 Hi, I'm Zor. Welcome to a new Zor education. I would like to talk about one very important property of alternating current. We will talk about alternating current induction. Well, I would say induction is probably the main property of alternating current, why we actually use it at our homes and everywhere in the industrial world. So, this is the fundamental property of AC, alternating current, and actually it's the base of the whole transformation of electricity and usage of electricity wherever we use it, which means everywhere actually. That's our main source of energy, which basically supplies, which moves everything in our world. And this is the property, induction is the property it's all based upon. That's the main one, why we actually use AC. Okay, first of all, we did talk about induction before. We considered a loop, let's say, and if you have some kind of a m-meter or m per meter, which is connected to this loop, if you will take a permanent magnet, let's say, and you will move it inside and out, in and out of this loop, you will see that electricity is basically generated. Well, that's the basic mechanism of induction. What we are doing, moving the permanent magnet, we are changing magnetic field. If permanent magnet is standing still, there is no electricity in the loop. But only if it's moving, when we have the variable magnetic field, then electricity is generated. More precisely, we have actually formulated as variable magnetic flux, flux which goes through this loop. So it all depends on intensity of the magnetic field, shape of the loop, etc. And we actually proved that the EMF, the electromotive force, which is inducted in this loop whenever we are changing magnetic field, this EMF is related to a changing magnetic flux. This is the rate of changing the first derivative. It's a rate of changing of magnetic flux, phi, which goes through this loop, where magnetic field or magnetic flux is actually the product of intensity of the magnetic field in Tesla's, if you remember, the units. And this is the area of this loop, and this is only whenever we are perpendicularly moving. If there is some kind of an angle, then there is a cosine of the angle, or sine of the angle, depending on how you measure the angle, from the vertical or from the horizontal part. So we will concentrate mostly on this formula, because we will use this perpendicular kind of magnetic fields. So there is no angle here. Okay, so intensity is changing whenever we are moving our permanent magnet. We are moving it closer, which means intensity is greater or further, which means intensity is less. So we did all these experiments with a permanent magnet. So why did we move this magnet? Because we wanted to create a variable magnetic flux. Now, with AC, we already have this variable magnetic flux. And here is why. If you will put another, let me put it at an angle a little bit. So this is another loop. These loops are in the parallel planes near each other. Now, if you have a variable AC, if you have alternating current in this particular loop, this is a source. What happens? Well, we all know that whenever you have a current around it, there is always magnetic field. But in this case, because our current is variable, AC means alternating current. It all depends on how we produce electricity. We were talking about the frame, which is rotating in the magnetic field, etc. So this is AC, which means our current is variable. Since our current is variable, our intensity of the magnetic field inside of this loop and outside in neighborhood is variable. So we don't have to move anything. In the previous case, I was moving the permanent magnet through this wire loop. In this case, I don't have to move anything. So these wire loops are parallel to each other and the magnetic field goes through the center of these lines of magnetic field. But again, since my current is alternating, the magnetic field will also be alternating. My current is changing in magnitude as a sinusoidal function. So it's changing the direction all the time, which means my magnetic field will also change direction and the strength. So from plus maximum to zero to minus maximum, back to zero to plus maximum, etc. So that's how my current is changing and that's how my intensity of the magnetic field is changing. And that's how the flux which goes through this secondary wire, the flux is changing. And since the flux is changing, we do have exactly the same thing. We have induced EMF in this particular thing and if you have this ampere meter, then you will detect that there is an inducted electricity current, which goes actually again back and forth, back and forth. Now with ampere meter, we are usually measuring the effective current. If you remember from the previous lecture, there is an effective current. But in any case, we understand that this is basically a sinusoidal change of flux and that's why sinusoidal change of the induced electricity. So how this is going through the formulas. Well, let's start from this thing. This is alternating current, which means we have the source primary source of EMF. This is the voltage here generated by an hydroelectric station, whatever. And this is basically a sinusoidal kind of thing, cosine, omega g. That's how we usually put it. Now from this follows that my current is also alternating. I0 is some kind of a maximum and cosine of omega g. Fine. Now, if you remember, intensity of the magnetic field, which is generated by the current, which goes through this wire loop. In the center, we did calculate it in the center. So intensity, primary intensity was, what was it? In the vacuum, it was mu0, which is permeability of vacuum times the current, which is running in the loop. And it's variable. That's why this is variable. And I think we should divide it by 2r, where r is the radius of the loop. Let me check if I... Yeah, something like this. So this was our formula. So whenever... Now, this is in the center. In other parts of the loop, quite frankly, I just don't know how it will look. It will probably be similar, but I'm not sure it's exactly the same, but probably similar. But in any case, it's always proportional to the current. Maybe some other parameters which determine how far from the center this point actually is. Through the symmetry, it's probably only another parameter with the radius from the center to a point to find out what exactly the magnitude of my intensity is. But it doesn't really matter. It will still be probably proportional. And approximately, I can really use this particular expression as the intensity. And if this is intensity, it goes through this loop. If loops are close enough, so almost all lines of magnetic lines are going through this secondary loop. That gives me the flux which goes through the secondary loop. Equals to B' of T times S, where S is the radius of the loop. And it's changing, obviously. You see, this is changing as I of T as current. Current is cosine. So whenever I would like to calculate what's my induced EMF, I just have to take the derivative of this with a minus sign. By the way, I didn't mention it, but minus sign was explained in the lecture about self-induction. Because the induced electricity always goes, induced EMF is always directed against the primary EMF. But that was addressed in one of the previous lectures. Okay, so now what we have to do is we can calculate our secondary EMF, secondary T. It's equal to this, which is minus. Well, S is a constant, obviously. The derivative of this is derivative of this. So mu is constant, 2r is constant, and all I have is basically derivative of I of the current. Now, this is I0, so it will be, again, this is a constant. The derivative of cosine is minus sign, so I will have plus sine omega T. And the derivative of the inner function would be omega here. So basically that's the formula for secondary, which quite frankly doesn't matter what it is. We can say it's S0, some kind of a zero, which is this, times sine of omega T. So as you see, my primary is sinusoidal, like cosine. And my secondary EMF induced by the principle of AC-generated variable flux, et cetera, is also sinusoidal. The only thing here is this is a cosine, this is a sine, which means they are shifted. Remember the graph of the sine and graph of cosine, they're just shifted by 90 degrees pi over 2. Okay, so these are basic calculations which show that this secondary loop will have certain generated induced EMF. And we can measure it in some way or another. Now, this is the theory, this is the basic principle. It's not really yet practical. And to make it practical, I would introduce few improvements to this very simple model. Okay, so let's forget about all these. This is all fine. All I wanted to prove, actually, that this sinusoidal kind of a character of secondary EMF. So my first improvement is the following. Now, you remember there was a constant Mu0, right? Mu0 is permeability of vacuum. Probably air is very similar. Now, this is something which depends actually on what's in between these two rings, these two wire loops, right? Now, there are different materials we can use, not only vacuum or air. We can put something which has a better permeability, which means that magnetic field goes easier through these materials. Well, it's all actually based on iron, ferromagnetic materials we know about them. They're used everywhere. So you know that if you will put, let's say, a wire around a nail and the wire will be connected to a battery. Now, a nail becomes a magnet. That's called electromagnetism. Now, why it happens? Because the current which is running through the wire around the nail, it produces its own magnetic field. And this magnetic field is reorienting atoms inside the iron, inside this material the nails are made of. And by orienting them, we are making actually this nail a magnet, because the property of magnetism is related to synchronous orientation, the same orientation of all the atoms or most of the atoms in this particular material. So, what happens if I will change the direction of the current? Well, these ferromagnetics are very sensitive to the current which is goes around them. Which means that they are very responsive. If the current changes direction, the magnetism is changed to the opposite. So, whenever we have an AC and the current is changing direction whatever number of times per second, like 50 or 60 times per second, my ferromagnetic material which is inside of this, if I will put it in, will also change the direction. And what's very important is that the permeability of ferromagnetic is significantly greater than permeability of the vacuum. So, the magnetic lines tend to be more concentrated. So, if you have, let's say, this wire loop with some kind of an AC going through this. Now, in general, magnetic field can be expressed as this type of magnetic lines. But, if you have an iron core inside this loop, the magnetic lines would be this. And then they will go out. Now, why would magnetic lines go through this ferromagnetic core rather than just outside? Well, that's very easy. Whenever you have certain flow, if you have more resistance in one way and less resistance in another way, let's say it's the river and the river is splitting into two, but one channel is very narrow and another is very wide. Where is the energy of the river goes? Obviously to the wide, much more than to the narrow. So, since it's easier for magnetic field to go this way, then most of the energy generated by current which is running in this loop will be going through this. So, what I will do, I will put a ferromagnetic core inside these two wire loops. What does it give me? Well, it gives me the concentration of energy generated by this particular current. Concentrating this in this ferromagnetic core, which means all the magnetic or almost all the magnetic energy, all the magnetic lines, all the magnetic energy going through the second loop. There is no dissipation like this. This is dissipation, but now with this core I don't have this dissipation. I have almost all energy directed here. So, that's my first improvement. By the way, this means much greater than and for iron, for instance, the mu is about 200,000 times greater than the vacuum. So, that actually allows to concentrate the magnetic field energy through this iron core. So, that's my first improvement. Now, let me do my second improvement. Now, what happens in this particular case? Well, magnetic energy still is dissipating here, right? So, how can I do even better? Well, simply. That's how. So, I will connect my ferromagnetic core, my iron core, would be a loop in itself. And again, since my iron has the permeability significantly greater than air around it, practically everything will be in a circle. So, magnetic field will not dissipate. I mean, it will dissipate, but tiny amount. Most of the magnetic field generated will be only here. Okay. That's very important. And now let's just think about self-induction. This is something which I never actually saw it in the textbook. But here is what happens. Now, since we have a variable magnetic field here, it will obviously induce electric current, not only in this, but also in this. Now, this new EMF will be the source of another change in the magnetic field. And another change in the magnetic field will be a source of changing of EMF. So, my point is that after a while, we will have exactly the same magnetic field, changing magnetic field, going through both wires, and it will probably equalize EMFs here and there. So, whatever is produced here, after a certain amount of time, when all these mutual effects, variable current produces variable magnetic field in the core. Variable magnetic field in the core induced a secondary self-induced EMF in this and some induced EMF here. So, it's the same magnetic field, variable magnetic field will go through this same two loops, wire loops, and it should actually equalize the EMF in both of them. So, and this is not just one particular step, like from variable electricity. We have variable magnetic field and variable magnetic field results in a self-induced electricity in this. No, it actually continues. I think it continues again and never actually saw it explained in this way, but it seems to be reasonable. So, the next change of the EMF here will change, next change in current, next change in the current will change magnetic field. So, it's kind of a, probably it might actually be calculated somehow through the infinite sum of infinitesimal increments, like integral. But I know it just my thoughts about this. It seems to be reasonable. Anyway, the EMF will equalize in this case. Okay. My next improvement, what if instead of one wire loop, I will have a double loop? So, it's one and another, like this. This is the source of electricity. Well, the current in one loop is producing certain variable magnetic field. It's a variable current. So, it's variable alternating current. So, it's variable magnetic field. And exactly the same current goes through the second loop, second turn of this wire, right? So, it will also produce its own magnetic field, magnetic field intensity. And intensities are like vectors that are adding together. So, I will have two times stronger magnetic field. By two turns of the wire, I will have double magnetic field strength. So, that's very important. Using the same source of energy, I can create a stronger magnetic field by using more than one loop. And if I'm using and P stands for primary loops here, I will have and P times greater magnetic field, stronger. Stronger magnetic field. It's just a multiplier. So, it's a magnetic flux is a function. So, it will be a multiplier in the magnetic field flux. And obviously, the resulting EMF induced in the second loop will be also double, triple times NP. So, that's how I can increase the magnetic flux here. And therefore, I will increase the voltage EMF. Now, what if I will have a certain number of loops here? Well, again, since every turn, every loop actually is a source of induced EMF. And now I will have like two or three or NS. NS stands for secondary. If I will have NS, I will have NS sources of EMF sequentially connected to each other, right? Because it's one and then another, they're sequentially connected. As a result, if I have sequential EMFs, they're supposed to be added as well. So, that's how I can actually take from fixed magnetic field, I can take more EMF. So, what happens here is that if NP is equal to NS, like one and one, or 100 and 100, I will have the same EMF in both cases. So, if these are equal, these will be equal. If, however, I have, let's say, twice as big, if let's say NP is equal to two NS. So, I have two times as many primary as the secondary. What happens here? Well, let's just, you know, think about this. I will produce more than I will take out. So, what happens is I will have only half of the energy. If I have the same, I will have the same energy, but if I have half of this, I will consume less magnetic flux. If I will consume less magnetic flux, in this case, half, factor by two, my EMF will be half. So, in this case, my UP of time would be twice US of t. If, on the other hand, my NS, my secondary is twice as big as primary. So, primary is equal to half of secondary. My primary EMF would be half of my secondary EMF. So, what happens here is, using different numbers of turns in my primary and secondary coils, I would call them coils now, it's not wire loops, it's coils actually. So, using the numbers, we can change the relationship between the EMFs in the primary and secondary. And that's very, very important, because whenever you want to transfer electricity along very long wire, you are interested in changing the current in this wire, because the current is the source of heat. Remember, I square RT. That's the amount of energy consumed by resistor R during the time t if there is a current I. So, we have to reduce this. But now, since we are changing the voltage, changing the EMF in both coils, primary and secondary, we still have the conservation of energy law. What is the energy of the electricity? It's U times I, right? Whether it's direct or alternating doesn't really matter. So, this primary should be equal to secondary. Otherwise, my energy would be produced from nothing, right? So, which means that if my secondary voltage is twice as big, my secondary current should be half as big as this one. So, that's how by increasing the voltage using the secondary coil significantly more turns than the primary, I will increase the EMF, right, in this particular case. But that would decrease my current. That's why immediately after producing the electricity, let's say on some kind of a power station, we are increasing the voltage using device like this, which is basically called transformer. We'll talk about this later. So, we increase the voltage, that automatically decreases the amperage. And whenever I have a very small current, very small amperage, it doesn't lose as much, because I is very small now, it doesn't lose as much energy just to heat the wire, which is transmitting my electricity to a long, long distance. And that's actually the purpose of the whole exercise, which I was just doing, because that allows us to transmit electricity to a very long distance. These transformers based on the induction, AC induction, alternating current induction are very important. Well, that's it. I would suggest you to read the notes for this lecture. There are some very nice pictures, much better than whatever I draw here. They are all on Unizor.com. It's called Physics 14 course, electromagnetism. And then you go to AC current, that's where you will find this lecture. That's it for today. Thank you very much and good luck.