Okay, on this slide here, we're going to look at this this other wave form right there and that wave form is the wave form across the resistor all right right there. Now in the previous slide we looked at this wave form right there. And if you look right over here, all right, we talked about this one again. And if you remember this was the voltage across the capacitor at at different points here. A B CMD here there are A, B, C and D. And we talked again, we talked about that in the previous slide. So now Now let's let's talk about the voltage or the voltage waveform across this resistor.

Now, I have two circuits. And I kind of simplified it. All right, this circuit here when the switches in this position, I'm actually charging this capacitor right there. When I put the switch in this position here, I've redrawn it, basically the capacitor is discharging through the resistor. Alright. So let me Let's stop, I'll clear the slide off and we'll continue.

So what I've done is I've broken this up here where a on the capacitor equals a one A to B point B on the capacitor is B one, B two on the resistive waveform. Point C or step C on the capacitor, the C one, C two on the waveform across the resistor. And then the D one, D two. So let's look at this. Well, there's a right there and we know that that's 63 dot two volts at a one, right, which is this value here. All right, it's 37 volts.

Well, if you look, what's my supply? 100 volts, right. So if I've got I'm in the charging portion right here. All right. So that means I'm charging up. All right.

So if I'm charging up at that instant, I've got 63.2 volts across the resistor. What do I have across the mean across the capacitor? What do I have across the resistor? I've got 37 volts. Actually what I did was I, I kind of rounded off to 63 to make this a little nicer. So we got 37 volts at this point here.

All right, so now my waveform stays high, and then my step voltage or my sawtooth goes to zero. All right, and what happens? All right, the capacitor now discharge is through This resistor and since my current is reversed, I go through the zero line here all right, and I go to some negative voltage and the negative voltage will be 37 volts which is here minus 100 All right, because my supply is 100 volts, so I will get a swing of 100 a total swing. So, if you can see here is 37 minus 100 volts is a minus 63 volts All right. Okay, so now I met B Two or Yeah, B two, B one I'm sorry, right here. And my capacitor up here has discharged.

All right over here B, it's discharged. Remember, discharge is 63%. So what I'm left with now is 23.3 volts. All right, and again, I do my math. I'm sorry, I do my math right here. And at v1, I made 76.7 volts, because I've got 23 volts, still left on the capacitor 23.3 and 23.3 from 100 It is 76.7 right there.

And again what happens is I discharge so I have a swing there of 100 volts. So you can see that 76.7 minus 100 volts is 23.3, that's 100 volts swing. Now, notice this curve here all right, that curve there is the opposite of of this curve, okay. So as this curve is discharging, the current through the resistor is following the same path as the discharge curve. So I get this exponential growth voltage. And this keeps repeating and repeating.

So for instance, on C right there, a point C i should say I've got 71.6 volts. So now what do I have across that point in time across my resistor, it would be 28.4 because 100 minus 71.6 is 28.4. All right, when we change when we go from 100 volts to zero volts almost instantaneously, my capacitor discharges and I get this flow of current through my resistor and we know that that's got to be 100 volts swing So we get 71.6 because 28.4 minus 100 is 71.6. And we keep repeating. So you'll notice, let me stop and I'm going to clear the slide off. You'll notice that these curves here are opposite, but they have the same exponential shape.

And that's because current through a resistor are in phase and it's the same. All right. Now this waveform here is if you look the Time, the time of the on portion, or the high portion of my waveform is point one seconds. And the low portion of my waveform is also point one seconds. All right? So what's my RC time constant?

Right there. So my on and off equals my RC time constant. And again, my RC time constant, is this times that. All right. All right. So we're going to see in the next two slides, what my waveform looks like when my RC time constant and my input waveform are maybe 10 times bigger or one 10th of the smile voltage.

So let's look at that in the next slides. All right, we're gonna stop here, this can be a little bit confusing or a little bit difficult for a new student to, to grasp. So what I suggest is you stop it, go over it, look at look at these charts that I've given you, and see if you can digest them. Now, at some point, I'm going to be putting some labs up there with this. Alright, and you're going to have to buy some lab equipment if you want to go that far. And actually will mimic will mimic these waveforms.

So just take a look at this. Try to understand it. You've got my contact information. And send me an email, we'll see if we can straighten it out. But look at it. And at some point we're going to be doing some labs.

They'll they'll become clearer they'll become, because you'll actually see the waveforms and you can play with it, you can change the frequency and it'll, it'll, it'll come clearer. So let's stop here. Go through it again, look at the charts, and we'll get you through this. Okay, on on this slide here, you'll notice that our RC time constant is still the same point one seconds. All right, but our step voltage, your square wave is increased. In other words, we have one pulse here, and that's one second and that is high.

And then we have the bottom portion of that way. form which is low and then we keep repeating it as you can see, all right. So, looking at our chart, we know from the previous slides in previous discussions that after five time constants my capacitors fully charged. Well, if my one time constant is point one seconds, okay five time constants are 0.5 seconds. So, five time constants will be 0.5 seconds. So here it is right here so what happens?

Okay, what happens well as I go, it just goes hi here, my Capacitor Discharge charges and It's fully charged right there. And it just continues on that line and then what happens? Well, we have a negative going edge on this square wave and my dis my capacitor discharges fully towards zero and again right there because that's approximately five time constants. And it repeats. So when I have a time constant, that is, or what I what I should say is when I have a step voltage right here, that is five, five times a greater than my time constant because in five time constants, my capacity is fully charged here, I'm going to get a waveform like that where the capacitor will charge up, stay charged and right here I get a negative transition. So now my waveform across the capacitor my voltage discharges and that also will be five time constants.

And we know that that will be 63% and adjust repeats. All right, it just repeats. And that again, that will happen when my step voltage highs and lows. The time is five times or greater than my time constant. So for instance, when one time constant is zero dot one second five time constants equal zero dot five seconds. What am I this, I'm up here, this is up on a positive level for one second.

So it gives the capacitor enough time to fully charge and fully discharge. Okay. Let's stop here clear the slide we're going to talk about the bottom wave. Now, the bottom waveform is actually the voltage across this resistor here. And basically I put a little switch in to kind of simulate my step voltage. So in this one, we're right here, we're up there and we're charging and when it goes down my switches in this position here, and I've I've kind of redrawn In a theater to make it look a little nicer.

So what happens? Well, up until at this point here, what do I have across that capacitor? Well, I've, let's look at this one here. I've got 100 volts, don't I? I've got 100 volts. And my polarity on my capacitor is minus and plus.

So what does that mean from our previous discussions? That means this side has a surplus of electrons. And over here I have a deficiency of electrons. All right. And what are electrons on a capacitor want to do? They want to equalize Let me clear the slide off and we'll go they want equalize so.

So we're up here. And that means the switches this way, and I have current flow or electron flow this way. Alright, so now I've got a lot of electrons or a surplus of electrons on this side of the capacitor and a shortage on this side as we stated earlier. All right. So now what do I do? I close the switch.

And electrons wanna flow this way, because we want to equalize or the capacitor wants to equalize. So now, what happens is right here all right. I have current flow in the opposite direction, it's discharging. And therefore, my voltage polarity will be the opposite compared to what it is when it was charging, discharging, and again, it takes five time constants to discharge the capacitor. So this is the voltage and the current. A current well the current flows through the resistor and the voltage is across the resistor and we just repeat that.

All right. We repeat that. So, what's happening here is we have current that that is charged current This charge current through the resistor there. And that's why we have these what I call these spikes that go above and below the zero volt line, which is there. All right. Okay, um, that's pretty much it.

Oh, let me add one thing and and the frequency depends on my step voltage, and my RC time constant. Okay, so with that said, we've got one more slide. I'm going to clear this off, we're going to go to the next one. And that pretty much does it for this. This, this this section here. All right, on this one here, look at what we've done.

Well, my step voltage stays pretty much the same, or is the same, I shouldn't say but I've increased my time constant to 10 seconds. So to fully charge that capacitor, how long would it take? Well, five times 10 seconds is 50 seconds. Is it ever going to get there never going to get there because my step voltage were high for one second and low for one second. So it's never never going to get there never. So what happens is, well, when I go high here, since I have a very long time constant, that time constant is what?

One time constant is 10 times longer than the positive step on my voltage. So it's just gonna ramp up one 10th of one time constant. So how can I figure the voltage here? Well, one of the ways is you can use that formula that we talked about earlier, I'm not going to do it, I've done it in the last one. And you just plug in what you you need to plug in and you'll get, you'll get the voltage. All right, and then the discharge cycle.

Well, it's going to be what the discharge cycle is going to be 63% of what it's charged here. If you remember, go back and review the, I think it was two or three slides up. So you're going to get a voltage here and we know that the voltage there is going to be 63% of that. And then it's going to charge up and down. Okay. But the point I'm trying to make here is because we increase the value of varn See, and we left our, the, the on and off time of our step voltage the same.

It's going to be a very, very long time constant, it's never going to get there and we're going to get just a very small charging district discharge increments. And then to calculate what's on the resistor, again, we did that I was two or three slides back, go up there, use the same calculation or the same method. And what you're going to find is that's going to be pretty much close to 100 volts here. And then we're going to go below zero, a very small amount and it's, it's going to continue that way. All right. So that's pretty much it on on this one here.

What I am going to do As I didn't take the time going over this actually the last two, because we kind of did it originally, but I'm, I'm going to give you some exercises. And I didn't do it. I didn't integrate it into this because the the discussions were long and I didn't want to make them any longer. So I'm going to be putting some problems up. And the problems may very be exactly what's on here. And you'll have the solution.

So look for the worksheets up there, and we'll give them to you. So with that said, this is Al from Al's electronic classroom saying, keep on truckin. Ladies and gentlemen, we'll get there and may all good things come to you. And we'll see on the next. The next course that I put up, take care bye bye now.