 Hi, I'm Zor. Welcome to Unizor education. Today we will talk about something which is called voltage drop. This lecture is part of the course called physics for teens presented on Unizor.com Well, on the same side you have prerequisite course, which is called math for teens, which I do recommend you to take or at least familiarize yourself with all the concepts which are presented in the mathematical part of this. Now, I do suggest you to watch this lecture and any other lecture of this course on the Unizor.com because every lecture has detailed notes which basically are like a textbook basically. And then the lectures are organized in some logical sequence and I do suggest you to take one after another in sequence including some problem-solving and exams. All right, so voltage drop Let me start with analogy. Let's consider a waterfall. So the water which is high up has certain potential energy. Now as it falls down, it hits the rocks one after another and on each rock it releases certain potential energy because it's already down there and the lower you go the less potential energy it has and at the very end it has none. Well, if we're talking about the ground level as the end, we can obviously talk about an intermediary level as it is as the end of this exercise. Now in the very analogous train of thought, if you have a boiler which supplies the hot water and it goes into one radiator, then another radiator and then goes down the water. So the hot water goes here. Now it actually releases certain amount of heat energy. It releases another amount of heat in this next radiator. So every next radiator what provided the pipes are insulated so they don't really waste the heat. So the heat is released in the radiators and the further you go along this circuit, basically, the less energy, less heat energy water has. And then it goes back to boiler where we heat it again and it goes again into a loop. Now this is a very very similar picture to what happens with electrical circuits because electrical circuit is very much like this one. You have certain source of electricity. Let's say it's a battery and then it goes to one resistor and then another resistor and then goes back. Now this is a positive. This is a negative. This is a direct circuit. So what happens in this particular case with voltage and the current? Well, let's say the voltage is U. This is a difference in potential between two terminals of the battery or a generator, whatever it is. Now electrons, well, this is the direction of the current very traditional from plus to minus, but electrons are actually going this way. It doesn't really matter. What important is that there is certain difference in potentials and this difference in potentials actually drives the whole electrons to to go around the circuit. Okay, now as electrons heat particular resistors, we were talking about why resistors resist? Well, because the electrons are trying to get through all these atoms and the atoms are trying to capture the electrons, etc. And depending on certain qualities and characteristics of the material this resistor is made of, this resistance is greater or less. So it looks like electrons should lose some energy as they go through this maze of atoms and it's actually exactly like this. It's exactly like the radiators are basically releasing some heat. Let's think about it. If you have a current I, now this current means amount of electricity, well, if you wish number of electrons, which going through a circuit per unit of time. Now, obviously, it's exactly the same at this point or at this point or this point or this point or this point because it's a circle. So the same amount of electricity per unit of time goes anywhere. So the I is here and the I is here and the I is here, everywhere is I. Everywhere is the same amount of electricity which is coming through this any point in the circuit because it's a circuit. Okay, now what is the difference in electric potential between these two points? Well, you, it's given. How about if we will measure potential between the end points of this guy or this guy? Well, let's recall the Ohm's law. The Ohm's law is I is equal to U divided by R. This is the difference in potentials, the voltage and this is resistance or if you wish U is equal to I times R. Now, from this and knowing that the resistance of the whole assembly of two resistors in a series is equal to some of them. That was a subject of the previous lecture. So what we can say from here that this I and this U and if you consider this as a whole assembly with resistance R, they satisfy this equation. Now, now let's apply the Ohm's law only to this particular resistor, the current which goes through it, which is the same I as we were talking about and the difference in electric potential, the voltage between these two points, the U1. Well, it should be the same I times R1. Similarly, U2, the voltage around the ends of this resistor should be equal to the same I times R2. So what do we have from here? Well, U is equal to U1 plus U2. Right? U is equal to U1, I times R1 plus U2. We also derive from here, what is the value of U1? If you would like to express it in terms of U and resistors, well, obviously, you know the U from here, so you can find I. So if I is equal to U divided by R1 plus R2, you substitute it here and you get that U1 is equal to I is U divided by R1 plus R2 times R1. And similarly, U2 is equal to U divided by R1 plus R2, which is I times R2. So this is how you can find out what exactly this voltage around this resistor and voltage around this resistor. But what I would like actually to point out this particular equation, it's very important because it shows that you have certain voltage between the terminals of the battery. It's a difference in potential. Same thing as we have a difference in the temperature of the water which goes out from the boiler, the hot water, and the water which comes back to the boiler, which is cooled down. It's a difference in temperature, it's a difference in energy. Where is this energy? Well, it was spent in one radiator and another. Same thing here. The difference in voltage, because voltage is an energy, right? You remember, voltage is amount of work which is needed to transfer one coolant of electricity from one to another, from minus to plus or from plus to minus, whatever. So it's energy. And this energy is the difference between these two things, the difference between potential energy on these two terminals is actually divided here. So this difference is split into this and this. So as we go from minus to plus, for instance, first we lose certain amount of potential energy on this resistor and then on this resistor. So that's why it's called voltage drop. So as we go from one terminal back to another terminal of the battery, the whole voltage which exists here is gradually lost here and here. Or if you have 10 different resistors in a series, it will be correspondingly for all 10. So this is a very important concept. Voltage is a difference in energy and the difference in energy is actually gradually divided between every resistor on its way from one terminal to another. That's basically it. I mean it's a relatively simple concept and again my very, I think, understandable kind of analogy is this radiator and the boiler relationship. The difference between the energy of the cold water and the hot water is actually the energy which we are spending on each radiator. Same thing here. The difference between energy of these two terminals is split between this and this and whatever other consumers of electrical energy you have on your way. This can be an electric bulb, for instance, or this can be a refrigerator. So we are losing, if you wish, or spending the energy which have come to us from the electric outlet or wherever. We are spending to all these electrical appliances which consume this energy. It's basically about the law of preservation of energy. Energy doesn't really disappear. It doesn't get created. It's exactly the same energy. We're just redistributing this energy. If it's a lamp, it goes to light and heat. If it's a refrigerator, it goes to take the certain amount of heat from one place to another from inside the refrigerator to outside. So in any case, it's all about energy here. Okay, that's it. It's a very short lecture today. Thank you very much and read the notes for this lecture and basically, again, take the whole course. Thank you very much.