 Hi, I'm Zor. Welcome to Unisor Education. Today we will talk about capacitors in the AC circuit, alternating current circuit with a capacitor. Well, this lecture is part of the course, Physics 14, presented on Unisor.com. I suggest you to watch this lecture from the website, because every lecture, including this one, has a text associated with this lecture, so you basically have both the textbook and the live presentation. Also, the whole course is arranged in obviously some segments, so there is order, lectures are arranged in menus, and you also have exams if you really want to challenge yourself. The site, by the way, is absolutely free. There are no ads. You don't even have to sign on. And there is a prerequisite course on the same site, Mass for Teens. Mass is a definite prerequisite for physics, and it's used everywhere. Okay, so we will talk about capacitors in the alternating current circuits. Well, first of all, capacitors were addressed earlier in this course, and I do suggest you to refer to the lecture about capacitors. It's in the topic about electrical field, I think. So you go to Unisor.com. The course is Physics for Teen, obviously. Electromagnetism is the main topic, and within that topic there is electric fields, and inside electric fields you have capacitors. So I assume that you know what basically capacitor is. Well, just briefly, it's just two plates, which can be parallel to each other, obviously, and they can store electricity. Why? Because if there is a negative charge on one plate, there is a positive on another plate, and they attract each other, but they don't touch each other, so they don't exchange electrons. They're just storing this particular energy as long as you have, well, either you have the voltage with a plus and minus from some battery connected to them, and then when they're charged, these two plates, you can disconnect the battery, the charge will remain. Now, in our case, the source of electricity is not a battery, which is a direct current, but some kind of a power plant which generates alternating current. So we will have alternating current coming into both plates, and that's very important actually. Now, first of all, let me just differentiate between capacitors used in DC, direct current, and in AC, alternating current. In case of DC, all you can do is you can charge the capacitor. This is the capacitor, okay? Two plates. Now, if you connect it to a battery, then the plus goes to plus, minus goes to minus, so a certain number of electrons will be accumulated here, and the deficiency of electrons will be there. That's basically it. There is no current running here. Now, what happens actually is electrons are generated by the battery. The battery has certain chemical reaction, let's say, which separates the top level electrons from the atoms, free electrons, so to speak. They're not really firmly attached to atoms. So the energy inside the battery separates the electrons. Electrons go here, absence of electrons, holes basically remaining in atoms are going there. So electrons are circulating basically from here to here. That's what's being done actually. Now, you have certain access electrons here, and obviously they repel each other. So this battery is pushing electrons, and it pushes up to a certain extent. When this plate is saturated, this battery cannot push it anymore. So it all depends on the capacity of the capacitor and the voltage which battery actually can develop. So the voltage and the amount of electricity accumulated in the capacitor are actually connected with a very simple formula that U is the voltage, and if you will multiply it by some kind of factor which depends on the properties of this capacitor, which is called capacity, you will get the amount of electricity which can be stored, the amount of charge actually. No more than that. I mean, because again, with certain voltage here, you have certain pressure of electrons. They will accumulate here until they saturate enough so their own repelling force will prevent pushing anymore. So that's what actually is established. This is a constant which depends only on the capacitor itself, the size of the plates and distance between the plates and what kind of a substance in between the plates. So this is just the characteristic of capacitor. But other than that, they are proportional, the voltage which develops the battery and the amount of electricity here. So this is the law of capacitors. We'll just keep it in mind. But what's important is there is no current running here. Electrons will go there and stop at some point accumulating a certain charge. There is no current. Okay, let's replace this with the source of alternating current. So we have an alternating voltage here. What happens in this case? Well, actually, the situation is very different. So what kind of an alternating voltage actually is developed? Well, we know that it's usually a variable which has a certain maximum and then sine of omega t where omega is angular speed of rotor rotating in the power station. Whatever the power plant is, there is something mechanical which is, which movements of which are converted into alternating current. So this is the angular speed of rotation of whatever, turbine or whatever it is, whatever the source of electricity is. And this is the peak value of voltage. And this is basically a function of time. So as the time goes, we have this voltage sinusoidally changing with time. Goes to the positive maximum, then down to zero to negative maximum, down to zero, etc. Same sinusoidal movement. So that's what happens here. Okay, so what happens here? Okay, when this particular function, the voltage, is in such a way that it develops positive here and negative there, then the positive charge goes here and again it reaches certain maximum as in case of direct current and stops. Negative goes here, the same thing and it stops. Okay, so now we have this positive and this negative. Electricity went to this and stopped. Electricity went to this and stopped. The charges, electrons are their absence, the holes. But then what happens? Then this thing is changing. So first it's increasing its positive thing to a maximum, then it's decreasing this voltage, this EMF, right? When it's decreasing, then the excess of charge here becomes stronger than the EMF here and the charge goes back here. Same thing here. So the positive goes back here and negative goes back here. Then we reach zero and that means there is no charge anywhere. Then the polarity is changing. Now this becomes negative and this becomes positive. So now the electrons goes here, negative and the positive goes here. And then again up to a certain saturation point when voltage reaches its other maximum, the negative maximum. And then again it stops. Then the negative maximum starts growing to zero. Now which means it's pressure from here and from here is weakening. So the charges go back here. Now negative goes back here, positive goes back here. And now we're changing again the polarity. Now the positive is here and negative is here. And basically the whole thing repeats and repeats again and again. So what happens is that although there is no connection here between the plates, but the electrons will flow here and here, here and here all the time. And then again and again and again. So basically that constitutes the current. Because if you will put something like a lamp here, it will be lit up. So my point is that though there is no actually physical circuit here, but with alternating EMF, alternating voltage here, the electricity will flow here and here and here and here. And that's very, very important. So capacitor in AC. Well you can say that it actually lets the current flow. Which is different from DC, from direct current when the capacitor actually prevents the flow. It reaches its maximum saturation point and then it stops. And by the way it reaches saturation point with a speed of almost like speed of light. So it's instantaneous basically. Okay, so that's done. Now I would like to go into calculations. I would like to know how exactly the current is going through this thing. Well, if it's a circuit, if it's a DC circuit, let's say I have a lamp here. Now if it's a direct current, that's obvious. We have U equals I times R. Voltage is equal to current times resistance of this lamp. Now if it's an alternating current, actually it's exactly the same thing. Different is that it's not just U equals this U of t is equal to I of t times R. So these are functions that are changing this time. How? Well, U is changing this way. And that's why I of t is changing similarly. I just divide by U max divided by R sine of omega t. So this thing becomes I max. So if there is no capacitor, my current is completely in sync with my voltage, with my EMF. Okay, fine. What if there is a capacitor? And the story is completely different. What is the current? Well, current is amount of electricity per unit of time. It's a rate of change of the flow of electricity. A rate of change of charge, basically. Well, we know the charge here, where U is actually U of t. U is a constant, and that's why amount of electricity accumulated on the plates Q will also be a function of time. And what is I of t in this particular terminology? Well, that's a rate of change, which is first derivative of amount of electricity of the charge derivative by time. That's what rate of change is, right? That's interesting. Now, let's substitute here C U max sine omega t. And that's derivative by time equals 2. This is the constant. So it's C times U max. Now, derivative of sine is a cosine, but I do have inner function. So I have to then multiply by derivative of the inner function, which is omega. And then cosine equals C omega U max. Now, I will change cosine into sine. I hope you didn't forget your trigonometry. This is replaced with this. These are identities. So what's the most important difference here between this and in case of direct current? In the case of direct current, my current is in sync proportional in sync with my voltage. In case of alternating current, my current is not exactly in sync. You see, this is omega t and this is omega t plus pi over 2. So if you will do the graph, this is sine and now we are shifting it by pi over 2. So this is shifted. So what's important here is that my current is shifted. They're saying it's a phase. Phase is equal to pi over 2. So it's phased by pi over 2 by 90 degrees actually over the voltage. So when voltage goes up, for instance here, my current goes down. Then voltage goes down and my current goes up to a negative sync. Then again voltage goes to a negative sync and the current goes this way. So there is a difference here. And actually it can be explained because let's see we start from the very beginning. Zero here, zero here. Now as soon as we start raising the voltage, let's say on this particular pole of the generator, we start increasing the voltage. Well this was zero. So the rate obviously would be the biggest because it's much easier to start from zero to increase let's say by factor of 2 from zero is very easy than if you already have something to increase by factor of 2, right? And the current is this rate of change. So the rate of change would be the biggest in the very beginning. You see here if this is u of t and this is i of t. So i is the biggest, current is the biggest when u is in the very very beginning, right after zero. Then as we go we accumulate certain charge here and that certain charge repels electrons. So it becomes more and more difficult. So this thing is increasing to its maximum but my rate of change of the charge here is decreasing to zero. And at the very end of this when my voltage is reaching the maximum my current is around zero. It does not increase anymore the rate becomes zero. Now what happens then? Well what happens then my charge starts diminishing, right? My voltage becomes less and less. Now as soon as we start diminishing my voltage the axis of electrons here which used to be on the maximum is decreasing and that's why when it's decreasing my rate is negative and that's why it goes negative. And obviously at the very end when there is nothing here my rate is maximum negative, etc. So basically I mean this is the logical explanation of why we have such a difference in phase. Okay, what's left? Well basically that's it. The only little thing is this is obviously called I max. So I have this I max equals to u times c times w max or u max divided by xc where xc is 1 over cw. C is a capacity, omega is angular speed. Now why did they introduce this? Because now it looks like an Ohm's law, you see. This is the current, this is the voltage and this is resistance. So basically this thing for capacitor is in some way equivalent to resistance. It's called reactance. They just come up with some terminology. I don't think it's very important quite frankly. Now what's the most important in this lecture is this pi over 2. So we also have sinusoidal current which goes alternating current. There's also sinusoidal in exactly the same fashion as EMF produced by the power plant. But the sinusoidal is shifted by phase by pi over 2. Now that's very important because in some cases we can have from the same source. We have one circuit of this kind, another circuit with some kind of resistor. Now we will have here certain current and we will have here certain current. But these currents are out of phase by pi over 2 because there is no resistor here. There is no capacitor and there is a capacitor there. So this will introduce a current which is shifted in its sinusoidal oscillation by pi over 2 over this current. And then we can use these two things. Currents both are sinusoidal but shifted by phase by pi over 2. That can be used in certain electrical motors and I will talk about this in the next lecture. Okay, so I suggest you to read the text for this lecture. You go to Unizord.com to Physics for Chains course. Go to Electromagnetism, Alternate Current. And among the Alternate Currents you will find this lecture about capacitors. Thank you very much and good luck.