20 cycles per second, or 100 cycles per second, I'm saying the same thing as 100 hertz per second or 20 hertz per second, it means, it means the same exact thing. And again, what we're showing you here is I have I have an alternating Current or an AC voltage, current is alternating back and forth, or changing directory. The X amount of time per second. So for instance, if I tell you that my AC frequency is 1000 hertz, then current will change direction twice. Alright, so actually current is going to change direction 2000 times and you say well gee gizelle What do you mean? Well, let's stop here.

I'll clear off the slide and show you what I mean. Alright, so here's my cycle. So let's say my frequency is two cycles or two hertz. What does that mean? That means I'm going to have two of these in one second. I go positive here.

So current is flowing in one direction there. And then when I go here and my sine wave transverses to the, through the zero line, then current flow changes direction. changes direction here and changes direction there. So I have two cycles. One, two, right? Positive, negative direction, positive direction, negative direction 1234.

So when I have our frequency, and I'm just picking this arbitrarily 1000 cycles per second, that means That current will change direction twice that a 2000 times per second. Alright, Nuff said. Let's go on to the next slide. All right, now we're going to talk about RMS voltage. All right? And why do we have an RMS voltage?

Okay. And again, let's start off with it. RMS stands for root mean square. And that's just one way of representing an AC waveform. Well, let's let me let me just draw a sine wave here and then I'll get our luck, erase it. And let's do that.

Okay, so I've got three cycles there. All right, what's the average value of that? zero volts. Because if I take the average of that wave, AC wave form, this value This value, okay, on all of them even though I didn't draw it very nicely. The, if I have a sine wave up here equal this, the area above the curve equals the air, I'm sorry, the area above the zero line equals the area below the zero line, if I take the average, the average zero, and I can assure you that if you grab onto that AC voltage line, it's gonna feel something other than zero. Okay, you're gonna, you're gonna get belted, okay, and number one, I don't recommend that you grab a hold of it, because it can kill you.

So let me state that right here. So don't go putzing around with the voltage coming out of your, your house sockets, because if you don't know what you're doing, you're going to hurt yourself very, very dearly, and you could die. So with that said, let's move on. So if if somehow if I take the reading of that, it's going to be zero volts and like I said, a few seconds ago. It's not. So they came up with this RMS value where we take the root, the mean, which is the, the average.

And then we we take the square, so RMS, right here, take the square of each individual value, and we, okay. And then we then we add the squares and divide the sum by the number of values and get the mean of the average. And then we take the square root of this, this value, and this is the RMS value. All right, and I believe there's an exercise on the next slide that will show you how we do this. All right, but again, the reason we have we came up with this RMS value, not me personally. But as as the evolution of electronics, and we understood this is so we can get a, a value for an AC voltage.

Because once again, if I have a pure sine wave, okay, the average value of that sine wave is going to be zero. And again, I put up a sine wave here and was saying the same thing, okay? It's drawn a little nicer here. So the average value of that is zero. Okay? Without me doing anything, the average value is zero.

All right, well, here's that example that I mentioned out of you, we're going to find the RMS value of 234. Now this there's only there's only like three, three points that we're we're looking at. But if you look at a sine wave, there's an infinite number. points. All right. So let's just take this 234.

So what we do is we take the square of each number, and I show you that right here. So the square root of twos for the square root of three is nine, four squared is 16, then I'm going to find the mean value. So I add them up, and I divide by three. And there's my number. I take the square root of that, and it's 3.99. So what we're saying is, the RMS value of that is 3.11.

And that's basically what you're doing when you measure an AC voltage only this algorithm All right, is is is programmed into the meter, or as part of the meter to read that, okay. And back in the old days, it was done hardware wise. I still think it's done some of the multimeters have some have some chips in there and stuff that would would do that. But the point I'm trying to make is, that's the RMS value. That's what we're doing with an AC waveform. Only there's wood, there's many, many, many, many more different points.

Okay, so now we're going to we're going to define some properties of a of an AC sine wave which I show you here. All right, so now the first the first bullet here is 120 volts RMS at 60 hertz. Well, I told you that 120 volts AC is is the line voltage that comes into your home. We talked about the RMS value in the previous slide. And we know that 60 hertz means 60 cycles. So I get one, there's one cycle from here to here.

And I get 60 of those in one second. That's what 60 hertz says, okay? All right. Okay, so now now you sometimes you're going to hear about the peak voltage of an AC waveform, okay? The peak voltage is 1.414 times the RMS value right there. So I give you a graphical representation is my zero volt line right here, and this would be my peak value.

So if I went from here to here, all right, my peak voltage or that voltage at that instant would be 1.414 times the RMS value. So if the RMS value is 120 volts, then I would multiply By 1.414 times 120 volts, and that's would be my peak value. The next thing we want to talk about or define is peak to peak voltage. All right, and again, here's my, my graphic, I'm going from one peak here to the lower peak, alright, and peak to peak voltage equals 2.8 to eight times the RMS, notice peak to peak is two times peak, all right? If my, my peak voltage is 1.414. If I multiply that by two, I get 2.828 times the RMS voltage, alright, or if I know what the peak voltage is, I can multiply the peak voltage by two.

All right. All right, RMS voltage equals point 707 times the peak voltage. So if I know what the peak voltage is, all right, I can multiply that value by 0.707. And I get the value. All right, so that's peak voltage. All right over here.

We have one over T equals F and one over F equals T. What does that mean? Well, let me clear let me stop and clear the slide off. Alright, so the time this is one cycle. So one over T equals up, so the time of one cycle and if I bring that over tea, I get the question. frequency. In other words, how many cycles per second.

And if I know the frequency, one over F in this example 60 hertz. If I put that if I do the reciprocal of that where it's one over 60 then I can figure out the time and I think in the next slide, we have a, I illustrate that with some numbers. All right, so what I've done here is we just went over this this portion on the previous slide, so I've given you some questions 60 volts AC, find the peak to peak. So, what would the peak to peak voltage be peak to peak is 2.8 to eight times RMS, or two times peak? Okay 90 volts AC peak to peak, find the peak voltage are harder than 70 volts AC peak, find the RMS voltage, okay? So RMS voltage is point 707 times a peak voltage, fine T for 60 hertz.

The time for one cycle, find F for 8.33. So if I've got one cycle, that take that takes 1.8 8.33 milliseconds, that's what MSX stands for milliseconds, what would be the frequency? Okay? So, stop the slide, do the problems. And when you go on, you'll see the answers. All right, we'll hear the answers.

Questions I'm going to go over them are 60 volts AC, find the peak to peak, it would be actually wouldn't be peak to peak, it would be find the peak voltage, so it's just one peak there. And that's 169 170 volts peak AC, all right, 90 volts peak to peak, what? 90 volts peak to peak, find the peak voltage, the peak voltage is half that. All right? So if I've got peak to peak, that's 90, and I only want to find a peak voltage, while half of that is 45 volts peak right there. All right, are the 70 volts peak, find the RMS so it'd be 170 times point 707 is my answer and find T for 60 hertz.

So it'd be Zero dot 1667 seconds, or 16 point 16 seven milliseconds. All right. So what that means is, if I have a freak sine wave when it's got a frequency of 60 hertz, meaning 60 of these in one second, the time for one cycle from here to here is 16.67 milliseconds. All right? All right. So find f, find the frequency of 8.33 milliseconds, that's 120 hertz.

So what that means is if I have 120 of these cycles in one second, the time of one cycle is 8.33 milliseconds in his my equations up there to find them. Alright, I'll fix the slide 60 volts AC, find the peak to peak voltage. That should be actually that should be peak. I'm not really sure. Let me let me take a look at that. And I wonder if I made a mistake on that guy.

So hang on, let me let me look at that. Now clarify that. All right, getting back to this. This is correct. I, I apologize, but that's correct. All right.

So if I have 60 volts AC, and I want to find the peak to peak voltage of 60 volts, it's 2.828. And if you get a calculator and you multiply 2.828 times that, you'll get this number and I rounded it off to 170 volts peak to peak AC. So that's correct. This is correct. So do History guide. Anything I said previously?

It's cool. All right, let's move on. All right, what I what I did here is I just kind of put this in just just to clarify it. Okay, most of the, the circuit problems that we've done so far have been with a, a battery source, which is direct current DC voltage. So just for the heck of it, I wanted to put one in with an AC source, what I'm showing you here, all right, that's all basically the calculations are the same. So if I'm looking for VR one, it would be v one right there, v one over r one over r one plus r two, the voltage divider formula and I do my math, and then I get 20 volts, but it's 20 volts AC RMS.

So if I put a meter across r1 I have to set my meter up for AC voltage. And I my meter should read 20 volts AC RMS. Okay. Same thing with VR two. All right, what I did was v one minus VR one, so 50 minus 20. So that I should get 30 volts AC.

And there we go. All right, the current flow through the circuit would be back and forth. Okay, because it's 60 hertz, but my current would be 10 milliamp ers, AC and I didn't put the AC there, so I'll do it now. So it would be 10 milliamp hours, AC, not direct current, alternating current. All right. And what I did here in this, this bottom one just for the heck of it, I put a parallel resistor in there, and we do the calculations of the state Same so VR one would be 50 volts AC divided by 20 over 5000.

And again, I get 20 volts AC because we know from the previous previous courses that I gave you are presented to you, I should say the voltage is dropped right across those two resistors. So therefore, the voltage across those two resistors are my source voltage, in this case 50 volts AC. So, now I did the math and I get 20 volts AC again, VR two would still be 30 volts AC. All right. And now when I'm looking for RT RT is r1 plus the parallel I'm sorry One plus r two in parallel with r three. So we would add these up, and then these two are in parallel.

If I go through the derivation, which I don't show you here, because we've done a lot of these in a previous course. Okay, my parallel resistances for 1428 ohms arm. And that's it. All right, that's our T. I one is right here. And I solve for it. All right.

And so that's pretty much it. I don't know what to tell you, other than we've pretty much finished this. The only thing I wanted to do up here guys is to show you that everything is the same Ah, I mean we we calculate our voltages and currents the same as we did in DC only the sources different. So instead of using 20 volts DC we use in 50 volts AC. And when I, what I saw for the voltages, it's it's an AC voltage and if I need to solve for the currents, it's an AC current. That's it.

Everything else is the same. Okay, I just kind of put this in here. All right, so, voltage conversions. one volt equals 1000 millivolts. Okay, milli is 1,000th of a volt, or a million micro volts, and one micro volt is 1,000,000th of a volt volt. All right, so we've got powers at 10.

One time standard third is milli one times 10 to the minus six is Microsoft Add 1000 volts equals one kilovolt one kilovolt is in the powers of 10 is one times 10 to the third. A million volts is a mega volts and that's one times 10 to the sixth. And I've also gone through this pretty quick. I'm not trying to sell my courses, but I don't want to convolute them and go through all the material time and time again. There's a course up on this platform called basic electronics, or electronics on math for electronics. I go through this slowly, deeply.

And I explain that now. Again, you don't have to take the course. You can go on the internet and research it you can get a book there's all kinds of resources out here in the internet for you to look at. You may have a math book at home, just bone up on it. Okay? bone up on it.

So when we talk about About Milly, you know, milliamp hours, you know that that's 10 to the minus three, a micro amperes, that's 10 to the minus six and so forth. kilovolt is 10 to the plus three and kilo means 1000 volts. That's what I want you to know. I want you to understand this. And that pretty much wraps it up for this, this course or this