 Hi, I'm Zor. Welcome to Unisor Education. Today we will talk about Ohm's law, law of Ohm. Ohm is the name of a German physicist. I think he's German. Now this lecture is part of the course called Physics for Teens, presented on Unisor.com. I do recommend you to watch this lecture from the website because it contains parallel to the BG. It has very detailed notes. And also it's a course which means on the website all these lectures are presented in certain sequence, divided in certain parts, chapters, whatever. And there are exams, there are some other related lectures to this one. And also on the same website there is another course called Mass for Teens, which I consider a prerequisite to Physics for Teens. You do have to know your mass. I mean calculus is definitely one of the most used in physics parts of the mass and vector algebra, stuff like this. Alright, so we'll talk about Ohm's law. We all know about main concepts of electricity, which is the electric potential or voltage and electric current or amperage. Well, the question is how are they related to each other. Now you just have to understand that the electric potential, the voltage, between two different terminals is basically amount of energy which is needed to transfer certain amount of electricity, coulombs or electrons, whatever the measure is, from one to another. Or it's the same thing actually, certain amount of energy which is necessary to separate initially neutral, electrically neutral object into certain parts. One of them is with access of electrons which is negatively charged and another is positively, because they are attracted to each other, so to separate them you need energy. Now, so the electric potential is basically a potential energy which is the result of the spending certain energy to separate these two electrical charges, negative from the positive. And since they have certain electric potential, if you connect them with some kind of connector, this energy will be transferred into some other form of energy, like heat or whatever else. Okay, so obviously the more potential energy you have, the more intense the flow of electricity you have between these two terminals. So if you have two terminals of something like a battery or generator, whatever, one is negative and other is positive. Now obviously the more potential energy is between them, the more voltage is between them, the more intense will be the flow of electrons and intensity of the flow of electrons is the current, electrical current, right? Because it's basically amount of electricity per unit of time. It's exactly equivalent to the water. If you have certain reservoir which is above the ground and you have some kind of a pipe which connects it to the ground and the water which is here will flow down. Obviously the higher the reservoir, the more potential energy this water has, the more intense the flow of the water will be in the pipe. Well, intensity means amount of water per unit of time. Exactly the same thing with electricity and electrons. Now, the person by the name Ohm basically discovered that there is certain very simple dependency between the difference in potential and electrical current. And the actual dependency is very, very simple. The electrical current is proportional to voltage and he introduced a coefficient of proportionality which is basically kind of a characteristic of this connection because there are different connections. There is a connection which made of copper, there is a connection made of wood and there is a connection made of anything else, or water for instance or some kind of, doesn't really matter. Or vacuum, vacuum is also a connection, although it doesn't really conduct electricity but it's still a connection. So depending on the substance which connects these two terminals with certain difference in electrical potential with different voltage between them, so depending on this characteristic the proportionality will be preserved. So for any particular characteristic of the conductor, for any particular conductor, the sigma is the characteristic of its conductivity. Well, the value which is inverse to conductivity is called resistance. So resistance is more often used as a term in electricity in which case the law looks like this. Now this is a traditional classical form of the Ohm's law. So U is the difference in electric potential or voltage between two ends of some kind of conductor. I is the current which is flowing through this conductor, the electrical current, the flow of electrons, and R is a characteristic of a conductor, basically. Different conductors have different characteristics, so this R is different for different conductors, but for any specific conductor, whether it's a piece of wire or a piece of wood or some liquid in reservoir with two terminals inserted in it, whatever it is, for every particular conductor this proportionality, R will be a constant obviously and the proportionality is preserved, which means you double the voltage between the terminals, you will have the double current. The amount of electricity per unit of time will be doubled. Now, as everything else in physics this proportionality is an approximation, but under very, very broad conditions you can consider this to be the law, this is the Ohm's law, and well, let me tell you, if you remember nothing else from the course of electricity, this actually must be remembered because this is the most fundamental law of electricity which basically is everywhere around us. Okay, fine. Now, it's very easy to basically finish the whole lecture at this particular point because I told you what is the Ohm's law and well, I said remember it, but I don't think it's very interesting. What's interesting is to understand why something like this is happening and to understand why we have to go deeper inside the substance from which the conductor actually is made, deeper to the atoms, nuclei and electrons. So, let's just think about how electricity actually is flowing within the conductor. So, as we know, electricity is the flow of electrons. Now, atoms have a certain number of electrons and some electrons are on different orbits around the nucleus of the atom, right? So, here is the atom's nucleus and this is one orbit, this is another orbit, this is the third orbit, whatever. Now, the further electrons are from the nucleus, the easier it is to basically force them out. Otherwise, I mean, nucleus is positively charged, there are protons there, electrons are negatively charged and that's why the nucleus actually holds to its electrons. But if you have a strong electric field which pushes electrons towards another end of the conductor, so let's say this is a very strong negative and this is the positive. Now, these electrons, not only they are attracted by the protons inside the nucleus, but they are repelled by the electrons here, right? So, if this force is very strong, it pushes the electrons out from the orbit where it's circling around. So, it jumps to the next atom. That next atom can actually capture this electron or can pass it forward or maybe one of the next electrons, one of the next atom's electrons will go out and will be replaced by the electron from this one. So, it's like a chaotic movement of all these electrons in the maze of atoms and some electrons, as I was saying, are captured by the atoms, some electrons are hit out from the atom's orbit. So, this chaotic movement, it exists not only when there is an electric field, it actually exists all the time. Electrons are changing, especially in certain metals, for instance. They are changing their nucleus, which they were attached to. They can jump out because of some whatever is happening there. I don't exactly know, but there is a chaotic movement but on the top of this chaotic movement, if there is a field, this chaotic movement has certain directional property and that's how the electric current actually is moving. Now, obviously, as the electrons are moved from one end of the conductor to another, as I was saying, they're hitting other atoms, other electrons, it's a semi-cautic movement. And in this particular case, it's kind of obvious that the more difference in potential between these two ends, the more intense this movement should be because the electrons are stronger pushed from left to right on this particular picture. Okay, so there is no doubts that the function is monotonic. If this goes up, this goes up. If the difference in electric potential increases between these two, the current should increase. So obviously it's supposed to be some kind of a... If you have it on a graph, this is u and this is i. This is voltage and this is amperage current. It should be something like this, always monotonic. We don't know if it's linear, but at least it should be monotonic, right? Now, the fact that it's linear function is basically confirmed by experiment. So that was basically what Ohm has done. He has done a lot of experiments and he found that this is actually a linear dependency. Okay, so as soon as he found out that, he realized that this is the sigma, the conductivity is a characteristic of the conductor. And again, he introduced it in some other form where this is a resistance of the conductor. So this is a conductivity, this is a resistance, and they are related very simply. Or r is equal to 1 over sigma. Okay, now let's just think logically. What happens if I have this particular conductor? What happens if I will have two conductors like this attached to each other? Well, basically I lengthened my conductor by the same length. So this is, let's say, L, this is 2L, the length. What happens? Well, let's just think about it. If the resistance of the conductor depends basically on how intensely the electrons are hitting the atoms or other electrons because this is actually kind of a chaotic movement directional but still chaotic, then it's obvious that the longer the electrons have to travel from left to right, the more obstacles they will have. So it's kind of intuitively obvious and experimentally basically confirmed that if you increase the lengths of conductor by certain factor, by 2, by 3, whatever, the resistance should also increase by the same factor. And that's why the current should decrease by the same factor. So if you have twice as long a conductor, then under the same circumstances at the ends, the same you, the same electric potential difference, you will have proportionally smaller current. So the resistance is kind of proportional to the length if our conductor is of, let's say, cylindrical form. Now, what does it mean from the standpoint of electrical schemas or electrical connections, etc.? It means the following. If this is my source of energy, electrical energy, this is a typical scheme of electrical circuit. So this is plus and minus. This is a symbol for electrical, battery or source of energy or some other. Well, let's just consider it's a general source of energy. You can call it battery, okay? The plus and the minus. And this is a resistor. Resistor is a term for certain conductor which has certain substantial resistance in it. These are wires which we assume for all purposes of this course that they have absolutely zero resistance. So the electrons are going through these very, very freely without any problems. And here they have certain resistance. And let's say this resistance is R, okay? Now, what happens if I will have two resistors like this in a row? That's basically equivalent to what I was just saying about doubling the lengths of the conductor, right? Because here we have basically a conductor with certain resistance and then we have exactly the same thing. And the amount of resistance which is here is actually doubled. It doesn't really matter if it's a one piece or two pieces connected with some kind of a wire which we assume has no resistance. It's exactly the same thing. So our resistance must be doubled. So in this particular case, our current, this is U and this is I. Now, in the first case, I had I equals to U divided by R. In the second case, I have I U divided by two R's, right? So resistance is doubling and that's why I put two R's. Now, if I put R1 and R2, then that's basically the same thing here. For instance, this is a piece of some material with a resistance of the lengths, let's say two centimeters, and this is five centimeters. We can always say that this contains two resistors of one centimeter each and this is five resistors of one centimeter each. So altogether, it's seven resistors of one centimeters each. So that's why it's supposed to be seven. That's why it's ailing. It's a very simple arithmetic in this particular case. So these two resistors connected in this way, it's called a series of resistors. So this is a resistor series or series of resistors. And we have a series of resistors. Our resistance is adding together and this basically is semi-intuitively and semi-logically consequence from basically whatever I was saying that the longer you have the resistor, the conductor which has certain resistance, the longer you have it, the proportionally greater is resistance and proportionally smaller is the current which goes through. So the more resistance we put into this circuit, the smaller will be the current under the same voltage of the generator of the electricity. And this is called a connection in a series. So it's very important to remember when we are connecting resistors in a series, their resistance, combined resistance is sum of resistances of components. Okay, so that's one way. Now, let's just think about the following. And it's purely theoretical. What if you don't have any resistances at all? So we just connect straight with a wire and the wire we assume has zero resistance. Well, zero resistance according to this formula results in infinite current. Well, again, obviously it's not zero, but it's a very, very small resistance. So under the same circumstances, the smaller this is, the bigger this is. So if this is some kind of a constant, whatever the battery actually does, but if you connect these two poles, these two terminals of the battery with some kind of a wire which has very, very little resistance, you will have a huge electric current. And that's what it's called short in electricity. So whenever you have an outlet and you have some kind of two wires, you stick it in and connect, that's what happens. Well, it might actually explode because it will be a very, very strong current along this short connection. And it will basically blow the fuses, it will melt the wire. I mean, its very big current is a very, very strong force, which somehow should, basically, it's amount of energy which is supposed to be immediately released, speaking about amount of energy. Now, you do remember from the previous lecture that basically the energy is released whenever you are connecting these two terminals. And obviously the more current you have, the more energy you have per unit of time. So that's why you have such a huge explosion or fuse burning, etc. Okay. Now, on the other hand, if r is equal to infinity, so let's say this is a vacuum inside. Well, obviously there is no current, so I will be equal to zero, if r is equal to infinity, i is equal to zero, there is no flow of electrons, there is no current. So that's kind of obvious. So the formula is really very, very good and it allows us to deal with small resistance, with big resistance, it's really very, very good. Okay, next. Next, you can think about a particular example of this resistor as an electric bulb. So you have two wires coming into the electric bulb and the electric bulb has this tangent spiral or filament and two ends of this spiral. Basically this filament, this is tangent spiral and it's connected through some kind of source of electricity here, right? Minus plus, plus, minus. Now, this tangent spiral has certain resistance and the thicker the spiral, the more electrons can push through it. The longer the spiral, the more resistance it actually has. Now, let's talk about the width, the thickness of the spiral. Now, again, if we go into the atomic structure and chaotic movement of electrons, if this is your conductor, these are your atoms, right? So electrons are pushing through this maze of atoms. Some atoms are capturing the electrons, releasing the electrons, etc. They have resisted that. What if you have a thicker wire? It gives you actually more room to move. It's like you have a highway and you double the widths of the highway. Obviously more cars can go through. Same thing here. If you increase the cross-section of the wire, the thickness of the wire, obviously the more electrons can go through. So resistance should decrease in this particular case. Now, what happens if instead of this connection, I have this connection, a parallel connection? Well, parallel connection of resistors is absolutely equivalent to increasing the thickness of the conductor. Now, what happens in this particular case? Well, let's say you have certain flow of electrons, the electric current here. It's split here, right? Some electrons go one way and some electrons go another way. So, what I have in this particular case, I have i equals to i plus i2. So in case of consecutive, instead of a connection in series where we have addition of resistors, here we have addition of currents because all electrons which are coming here should split. Some of them go this way, some of them go that way, and then they merge again. Now, let's apply the Ohm's law to this and this separately. What happens? Well, u is still the same. I mean, this e is just wiring which has zero resistance, so u is still the same, right? And so I applied the Ohm's law here. And at the same time, let's just consider this as one particular assembly which is supposed to have some kind of a resistance r. What if some kind of a black box? I don't know what's inside. Whatever is inside has certain resistance r which I don't know. I have to determine it somehow, right? In case of a series, my resistance of 2 is equal to some of the resistances. But what if it's in a parallel connection? I don't know. I have to determine it. How? Well, again, by knowing this, this is my unknown resistance of the whole parallel assembly. This is i which is here. So this is also the Ohm's law, but for the entire circuit. This is the Ohm's law for the first component. This is for the second component. And this is for an entire line, right? So what I can see from here is the following. i1 from the first one is equal to u divided by r1, right? i2 is equal to u divided by r2 from this one. And the total r is equal to u divided by i. Or, let's put it differently, i is equal to u divided by r. Now, I know that this plus this equal to this, right? i1 plus i2 should be equal to i. What does it mean? Well, it means that u divided by r is equal to u divided by r1 plus u divided by r2. That's what it means, right? Obviously, you can be cancelled out. And I have equation for parallel connection. This is the resistance. Well, it doesn't define resistance. It defines actually 1 over r. But it looks better in this particular way. I mean, obviously, r is equal to 1 over 1 over r1 plus 1 over r2. It doesn't look as good. This looks better. So in case of serious connection, my resistance is sum. Instead, in case of parallel connection, my resistance is inverse resistance is equal to sum of inverse. And this is actually a conductivity. So you can express this one as sigma equals sigma1 plus sigma2. Where sigma is a conductivity equals to 1 over r. Sigma1 is equal to 1 over r1 and sigma2 is equal to 1 over r2. So in a series, we have resistance added. In a parallel, we have conductivity added together. What else? And the last one, which I would like to talk about today, is how do we measure resistance? Well, that's a very simple and easy thing. If you have one volt of voltage and if you have one ampere of current, then this is a unit called ohm, the same ohm, and it's a Greek letter omega, capital omega. That's the unit of resistance. So one ohm of resistance is such a resistance. Now this is u, this is i, and this is r, right? It's exactly the same ohm's law. u is equal to r times i, sorry, u is equal to i times r, i is equal to u divided by r, whatever it is. All of these are equivalent to each other. So this is the ohm's law, and from the ohm's law, we derive the unit of measuring, unit of measurement of the resistance. So it's one ohm, if my one volt of voltage allows me to have one ampere of the current in the circuit. Basically, that's it. That's for the ohm's law and that's two basic rules how we calculate the resistance in case of series and parallel connection of the resistors and the unit of measurement. That's it. Now I would like to recommend you to read the text for this lecture, the notes, very detailed notes. Like a text book, basically. Maybe I missed something, I hope I didn't. So now this is the first lecture, which is basically dedicated to ohm's law and all the consequences from it. And it's really a very big chapter of the electricity. And what's very important is for you to understand that the ohm's law is the basic, it's the fundamental law of electricity. It's used like everywhere and I will have probably some problems and exams related to ohm's law. So try to take all these lectures which are under the heading ohm's law. There are probably like four or five different lectures. This is the first one of them. Try to go through them very diligently. Okay, thanks very much and good luck.