Hi. In previous series we took a look at Dc circuit fundamentals and that was quite a few videos and we covered lots of stuff including inductors and capacitors and transient circuit analysis as well, which you a lot of people might have thought was actual Ac circuit theory, but it's not. It's Dc transient circuit theory because as we're going to look at today, we're going to do an Akadaka and we've got to look at Alternating current basics. So now we have to move on to Ac circuit theory, and that includes Ac signal generation, the importance of sinusoidal waveforms as we'll see in this video, and then on to Ac circuit theory, which can actually be pretty much identical to Dc circuit theory, the Ac Ohms law as we'll look at in future videos, but it can also be surprisingly different in many ways.

So let's have a look at Alternating Current basics. So what is alternating current compared to Dc or direct current? Well, it's obvious it alternates polarity. If we've got our waveform like this, Dc would just be like this is zero volts. This is one volt.

Oh wait, got current here. So let's say zero Amps One amp up here. Dc direct current would be just a straight line. Like that, it'd just be one amp.

But alternating current. It changes direction. It's positive uphill in this case. positive one amp and then it goes negative one.

Amps like this. it physically changes direction in the wire. Like that, the current, the electron flow actually changes direction. and that's pretty much the definition of Ac or alternating current.

Which is confusing because you can go Ac voltage and it's like or alternating current voltage. That doesn't make sense, but that's the terminology. Ac voltage. You'll find lots of stuff like that in engineering, but and that's pretty much the definition of Ac is it really has to change polarity like this.

If you've just got Dc up here which might have some ripple on it like this, that might look like alternating current, but it's still direct current with ripple. and yeah, flame wars. in the comments down below, the difference between is this actually Ac and is it Dc. Anyway, we'll get into the details of this, but suffice it to say for this video, we're talking about alternating current.

That's physical current, physically changing direction and this is super important theory because most of our power generation and our telecommunications Rf signal transmission, this all happens in the Ac domain and this all happens with the sinusoidal wave like this. and there's actually something very special about the sinusoidal wave as we'll go through in a minute. now. the sinusoidal wave shape like this comes about naturally in rotating magnetic fields like you get in generators which is used for most of our power generation be it a wind turbine generators, hydro power generators, steam power generators which are also nuclear nuclear energy just heats up steam basically which then drives a a turbine which drives a generator like this and that generates always a sinusoidal output actually you want as close to a perfect sinusoidal output like this as possible on a generator for reasons where that we're going to get into.

So we're going to look at how a basic generator here works and this brings us back to a formula you've seen before in even Dc fundamentals when we talked about inductors. Faraday's Law of Electromagnetic Induction the induced voltage in volts is negative. The chain which is lenses law won't go into details. watch previous videos.

the change in the magnetic flux in Weber's per second. So basically defy Dt Here just means the change of magnetic flux over time in Webers per second and that's it. And then I won't derive how we actually get down to here. But basically this formula here you should pretty much remember along with Faraday's law.

this is the formula for the induced voltage in a conductor in a magnetic field, and it's equal to the flux density in Tesla's B multiplied by the length of the conductor at 90 degrees to the magnetic field in meters multiplied by the velocity of the conductor through the magnetic field in meters per second. Simple, and of course, we've got all that stuff inside a generator like this. so let's have a look. We've got a north pole of a magnet.

South pole of a magnet like this. We've got a shaft in there like that which contains a core and that red, uh part around. There is just a single turn coil. Of course it can be multiple turns.

You wouldn't have a single turn coil in there. Not very efficient, but we'll run with a single turn for today. and the wires come out here like this. Now I won't get into details of how the power actually gets out of there.

I go into like the mechanical slip rings and everything like that doesn't matter. Okay basically voltage current comes out of the coil like this as it rotates in a magnetic field. And if we have a look down here, this is like a side cross section of this 3d model up here. Please excuse the cruditive model.

Didn't have time to build the scale or to paint it at north and South pole Here we've got a uniform magnetic field through here. Let's just assume that it's a uniform magnetic field and then we've got our coil here and here like this. and the coil will rotate through the magnetic field like that and go around and around and around and this will actually produce a sinusoidal wave shape. How does it do that? Basic trigonometry you learned in uh, school.

If we uh, take like the vertical axes like this as the the angle of the coil like this is Theta Here and Theta is the angle. and of course you know your basic trimming and trigonometry. It's just sine. Theta is the angle through that field so as it goes through it actually naturally develops.

Assuming you've got a uniform magnetic field and everything's hunky-dory You get a sinusoidal wave shape out like that. and when the coil is right in in the horizontal position like this, this is the actual maximum Uh. velocity through the magnetic field Like this. It's at its highest velocity at this point.

So at 90 degrees like that, this is when you'll generate your peaked voltage here and here. like this. Depending on which orientation it is, depends on which whether it's positive or negative peak. But when it's up right at 90 degrees like this, it's not.

There's basically no movement through the magnetic field. The velocity drops to zero. Because it's not going through the magnetic field. the magnetic field's going in this direction.

It's basically it. It reaches a point where it's it's zero. So here here here, it's basically generating nothing when the coil is vertical like that. Pretty simple, but that's your basically basic formula for induced voltage in a magnetic field.

So basically our maximum voltage here. our peak voltage we're going to get is B times L times V. So the instantaneous voltage here. So let's suppose this could be E voltage.

Here, the instantaneous voltage at any point in time here equals E Max, which is the maximum assuming it's like 1 up there multiplied by sine Theta the angle of the coil in the magnetic field. So therefore, you end up with that sinusoidal shape. Simple. So in basic maths, when you're talking about sinusoidal waves and cosine and tangents and everything else, you might talk in terms of degrees like this: So 0 degrees, 90 degrees, 180 degrees, 360 degrees.

And in electronics we do talk about. In in Engineering, we talk about Uh degrees in terms of phase difference. So if you have two waveforms and they shift like this, we generally talk in terms of Uh degrees. But what's more helpful to use when it comes to talking about Ac stuff is to talk in what's called angular frequency.

So we use W to represent that, which is actually Uh Omega in the Greek alphabet. It's not just the Ohm symbol, it's also the little W thingy. Anyway, Greek alphabet rubbish anyway equals 2 Pi F. So we talk about this in terms of Pi.

So 90 degrees is actually Pi on 2, 180 degrees is just Pi and 270 degrees is 3 Pi on 2. or however, you want to represent that, and 2 Pi is 360 degrees I.e a full cycle of an Ac waveform like this. Because one thing I actually didn't point out before is like another definition of Ac or something that it needs to include this to be like deemed to be Ac. And this is what differentiates it from the transient analysis.

in Dc. you just have a single transient like this. Ac actually has to have a frequency, It's got to have a period, and it's got to basically repeat that for infinity or x amount of time to really be considered ace Ac in quote marks. So yeah, it's It's got to be more than just if it's one cycle.

Hmm. if a tree falls in the forest, do you hear it? And if you've only got one cycle, is it still Ac? Comment down below. Anyway, the angular frequency is 2 Pi F and you'll find this 2 Pi everywhere in electronics and 2 Pi F is very important. and in this case, we're talking about angular frequency like this instead of degrees.

Anyway, this is in units of radians per second. So and we can do once again, the instantaneous voltage E equals E max times C a sine omega T Like this. and then if you run it through the wash, T equals one on F and with T being your time period like this, and, well, that's one of the most fundamental equations in all of electronics. how to convert time into frequency.

It's just inverse. and this, by the way, is why your confuser here almost certainly has a degrees and radians and gradients. Button gradients, gradient Some weird French thing that surveyors might still use i don't know. Degrees and radians mode.

Your calculator's got it. Guarantee it. That's what it's for. So that's what it's for on your calculator.

degrees, radians, or gradients. Which is like 400 gradients for one, uh, one time period. One t, one turn of your generator is 400 gradients. Meh.

Anyway, Radians Beauty. So if we do Pi on our calculator in radians mode like this and get the sign of that, it's zero because it's in the middle of the waveform that we saw there. But if we do Pi divided by two equals and then sine. Ah, it's 1 because that's when our waveform peaks right up there.

Beauty. And then 3 times Pi divided by 2 equals sine minus 1.. the maths works and once again, with all this stuff, you can really go down the rabbit hole to the physics side of things and advance mathematics of it and everything. And it's like, but anyway, let's get on to the importance of the sine wave and more circuit theory related stuff because I know that like motors and generators, might be boring.

but it's important that you know where that sinusoidal wave shape can come from physically. And it does in the real world, you know? But probably a majority of the power that comes out of your powerpoint was generated with a Gen with an Ac generator like this. So I mentioned before specific benefits of sinusoidal Ac. So let's take a look at them.

and this basically applies to sinusoidal shape. Ac is because it's the ideal Ac waveform. Sure, you can get square waves which are Ac, and you can get triangular waves. You can get all sorts of you know, pulse width, modulated waveforms which can be Ac, and all sorts of stuff.

but in particular, sinusoidal ones have specific benefits. Let's take a look at them. It's easy to physically produce high powers. as we looked at those generators.

This is how the vast majority probably of the power that you're using is generated using perfect sinusoidal Ac from a generator. Sure, of course, these days solar is a big thing and it generates Dc. But um, you know still, the majority is probably going to be coming from some sort of Ac generator, be it wind, hydro, coal, nuclear, whatever it is. And because the sinusoidal waveform is only one frequency, and I'll talk about that more about that in a minute.

it's easy to efficiently transform and isolate these voltages using Transformers. Those so you go from like 500 000 volts, 500 kilovolts, or even 700 kilovolts. I think these days Ac transmission lines those huge ones. They're easy to step down, and you can do that very efficiently using Ac.

Sinusoidal Ac. In Transformers, they're incredibly efficient and you can use those at the signal level as well. If you're designing circuits, audio and other telecommunications type stuff can be isolated using Transformers. Easy peasy because the transformer is just a coil of wire and like a piece of ferrite.

It's really simple stuff and it's what's used for all. basically all Rf and communications technology is. basically. you can't just put Dc on an antenna and have it transmit something.

It's got to oscillate. and if it oscillates using a sine wave, that is one pure frequency. because don't want to go into in this video. but you've probably heard me mention, uh, fourier before and furious Theorem Or Thuria Transforms as you've heard about Ffts in basically oscilloscopes.

This is how like a spectrum analyzer works in your oscilloscope Fourier transforms. Fourier Theorem basically says that any wave shape at all is made up of sine waves. So if you've got a square wave like this, it's actually made up of sine waves at lots of different frequencies. So when you plot a frequency spectrum instead of time, that's F, that's supposed to be F there.

Trust me. Frequency like this. If you've got a sine wave, it's just one line on your spectrum analyzer. Say that's one Kilohertz or something like that, and then you might have another line here at harmonic multiples of that.

Things like that. But any waveform doesn't matter what it is. Sine square, triangle, wiggly piggly your heart, you know, cardiac wave form or whatever it can be made up as long as it's periodic, can be made up of sine waves. And if you've only got one sine wave, then you can actually transmit exactly on that frequency.

There's no other harmonics either side of it, so you can fit a lot more different bits of information in the same bandwidth using different frequencies, and that comes down here. They can be sharply filtered as well, so that allows all sorts of Rf and you know, telecommunications magic to actually happen. All done with sine waves. And as we've seen, sine waves are naturally produced in uh, generators, but they're also produced in oscillator circuits as well.

William Bridge oscillators, coal pixels, oscillators, you know, phase shift oscillators or whatever. and also when you filter stuff, what comes out of it. If you've got a simple Rc filter and you feed a square wave into it, it could be Lcrc. It could be an active filter.

Whatever it is, feed into a filter. What comes out, hopefully a perfect sine wave. The better the filter, the more perfect a sine wave comes out. And this is a really interesting point.

The sinusoidal wave shape is the only wave shape that is not distorted by when it passes through capacitors and inductors. because, well, that's what magically comes out. So if you feed in a sine wave, you're going to get a sine wave out of a filter even though the field is made up of inductors and capacitors. And well, that's an inductor.

There little hairy resistor is an inductor. Who knew that? Anyway, you feed that in and it's not. You can filter them out, but the actual wave shape is not distorted by those components. Whereas if you looked in the previous videos of Dc fundamentals where we looked at transient circuits in capacitors and inductors, yeah, they.

it actually distorts them. And yes, I know if you feed a square wave through a series capacitor like that with no load, then you're going to get a square wave on the output. Except that if this is Dc here, the Dc will now be. Well, Dc will be removed because it's an Ac coupling capacitor.

It moves all the Dc. But anyway, once you start trying to drive that into a load and actually pass in like a large current through that, yeah, you're going to come a gutzer. Also, Sinusoidal Ac is great for motor drives and things like that. You can get multi, three-phase or multi-phase motor drives and stuff like that.

Really efficient stuff anyway. But some of the problems with Ac of course. Well, you can't store it of course like you can in batteries. It just sits as electrochemistry inside a battery.

and it's not actually not that easy to measure as we'll look at in a minute. You basically have to let rectified in order to measure the value of it. Unless you do it, there's other ways you can do it. but anyways, it's actually not as easy to measure as Dc.

And basically Ac is not a thing and even can be a problem. For like much of the electronics out there, all your digital stuff and all the other things like your Dc power supply. you want a rock solid 3.3 volts or 5 volt supply if as we saw before like it has some ripple on, you know if it's got some ripple on there. If you've got some 50 hertz ripple from your transformer power supply or something like that that can ruin your day, you don't want that.

You want to get rid of Ac from any sort. You know it's a much of modern electronics, but it's useful for a whole range of stuff. So there's tons of benefits to sinusoidal Ac. and that's why it's pretty much the duct guts in this.

sort of like high power and Rf stuff and things like that. You just can't do the same sort of stuff you can with Dc, at least not easily. And yes, you can actually, uh, transmit the power using Dc high Voltage transmission. I've actually done a video.

I'll link it in down below and up here. It's very interesting about high voltage Dc transmission. It's over on my Eevblog2 channel, so check that out. But basically, yes, you can use Dc to like transfer large amounts of power over transmission lines and stuff like that.

But then ultimately you've got to like chop it up and do some Dc stuff. Dc to Ac conversion to actually convert it and then basically convert it back to Dc. So you're never going to escape Ac and all of your Dc to Dc converters or your switch mode power supplies and things like that you're so used to using in modern electronics. Well, it's Dc, it's chopped up.

It becomes Ac basically. and that's what you're feeding through the transformer. And this brings us to some really important terminology you use all the time in electronics and it can be used for both voltage and current. So we're just going to use voltage here.

So we've got our original waveform. Like this doesn't have to be sinusoidal. We'll get into that. So basically got four different ways to define the voltage of this waveform.

As I said, it's actually not that easy to measure, let alone be able to communicate what the actual value is to somebody else. So what we've got is four different ones. We've got peak, peak to peak average, and Rms or what's called root mean squared. So a peak the voltage peak here is from zero, or a reference point doesn't necessarily have to be zero, but it's defined as the reference point of the waveform.

And because it's Ac, it'll go negative as well. So the peak value is simply the value where it reaches absolute maximum in one direction like that relative to the reference. In this case, it's one volt. So you might say one volt peak and it'll be usually represented by either pk or just p.

If you just see p on its own, you know that's peak. But the peak to peak voltage, as it's called is the value. From the negative excursion bottom down here to the positive excursion up here like that, that is your peak to peak voltage. and if you've got a symmetrical waveform, the peak-to-peak voltage is going to be twice the peak voltage.

obviously. Now, one of the downsides about peak and p to peak voltages: While they're very commonly used, they don't actually tell you anything any information at all about the way the actual waveform shape. it doesn't actually care. This could be a perfect sine wave.

Could be a triangle wave. A square wave. Doesn't matter what this waveform is, If it goes to plus one up here and minus one down here, it doesn't matter. It could have a tiny little spike like this tiny little spike down here.

It could be like a you know, that could be a very poor power factor as we've looked at White Mains waveform or something. The peak to peak. It doesn't matter what the waveform is, the peak to peak is just the actual instantaneous peak value. Like that, but average and Rms they're different.

They actually take into account the actual waveform itself. Now the average value is defined as this and there's several different ways to sort of explain it, but this is the way I'll do it. It's the total area under the waveform divided by the period of the waveform. So the total area under the waveform.

That means all this area under here like this. like to the axes. you've got to have it like 2a reference axes. so all the area under there.

But we've also got all this area under here and this one's positive and this one's negative. And because it's a perfect sinusoidal waveform or it could be a perfect square wave for example, it doesn't actually matter if the area above the axis here is equal to the area below the axis here. and they're both the same amplitude like this, the average value will actually come out at zero. So if you feed an Ac voltage a perfect Ac voltage with no Dc offset into your Dc multimeter which reads average value, it'll read zero.

And also for multimeters that aren't true Rms multimeters, that'll have true Rms written on them. Usually they will actually be what's called an average responding multimeter for Ac. So what that means is that it assumes that the waveform you're measuring in Ac voltage mode or Ac current mode on your multimeter is a perfect sine wave. If it's not a perfect sine wave, it's going to give you an error.

It's not going to be accurate because the multimeter has only been calibrated to assume a perfect sine wave. To give you another example from digital electronics you might be uh, familiar with if you've got a V here. So let that goes up to one volt. there.

this is time. and if you've got a pulse width modulated square wave that is, you know, like this, let's say that this is ten percent of the time. This, and it's zero. Ninety percent of the time like this.

what is the average value going to be? Well, our axis is zero volts down here. Like this, everything's above the axis. It's not actually an Ac waveform. It doesn't go negative, but this can actually apply to doesn't matter where the reference point is, our reference point in this case, is 0.

Okay, the total area under the waveform. So the period from here to here, it'll be one volt for ten percent of the time, multiplied by nine zero volts for ninety five percent of the time. So therefore, it'll actually equal one tenth of that, or 0.1 volts will be your average value over the period of one wavefull. So let's analyze a half wave, rectified sine wave and you'll be familiar with this if you've done made any do-it-yourself basic power supply from a transformer.

So this is how I see a transformer. Just got a single identity in there, but just driving a load. There's no filter capacity because that smooths it out and ruins your day. So we've got a waveform that looks like this: It's here's our total period here from zero to two Pi or zero to three sixty degrees.

And it's as its name suggests, is a half wave rectifier. It only rectifies the positive half the other half of the waveform down here when it goes negative. The Diode is, uh, reverse biased so it doesn't conduct at all, so you just get zero. So you get this half wave rectified waveform.

Now, we'll analyze this waveform using our formula here, and there's several different ways to look at it. But because it's a sine wave, what I'm going to do is like this half of the sine wave from here is identical to this half here. So what I'm going to do is just split it into quadrants like this. So just assume that there's like four different areas that we're calculating here for our one waveform from zero to two Pi.

So it's the area of A here, plus the area of B plus the area of C plus the area of D. Remember, it's the total area under the waveform divided by the period of the waveform, which is 2 Pi. So area A plus B plus C plus D divided by 2 Pi. Now, we'll just normalize the area to 1.

we'll just call it one because we're not talking about any actual absolute value here. So we'll just normalize it to say that area A is one. Area B is identical to area A. Obviously, it's a perfect sine wave.

So one plus 1 and then area C and D are, of course, 0. There's nothing there. So it's 1 plus 1 plus 0 plus 0 or 2. divided by 2 Pi is equal to 0.318 not 0.318 volts.

0.318 is the factor that you then multiply by your peak value up here, but that is just a factor that you multiply by the peak value up here to give you your actual average voltage for a halfway rectified waveform. And that's a common number. You'll actually see that a lot, and especially when it to do with like half wave stuff. If you see that number, you go.

Oh yeah, that's halfway and we'll now look at a full wave bridge rectifier. I haven't bothered to draw it, but basically I'm familiar with the four. I'll put up the circuit here here. It is.

now. This will give us a waveform that then looks now like this. so we'll get two humps because it does the positive and the negative cycle as well. But because that's now identical and we've doubled our frequency, say it's 50 Hertz here in Australia, not any of that 60 Hertz Yankee rubbish.

If it's 50 Hertz and then it actually becomes a hundred hertz Now because the waveform is repeated so our period is not two Pi anymore. It's just Pi like this. So it's one plus one area of A plus area B divided by Pi which is Six Three Six Wait Wait no, that's isn't that meant to be Six Three seven. Here's sagan.

Hey, Six Three Seven yeah, Why why would it be Six Three seven? Because when you go into the calculator here, if you go two divided by Pi equals of course Zero Point Six Three Six Six. So you record it up to zero Point Three 7. Well, I'm gonna say that it's 636 because that's kind of like symmetrical and it's double 0.318 that I rounded before. So I'm sticking with Six Three Six.

You reckon Six Three Seven I like. I'm the type of person who likes symmetrical and all. But yep. Six Three Seven.

Okay, leave it in the comments down below. Thanks again! Now the thing about peak, peak to peak and average voltages is that they're abs and currents. is there useless for measuring power? You'll get the wrong value. In fact, you'll get zero because let's just assume that this is a current waveform.

Okay, and you've got it: Dissipating power into a resistor. There's going to be power dissipated in the resistor. On the positive half like this, there's going to be power dissipating the resistor. On the negative part of this, because power doesn't care whether the voltage is positive or negative.

it's just the power dissipated in the resistor or the load. then. well, you're But if you measure the average current, the average current is going to be zero. And zero times at P is I squared r Zero squared times r is zero.

So you've got zero power dissipation. Go try it. Put an Ac waveform into a resistor. You're going to dissipate power so it doesn't work.

In this particular case, we have to use Rms. So Rms stands for it's right in the name. The Root mean squared. where does the Squared.

bit come from? Well, Power equals I squared r. There's a squared factor in there, and when you square that, that is the mean squared. So if we have a look at the waveform over here for current, we've got our regular Ac current waveform. We'll call that I a C here.

Then if we square that current, we square it like take every single point on this waveform and square it the number. Any negative numbers, they're going to go positive like this. so it's going to be squared. So it's going to be much larger like this and it's all going to be shifted up on the positive half of the reference axes like this.

So we'll call that I squared Ac. So that's where our squared factor comes from. So what you do is you actually work backwards. You take the square first, then you take the mean, and then you take the root the square root.

So we've done our squared business. Let's now take the mean. We've looked at the mean before. The mean is the average.

Okay, it's just another word for average. The mean. They're the average is smack in the middle like that, because that's a perfect sinusoidal waveform. Squaring.

It doesn't change the wave shape. It simply shifts it up and changes the amplitude like this. So we'll call that I squared Ac Average Like that. That's our average value.

So we've done our squaring business. We've done our mean or average business. now. We need to take the square root of that average value.

But what is that average value? Well, it's pretty easy. As we looked at before, this is the peak to peak value. Well, it's the peak to peak value of the waveform. It's now the peak value of the waveform.

I squared Ac is also I squared peak. It's the peak value of the waveform. and the mean value is going to be the peak divided by 2. It's smack in the middle.

Simple. So this is I squared Max as we'll call it over here. Now, let's actually go through and derive the actual answer for our Rms, and you might be familiar. 0.707 We're getting there now.

The Dc power must equal the Ac power, because that's the basically the definition of Rms is that, uh, it's the equivalent heating in a resistor for. uh, the same for the equivalent value of Dc. So that's what the Rms value actually is. So how we derive this is, well.

the power in Dc is I squared r. We learned that back at day one, and the power Ac here is actually the average value here. Now that we're squared, it's no longer zero. It's right up there.

It's going to be the average value times the times the resistance in the load. So it's of course that average value is going to be half of the peak value I max so that you could put average in there if you were like Ac average in there if you want. but we'll put half I squared r max now because we've got R on both sides of equations. we can actually take that out and Idc is equal to the square root because we had square here.

so we have to bring it over and now it becomes square root half times that I squared max. and then you can just rearrange that again to be I max on the square root of two. And well, if you say I max is one then it's 0.707 That's your answer. But the this is the this is the formula for Rms value is 0.707 times the maximum current there.

So anytime you see 0.707 in electronics, you know you're talking about one on square root of two and it's basically Rms and this also applies to voltage as well. So V Rms the Rms voltage is equal to 0.707 times V Max which is actually V peak-to-peak So the equation that you have to remember is Volts Rms equals Volts Peak divided by the square root of two. Or you can remember the uh 0.707 if you want. but square root of Two will give you a more precise answer.

So and that if you just rearrange that formula, V Peak Peak voltage equals the Rms voltage times the square root of Two. Easy. And there's other formulas which derive you know you can go directly from volts, Rms to peak to peak, or peak to peak to Rms or whatever. you know.

there's various combinations of these, but if you just remember, well, if you remember one of them, you can derive the other, and then you can derive the peak to peak from the peak, etc. etc. Now, we've only looked at ideal sinusoidal waveforms, but what if you've got i don't know a sawtooth waveform like this, or you've got like a a high crest factor, we might go into that. um, a waveform like you know, current waveform like this.

How do you get that? Well, we start looking at integrals and this is where you get a little bit more advanced calculus, which we don't really want to go into here. So the average value one on T, the integral from zero to T, and then the function of that. and we won't go into the details. You can do this yourself, but it's basically um, an integral is just the area under the curve and I've done a practical video I believe showing this somewhere.

I'll try and link it in on an oscilloscope. Um, the integral is just the area under the curve. so it's exactly what we did before, but you can actually do the average uh, derived. You can derive the average formula we did before using integrals and stuff.

But anyway, it's that. and the Rms version of it is simply the square root with the squared in there. It's exactly the the squared factor, the mean uh factor, and then the square root in there. So anyway, we won't go into details.

it's basically just getting the area under the curve. so you just have to get this area under the curve here. and you can do that using graphical methods. If it's just like a sawtooth waveform or something like that, or even, uh, you know, a pulse current.

uh, waveform like that. like a poor like power factor on a Dc to Dc converter, you'll get a waveform like that. I'll show on that in previous videos. You can do these actually using our graphical methods or you can do it using uh, differential calculus.

Now the absolute last thing we're going to look at, I swear for this video. Anyway, just to round this off is what's called crest factor. This is important for uh, Rms true Rms measurement you might get on your multimeter for example. this is also known as peak factor as well.

and the crest factor or peak factor is the peak on Vrms. So if we've got our waveform here, obviously, we've got our peak value up like this. Easy. and our Rms value is going to be 0.707 times the peak there that we've seen.

and that gives a crest factor of 0.414 Beauty? No worries. But if you've got a horrible waveform like this, like the sine wave is like this, but you've seen this in videos where you might have a non-power factor corrected uh, mains power supply. for example, current peaks could be up like this. And if you're trying to measure, say, with your multimeter using your true Rms converter in your multimeter of this waveform like this, if it has a too high, too higher crest factor like this, your true Rms converter won't be able to handle it.

And you often find uh, the maximum crest factor value in the data sheet for your meter or your true Rms converter chip measurement system. Whatever it is. So there's a maximum. You know they can't tolerate an infinitely small pulse like this.

There's going to be a point where they come in guts and just go. I'm going to give you know I'm not going to give an accurate value. I'm going to read low so you can see that the in this particular case, the the peak value might be absolutely identical. Say it's one between the two of them, but because it's much shorter like this, the Rms value of course is going to be much lower.

It's not going to be 0.707 anymore because there's no longer a perfect sine wave, So it could be could be you know 0.2 or something volts or something like that. So it's going to be 1 divided by 0.2 For example, it's going to be a crest factor of 5 and that that starts getting up there towards where you know you're a true Rms uh, converter multimeter because there's different methods for Rms conversion which we want to go into. Maybe I've done that in another video, don't know, done so many videos and yet that's getting you know that's getting pretty high. So once this gets narrower and narrower and narrower or the you know the ratio it doesn't like.

The waveform could be different. It can be any type of waveform, but the crest factor V peak on Vrms. if that's too high, then yeah, Screws up your Rms calculations and you need basically you know better, faster sampling hardware for your Rmsr converter chip to actually measure it. Or you might have to go to some method that there's Rmsr converter chips that actually measure the heating in the resistor so they don't actually you know, do it Sampling wise.

they actually like physically measure how much power is dissipated in the resistor. That's old school 1960s 70s stuff. so I hope you found that introduction to Ac useful. I know it's very long and there's lots of stuff to cover.

I could have broken it up, maybe into smaller videos, but there's a lot more to come. We haven't even gotten into other stuff like Transformers and circuit theory and all sorts of other stuff and Ac. Ohm's law and all the rest of it. But yeah, a complex numbers and things start coming next.

but this will all be in part of the Ac circuit Theories a circuit theory series. There you go, if you liked it, give it a big thumbs up. As always, discuss down below. Catch you next time you.