 Hi, I'm Zor. Welcome to Unizor Education. Today we will talk about a device which is called Inductor in alternating current circuit. Well, this lecture is part of the course called Physics 14 presented on Unizor.com. There is a prerequisite course on the same website called Math 14, so I do recommend you to take it first or at least be familiar with all the concepts which are in that course. Now, I do recommend you actually to watch this lecture from the website rather than from, let's say, YouTube or wherever you found it, because the website contains, well, logical arranged lectures. There is a menu and you can basically have the whole course in front of you. And there are many problems solved and there are text notes for each lecture, which is very important because after you watch the lecture, I do recommend you usually to read the text which accompanies. It's like a textbook, basically. And for those who prefer some challenge, there are exams. You don't have to even sign in. It's completely anonymous or if you want, obviously, you're welcome. There are no ads, no financial strings attached, so I do recommend you to use the site. Okay, so let me first explain one particular experiment which I believe is very important and it kind of demonstrates the concept which I would like to explain right now. So let's consider you have a circuit with AC which includes the following. It includes some kind of a consumer of electricity, like a lamp. And it also has, let's say, it's a solenoid, for instance. Well, in any case, it's any kind of a wire which is looped around something. So basically this device, we will use the term inductor. So it's a wire wound in the loop or in the form of a solenoid. It doesn't really matter. As long as there are loops, there might or might not be core around which everything is wound. So this is an AC. This is AC. It has certain voltage. And as it is pictured right now, well, considering this is not a very heavy reel of wire, let's say it's a solenoid which was, I don't know, 20-30 different loops around something. The lamp will probably light up as usually, like a normal, whatever it's supposed to be, light up. Now, let me do the following. Let's say I have some kind of an iron core which I can insert into this solenoid, into this inductor. It's called inductor, more general. Well, what happens? Well, all of a sudden you will see that the lamp is just going down, down, down the brightness of the lamp. And the more I insert this core inside the solenoid, the less light I will have from the lamp. Just remember this particular experiment because that's exactly what I'm going to explain and it actually demonstrates what I will explain from the theoretical standpoint. So whenever we're inserting iron core into the solenoid, something is happening which is kind of equivalent of growing resistance of this particular part of the circuit because what else can actually reduce the voltage of the lamp? Well, resistance, some kind of a resistance. But it's not a resistor, it's just a wire bound in the loop, in many loops, let's say. And also this iron core is very important in this particular case. Okay, so being as it may, just remember this particular picture. I will wipe it out and that will continue next. Okay, next I would like to make sure that you remember the concept of self-induction. Self-induction is the key to understanding this particular lecture. Now self-induction and Faraday's law were explained previously. Well, by the way, that's why you need to watch this lecture on Unisor because now you have to really go to one of the previous lectures so you need the menu, find the lecture and go to this particular lecture. Okay, so self-induction and it's based on a very simple concept. Whenever, if you have some kind of a loop, let's say, whenever there is a magnetic field changing, which goes through this particular loop, there is an emf, electromotive force generated. So there is always magnetic field around any kind of a current. So if you have just a plain current and have a direct current in it, even direct current, you will always have magnetic field around it. Now if you have it in a loop and you have a direct current here from a battery, let's say, obviously you will have magnetic field which basically goes inside this loop and then outside and around. If you have more than one loop, if you have something like a solenoid, and the magnetic field would go like inside and outside, inside and outside, one of them would be equivalent to the north, another would be equivalent to the south, because it's really, if it's a direct line, direct current. So this is basically behaves like a magnet. So you know that. So if you have a current, it generates a magnetic field. Now let's go in reverse. What if you have a magnetic field? Well, if magnetic field is changing, only if it's changing, there are no sources of energy, no battery or anything. But if you have a magnetic field changing which goes through this particular loop, it will generate EMF, it will generate electromotive force and electric current will go. Depending on the direction of the magnetic field change, the direction of the current will be here and there, one side or another side. Okay. Now what if this is AC, alternating current? Well, now let's think about this. If this is alternating current, since it's a current, it creates its own magnetic field. But since it's alternating, so it goes this way and that way, this way and that way. When it goes this way, magnetic field inside this loop goes in one direction. When electric current goes in the opposite direction, magnetic field will be in opposite direction. So magnetic field is always changing. So not only you have a magnetic field which is generated by the original AC, but also we have a magnetic field induced by the fact that the first original magnetic field is changing. So you have self-induction. That's what it is, self-induction. You have additional EMF. So you have one EMF which is created by the source, original source of AC, of alternating current. And then you have an EMF induced by the fact that this magnetic field is changing. And induced EMF, the self-inducted, so to speak, EMF is always against the original one. It tries to basically move to the opposite direction, move electrons to the opposite direction. So whenever the field, for instance, goes into this way, then the electromotive forces the electrons to go this way. The electromotive force, which is related to self-induction, tries to go to the opposite way. So it's always working against it. When this thing is increasing, the original one, the self-inducted EMF is trying to reduce the speed of this increase. If this original EMF is reducing, then the EMF, which is generated through self-induction, is trying to support it. So this is the concept of a self-induction. It's very important. Again, remember it. It will be used. This is just a repetition of whatever it was before. Next. Okay. What we will do next is go to some kind of a theory. So there is a Faraday's law, which basically tells us that EMF generated in the loop by variable magnetic flux is basically a rate of change of this magnetic flux. So this again was in one of the previous lectures. It's about the Faraday's law. This is a very important formula. Now, this is a self-inducted EMF generated by changing magnetic field. Now it's time to go into inductors in the AC current. Inductor is basically, as I was explaining before, it's just a wire bound in multiple loops. Solenoid is just one of the examples. Or you may just have a reel of a reel, and then this reel of wire like this. So you have two ends. And this is also an inductor. Now, this inductor creates magnetic field if there is a current going through it. Obviously if the current is AC, then the magnetic field is also changing all the time together with this original AC. Now the magnetic field created by the wire is proportional to current, which is running in the wire. So even in a simple case of direct current, straight line and magnetic field around it, the intensity of the magnetic field, B, depends on its proportional actually to the electric current going through the wire. So what is happening with electric current here in case we have this inductor? Well, if it's connected to alternating current, my original EMF is pulsating. It's like sinusoidal change. It's some kind of a maximum times sine of omega t. Right? Now, obviously my original current in this particular circuit is also from the plane Ohm's law. It's exactly the same. So let's just consider that we have, we don't really need this right now. We have this. Now, from this follows that since my intensity of the magnetic field proportional to current and my flux, which is basically the product of intensity times the area of the loop, intensity of the field which goes through it and intensity. This is magnetic flux intensity. This is the area. B is proportional to I. I is changing, whatever it is changing as a function of t. Well, by the way, I forgot to mention omega is just an angular velocity. Whenever my AC generated, there is an angular velocity of the rotor. So that's where omega comes from. Again, it's all explained before in one of the previous lectures. So from this follows that magnetic flux which goes through this reel is actually proportional to the current which goes through the wire. Now, this is the function of t of time. So this one also is function of t. Now, L is a proportionality which basically depends on this particular inductor. For instance, if you have two wires, two loops of wire instead of one, you will have double L because the magnetic flux would be twice as big, right? But it also depends on geometric shape, not only on the number of loops, but also geometric shape, how big the radius of this loop is. And that's also very important whether there is or there is nothing inside this inductor. Now, let me go back to experiment which we did in the very beginning. When I was inserting the iron rod into the solenoid, it looked like our resistance of the whole circuit was growing. Why was it? Well, here is why. I will explain that everything depends actually on this inductness, this coefficient of proportionality is called inductness of this inductor. So if I have an iron rod inside the solenoid, magnetic field concentrates inside. It's not really dissipated all the way around it, but the iron rod actually concentrates the magnetic field. It's easier for magnetic field to go inside the iron than in the vacuum or air or anything. So the whole energy goes through the iron. That's why the inductness of this inductor is growing. It's bigger. It's more energy, magnetic field energy accumulated through it. And that's very important for something which we will actually come up as with a resistance of this inductor. Now, let me talk about resistance. Okay, so let me go from here. We know that variable magnetic field, variable flux actually creates a self-induction EMF and it's going against the original EMF. Now, let's just talk about this, what happens here. Well, we know that I of t, this is the current as a function of time, is this. All right? So my flux is equal to L times I max times sin omega t. Now, let's talk about self-induction. So as we know variable, and this is variable, magnetic field flux creates the EMF, generates, induces EMF, which basically prevents, but it works against the original EMF. So let's just calculate what it is. This is coefficient for proportionality, this as well. Now, derivative of sin is a cosine. And then we have to do derivative, derivative of inner function, which is omega times t, derivative is omega. So that's my derivative. So my E of self-induction, I put ii, this induced EMF is equal to L times minus, minus L times I max times omega times cosine omega t. Now, from trigonometry, we know that we can actually replace this with a sin of omega t plus t over t. Again, if somebody forgot trigonometric identity, there is a prerequisite course in unisor.com, math for teens, and there is a very good trigonometry chapter. So this is an induced EMF, which works against the original one. Now, let's go back to the original experiment when our lamp was actually going down, when I insert the iron rod. When I insert the iron rod, the inductness of the solenoid was increasing because of magnetic properties of iron. And since it was increasing, my induced self-induction is also increasing in absolute value, but since it's a minus, it prevents, it goes against the original EMF. So basically, it's reducing original EMF as any resistor. So basically, inductor works against the alternating current EMF like resistor. So that's very important. That's why whenever we're inserting iron rod into the solenoid in the AC circuit, the resistance, so to speak, resistance of the inductor was actually growing. And so much that our lamp, which was in the circuit, actually was getting less EMF, less voltage. So it lights actually much less. Okay, now, where are we? What's important here is that this induced EMF is also a solenoidal, but you see this plus pi over 2? Whenever you have a function and another function, which has argument shifted by plus pi over 2, it means that the whole graph is shifted to the left by pi over 2, which also was explained in the mass for teens prerequisite course. Any function, whenever you have a function f at x and then you have f at x plus a in parenthesis, it's shifted by a to the left. Very easy to prove, by the way. So it looks like this induced EMF is shifted, the sinusoid actually is shifted relative to the current. So if the current is plain sine, my induced EMF would be shifted by pi over 2, like this. No, not like this. Sorry, this is pi, pi over 2, like this. So if this is i, this is e. So it shifted to the left by pi over 2. So alternating current i and generated self induction are actually going with a pi over 2 shift, which is called a phase shift from each other. Okay, now what's interesting is that in absolute values, I can always call this as e max. So e max, sorry, e max, this is the maximum, the peak value of EMF. It's equal to i max, well in absolute value I want, times l times omega. I just want to ignore this minus, that's why I put absolute value. Now what's important is this thing. Sometimes they're using x with the l index to signify this value. It actually behaves like a resistance. Remember the Ohm's law, when you have the voltage is equal to current times resistance. So this is actually logically equivalent to resistance. And that's very important actually, because our original experiment was actually demonstrating that it behaves, this inductor behaves like a resistor. And the more inductance of this inductor is the greater the resistance. Omega is kind of a constant. Whenever you're inserting the iron rod, you're increasing the inductance of this inductor. So this is kind of an equivalence of the Ohm's law for AC, for alternating current chain, with XL playing the same kind of a logical role as a resistance, in case if it's a real resistor in the circuit. Okay, now let's talk about units of measurement. That's very important actually. Let's just talk about this particular thing. What are the units of this? Well the inductance is basically seen from here. So what is on the left? Volt. Inductance is measured in units called Henry, HR. Current is measured in Amperes. Omega is angular speed, angular speed means radians per second. Well radians is a scalar, so you have one over second here. Sin is just a scalar. It doesn't have any kind of measurement. So from here, basically one Henry as a unit of measurement of inductance is equal to one volt times one second divided by one ampere. So this is measurement of the inductance, Henry. Now we were talking about L times omega as just another kind of a letter we used and we call this inductive reactance. Many terms. It doesn't matter how it's called. Inductive reactance. So that's why we have this particular one letter with an index abbreviation to basically signify and we were talking about this thing behaving like a resistance of some kind of resistor. Well it's called basically reactive resistance to differentiate it from active resistance of real resistors. Now let's think about what kind of units of measurements we have here. Well the unit of measurement is L times omega. Omega is one over second, right? So the multiplication of Henry and this is one over second would be Henry per second, right? One Henry per one second. And what is this? If we will divide second to here it will be volt times ampere. What is volt divided by, divided, volt divided by ampere. What is volt divided by ampere? One volt divided by one ampere is one ohm. Remember that's the ohm's law. So the reacting, reactive or inductive resistance whatever is measured in ohms. The same units as the real resistance, the active resistance which we have. So active resistance is measured in ohms and reactive resistance also measures is measured in ohms. So that actually makes this thing really behaves like a resistance and that's why they call it reactive resistance. So any kind of an inductor when it's in AC circuit demonstrates certain qualities like a resistor but again it's just a completely different device. It's not the one which just slows down the electrons because they have some physical resistance. This is a device which basically slows electrons because it generates the electromotive force which works against changing of the flux which goes through this inductor. I understand it's my maybe a little difficult concept but in any case it is what it is. We just have to learn whatever the nature actually presents to us and that's what it presents to us. But very important property again it's all based on Faraday's law when the changing magnetic flux is generating EMF which is working against the original EMF which produced this magnetic flux. So what else I missed? Okay I think what's important is to emphasize the difference in phase. So this particular EMF which is generated by AC going through inductor is shifted by pi over 2 relative to original current which circulates inside the circuit. That's basically it. I do recommend you to read the text which is accompanying this particular lecture on Unisor.com. You just have to go to Physics 14's on Unisor.com, choose electromagnetism and within alternating current chapter you will find the lecture about inductors, AC inductors. Before that there was AC conductors, no not conductors, capacitors sorry, and capacitors also behave like inductors. They do have certain again reactive resistance and there was another formula for X with an index C for capacitors introduced in that lecture and it was also a shift in phase whenever you go through a capacitor in the AC circuit. So both capacitor and inductors behaves like resistors but they also shift the EMF. One shifts into one direction and another to another direction. Anyway read the text. The text is probably a little bit more I don't know logical theoretical than whatever I'm trying to explain here because it's a lot of different material here in one lump sum. So read the text and good luck.