Resistivity, and Ohm's law
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Introduction to circuits and Ohm's law
- [Instructor] What we will introduce ourselves to in this video is the notion of electric circuits and Ohm's law, which you can view as the most fundamental law or the most basic law or simplest law when we are dealing with circuits. And it connects the ideas of voltage, which we will get more of a intuitive idea for in a second, and current, which is denoted by capital letter I, I guess to avoid confusion if they used a capital C with the coulomb. And what connects these two is the notion of resistance. Resistance, that is denoted with the capital letter R. And just to cut to the chase, the relationship between these is a pretty simple mathematical one. It is that voltage is equal to current times resistance or another way to view it, if you divide both sides by resistance, you get that current is equal to voltage divided by resistance. Voltage divided by resistance. But intuitively, what is voltage? What is current? And what is resistance? And what are the units for them so that we can make sense of this? So to get an intuition for what these things are and how they relate, let's build a metaphor using the flow of water, which isn't a perfect metaphor, but it helps me at least understand the relationship between voltage, current, and resistance. So let's say I have this vertical pipe of water, it's closed at the bottom right now, and it's all full of water. There's water above here as well. So the water in the pipe, so let's say the water right over here, it's gonna have some potential energy. And this potential energy, as we will see, it is analogous to voltage. Voltage is electric potential, electric potential. Now it isn't straight up potential energy, it's actually potential energy per unit charge. So let me write that. Potential energy per unit, unit charge. You could think of it as joules, which is potential energy, or units of energy per coulomb. That is our unit charge. And the units for voltage in general is volts. Now, let's think about what would happen if we now open the bottom of this pipe. So we open this up. What's gonna happen? Well, the water's immediately gonna drop straight down. That potential energy is gonna be converted to kinetic energy. And you could look at a certain part of the pipe right over here, right over here. And you could say, well, how much water is flowing per unit time? And that amount of water that is flowing through the pipe at that point in a specific amount of time, that is analogous to current. Current is the amount of charge, so we could say charge per unit time. Q for charge, and t for time. And intuitively you could say, how much, how much charge flowing, flowing past a point in a circuit, a point in circuit in a, let's say, unit of time, we could think of it as a second. And so you could also think about it as coulombs per second, charge per unit time. And the idea of resistance is something could just keep that charge from flowing at an arbitrarily high rate. And if we want to go back to our water metaphor, what we could do is, we could introduce something that would impede the water, and that could be a narrowing of the pipe. And that narrowing of the pipe would be analogous to resistance. So in this situation, once again, I have my vertical water pipe, I have opened it up, and you still would have that potential energy, which is analogous to voltage, and it would be converted to kinetic energy, and you would have a flow of water through that pipe, but now at every point in this pipe, the amount of water that's flowing past at a given moment of time is gonna be lower, because you have literally this bottleneck right over here. So this narrowing is analogous to resistance. How much charge flow impeded, impeded. And the unit here is the ohm, is the ohm, which is denoted with the Greek letter omega. So now that we've defined these things and we have our metaphor, let's actually look at an electric circuit. So first, let me construct a battery. So this is my battery. And the convention is my negative terminal is the shorter line here. So I could say that's the negative terminal, that is the positive terminal. Associated with that battery, I could have some voltage. And just to make this tangible, let's say the voltage is equal to 16 volts across this battery. And so one way to think about it is the potential energy per unit charge, let's say we have electrons here at the negative terminal, the potential energy per coulomb here is 16 volts. These electrons, if they have a path, would go to the positive terminal. And so we can provide a path. Let me draw it like this. At first, I'm gonna not make the path available to the electrons, I'm gonna have an open circuit here. I'm gonna make this path for the electrons. And so as long as our circuit is open like this, this is actually analogous to the closed pipe. The electrons, there is no way for them to get to the positive terminal. But if we were to close the circuit right over here, if we were to close it, then all of a sudden, the electrons could begin to flow through this circuit in an analogous way to the way that the water would flow down this pipe. Now when you see a schematic diagram like this, when you just see these lines, those usually denote something that has no resistance. But that's very theoretical. In practice, even a very simple wire that's a good conductor would have some resistance. And the way that we denote resistance is with a jagged line. And so let me draw resistance here. So that is how we denote it in a circuit diagram. Now let's say the resistance here is eight ohms. So my question to you is, given the voltage and given the resistance, what will be the current through this circuit? What is the rate at which charge will flow past a point in this circuit? Pause this video and try to figure it out. Well, to answer that question, you just have to go to Ohm's law. We wanna solve for current, we know the voltage, we know the resistance. So the current in this example is going to be our voltage which is 16 volts, divided by our resistance which is eight ohms. And so this is going to be 16 divided by eight is equal to two and the units for our current, which is charge per unit time, coulombs per second, you could say two coulombs per second, or you could say amperes. And we can denote amperes with a capital A. We talked about these electrons flowing, and you're gonna have two coulombs worth of electrons flowing per second past any point on this circuit. And it's true at any point, same reason that we saw over here. Even though it's wider up here and it's narrower here, because of this bottleneck, the same amount of water that flows through this part of the pipe in a second would have to be the same amount that flows through that part of the pipe in a second. And that's why for this circuit, for this very simple circuit, the current that you would measure at that point, this point, and this point, would all be the same. But there is a quirk. Pause this video and think about what do you think would be the direction for the current? Well, if you knew about electrons and what was going on, you would say, well, the electrons are flowing in this direction. And so for this electric current, I would say that it was flowing in, I would denote the current going like that. Well, it turns out that the convention we use is the opposite of that. And that's really a historical quirk. When Benjamin Franklin was first studying circuits, he did not know about electrons. They would be discovered roughly 150 years later. He just knew that what he was labeling as charge, and he arbitrarily labeled positive and negative, he just knew they were opposites, he knew something like charge was flowing. And so, in his studies of electricity, he denoted current as going from the positive to the negative terminal. And so we still use that convention today, even though that is the opposite of the direction of the flow of electrons. And as we will see later on, current doesn't always involve electrons. And so this current here is going to be a two ampere current.