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Introduction to circuits and Ohm's law

Video transcript
Well, we've spent many videos talking about electrostatic fields and the potential on a charge or the potential energy of a charge when it's in one place. But let's see what happens where, given a potential, what happens when we actually allow the charge to move? And this will probably be a lot more interesting to you, because you'll learn how much of the modern world works. So let's say that I have a source of voltage. Let me see how I want to draw that. I'm going to draw that like that. I'll draw it in yellow. So this is my source of voltage, often known as a battery. This is the positive terminal. This is the negative terminal. It's a whole other subject, a whole other video, and I'll make one eventually, of how a battery works. But let's just say that no matter how much current-- well, actually, let me explain in a second, but no matter how much charge flows out of one side of a battery to the other side of the battery, that somehow the voltages remain constant. So that's kind of a non-intuitive thing, because we learned about capacitors, and we will learn more about capacitors in the context of circuits, but what we learned about a capacitor is that if we got rid of some charge on one end, the total voltage across the capacitor will decrease. But a battery is this magical thing. I think it was invented by Volta, and that's why we call everything volts and voltage and all of that. But it's this magical thing that, even as one side loses charge to the other side, that the actual voltage, or the potential between the two sides, actually remains constant. That's the magic of a battery. So let's just assume that we have one of these magic instruments. You probably have one in your calculator or your cellphone. And let's see what happens when we allow the charge to actually travel from one side to the other. So let's say that I have an ultra-good conductor. Let's say it's a perfect conductor. It's normally drawn straighter than what I'm capable of doing. And no, I haven't had anything to drink before making this video. So what did I do here? So in the process of kind of connecting this positive terminal to the negative terminal of the battery, I'm also exposing you to common schematic notation for electrical engineers and electricians, et cetera, et cetera. So what this is, these lines here essentially are wires. There's no reason why I drew it at a right angle here. I just did that to be neat, those right angles. And it's assumed that this wire is an ideal conductor, that charge can flow freely without being impeded. This thing right here, this scratchy line, this is a resistor, and this is something that will actually impede the charge. It'll keep the charge from going as fast as possible. And then, of course, out here, this is a perfect conductor again. Now, which way will the charge flow? Well, I think I've mentioned this before, but in electric circuits, it's actually the electrons that are flowing. The electrons are those small particles that are going really, really fast around the nucleus of an atom. And it's actually the electrons that have this fluidity that allow it to flow through a conductor. So the actual movement of objects, if you call an electron an object, some would argue that they're almost just notional objects, but the actual flow is the electrons from the negative terminal to the positive terminal. But the people and all who originally created circuit schematics and were the pioneers of electrical engineering and electricians and whoever, I don't know who came up with it, they decided to say-- and I think the point here was to confuse people-- that the current flows from the positive to the negative. So the direction of the current is normally given in this direction, and current is specified by I. And what is current? Well, current-- so wait. Actually, before I tell you what is current, just remember, even though people say that the current-- and most textbooks do this, and if you become an electrical engineer, people will often say that the current is flowing from the positive terminal to the negative terminal, the actual flowing of things actually occurs from the negative terminal to the positive terminal. It's not like somehow these big heavy protons and nuclei are somehow traveling this way. Once you compare the size of an electron to a proton, you would realize how crazy that is. It's the electrons, these little super-fast particles that are moving through the conductor from the negative terminal this way. So you could almost view this current as, the lack of electrons are flowing this way. I don't want to confuse you. But anyway, just remember that this is the convention, but the reality is to some degree the opposite of the convention. So what is this resistor? Well, as the current is flowing-- and I want to stay as close as possible to reality so you have a good visualization of what's going on. As the electrons are flowing, you have these little electrons, and they're flowing in this wire. And we assume for some reason this wire is just so amazing that they don't in any way bump into any of the atoms of the wire or anything. But when they get to this resistor, that's when these electrons start bumping into things. They start bumping into the other electrons in this material. So this is the resistor right here. They start bumping into the other electrons in this material. They bump into the atoms and molecules in this material. And in the process, the electrons essentially slow down, right? They're bumping into things. So essentially, the more things that there are to bump into, or the less space there are for the electrons to flow through, the more that this material is going to slow down the electrons. And as we'll see later, the longer it is, that only increases the chance that electrons bump into things. And this is called a resistor and it provides resistance, and it dictates how fast the current flows. So current, even though the convention is it flows from positive to negative, current is actually just the flow of charge per second. So we could write that down. I know I'm saying this in kind of a disjointed way, but I think you get what I say. Current is flow of charge, so change in charge per second, or per change in time, right? So the way you could think about it is, what is voltage? Voltage is how badly does current want to flow? So if there's a high voltage difference between these two terminals, then the electrons that are sitting here, these electrons want to really badly get here, right? And if the voltage is even higher, these electrons want to get there even more badly. So before people understood that voltage was just a potential difference, they would actually call this desire of the electrons to get from here to here the electromotive force. But what we've learned now, it's not actually a force. It's just this potential difference that makes the-- we could almost view it as an electrical pressure, and that's what people used to actually call voltage, electrical pressure. How badly do the electrons want to get from here to here? As soon as we give the electrons a path through this circuit, the electrons will start traveling. They'll start traveling, and we assume that this wire provides no resistance, that they can travel as fast as they want. But when they get to this resistor, they start bumping into things, and this limits how fast the electrons can travel. So you can imagine that if this object right here is somehow the rate-determining factor in how fast the electrons travel, no matter how fast the electrons can travel after that, this was the bottleneck. So even though electrons can travel really fast here, they have to slow down here, then they could travel really fast here, the electrons here can't travel any faster than the electrons through this. Well, why is that? Because if these electrons are traveling slower, so the current here is lower-- current is really just the rate at which the charge is traveling, right? So if the current is lower here and the current was higher here, we would essentially end up having a buildup of charge someplace here while all of the current were waiting to travel through this. And we know that that's not the case, that all of the electrons actually travel at the exact same rate through the entire circuit. I'm going in the opposite of the convention right now, because the convention is that somehow we have the positive things traveling this way. But I want to give you a really intuitive sense of what's going on in a circuit, because I think once you understand that, once problems get a lot more complicated, they won't be so daunting. So what we know, and this is called Ohm's law, we know that the current is actually proportional to the voltage across the circuit. So we know that voltage-- or we could view it the other way, that the voltage is proportional to the current through a circuit. So the voltage is equal to the current times the resistance, or you could say that the voltage divided by the resistance is equal to the current. This is called Ohm's law, and this is true whenever we're at a constant temperature. We'll go into more depth later, and we'll learn that if a resistor actually has temperature increases, then its particles and its molecules are moving around more, they have higher kinetic energy. And then it's even more likely that electrons will bump into them, so actually, the resistance increases with temperature. But if we assume at a constant temperature for a given material-- and we'll also learn later that different materials have different resistivities. But for a given material at a constant temperature in a given configuration, the voltage across a resistor divided by the resistor is equal to the current that flows through it. An object's resistance is actually measured as ohms, and it's given by the Greek letter Omega. So let's do a simple example. Let's say that this is a 16-volt battery, so the potential difference here is 16 volts between the positive and the negative terminal. So it's a 16-volt battery. Let's say that this resistor is 8 ohms. What is the current flowing through-- and I keep doing it in the opposite of the convention, but let's go back to the convention. What is the current flowing through this circuit? Well, it's fairly straightforward. It's just Ohm's law, V equals IR. The voltage is 16 volts, and it equals the current times the resistance, times 8 ohms. So the current is equal to 16 volts divided by 8 ohms, which is equal to 2, and this is 2 amperes. Or sometimes they're called amps, and that's the units for current. But as we know, all current is, is the amount of charge per amount of time, so an ampere is just 2 coulombs per second, right? Oh, I'm already at 11 1/2 minutes. So I will leave you there. You now know the basics of Ohm's law and maybe a little bit of intuition on actually what's going on in a circuit, and I will see you in the next video.