Capacitors & Capacitance

Alright, guys. So now we're going to start talking about capacitors and capacitance, These air common objects you will see in electricity and we'll definitely need them. When we start getting to circuits, you'll need to know what they are and how they work. So let's go ahead and take a look. So imagine that I have these two charges we talked about. How positive and negative charges, if you have them some distance apart, basically have some energy between them. So, in other words, this this positive negative charge which, by the way, we called an electric dipole The fact that these two charges are positioned some distance apart, they have some electrical potential energy between them. And basically what happens is that a capacitor is instead of just having one charge and one charge, we now just have a sheet or a surface of charges in which all of these charges air positive. So we have a positive Q and then we have another surface that has negative charges built up on it. So we have negative que. And now what happens is that the fact that these plates are these surfaces are some distance apart. So we have some distance right here. These carry a lot more potential energy between them. And this is basically what a capacitor is. A capacitor is two surfaces of equal and opposite charges. And the fact that these are equal and opposite basically serves to store potential energy between them. It stores a lot of potential energy that because nothing, none of these charges are actually moving. Okay, so how do you get these charges to get on these plates? Are these surfaces in the first place? Well, to do that, you have to connect this capacitor to a battery. And in doing so, you produce what's called a simple circuit. We have a diagram of a simple circuit right over here, but basically and we're gonna talk a lot about circuits, uh, in later videos. But these circuits are basically just conducting wires, which are the black lines. And these conducting wires just means that charges could easily flow between them and the So it's these conducting wires and some other stuff, which we'll talk about later. So you have this capacitor that is hooked up to a battery. So all of these charges that basically build up on the surface is off this capacitor. The source of those moving charges comes from potential differences. So we know that any charge that as it moves through a potential difference is going to gain or lose some energy. Now, this potential difference the best example is commonly called a battery. So what a battery is. And by the way, this is just the standard symbol for a battery. Doesn't actually look like this. This is just what we've chosen. Now the standards set up for a battery is that the longer end end right here? The longer terminal is really what we call the positive terminal. This is just something that physicists have decided for 100 years ago that this is just gonna be with the way it is. So the longer terminal is gonna be the positive. The shorter one is gonna be the negative and by convention, because we didn't actually know how electrons move back and what specific direction we just chose that electrons we're gonna move in this direction. This is just something that we chose. It's not gonna effect the physics in any way, but you're just gonna have to get used to it. So the electrons will start moving along this direction right here. So we have the direction of motion of these electrons. And what ends up happening is they start building up on the surfaces off these capacitors. You're gonna have a whole bunch of negative charges that start building up over here as the electrons air flowing through the circuit. Now what happens is that these, like, charges we'll want to repel and the op opposite charges want to attract. So that means that on the other side of the capacitor, the electrons will keep on going. They'll basically flow upwards here because now they have some potential. And you have the negative. Sorry, the positive charges that will start building up on the other side of the capacitor now. So basically, what happens is I'm just going to start making up some numbers here. Imagine that we had a four volts potential over here and a negative four volt potential on this side of the battery. What is happening is that these electrons will start to move. They'll start to set up thes thes surfaces of charges right here. And basically all of this will happen until the potential on this side of the plate is equal to negative four volts, and the potential over here is positive. Four volts. Now what happens is essentially the potential differences between the battery and the capacitor are always going to equal when you have a situation where you have one battery and one capacitor. So, in other words, the voltage of the battery. So if I wanted to figure out the Delta V the voltage, that would just be, let's see, final minus initial. So if these electrons air moving towards this side right here, which is gonna pretend that they dio the potential difference would be final, which is the negative four minus initial, which is the positive. For some of the words. This Delta V would just be negative eight volts so that we have the potential difference that these electrons experience now as they move across the capacitor. Now what happens is the potential difference Over here. Delta v of the capacitor is gonna be four minus negative for so that means that this voltage is gonna be positive. Eight volts. So now we can see that the voltage of the battery in the circuit here Delta V. B and the voltage of the capacitor are basically going to equal each other. Now, that's basically a really, really important part now has for the charge that builds up. We can actually relate to the charge and the voltage using this equation right here. The charge that builds up across these capacitors is Q equals C times V. Now I want to point out some things right here. The first is that this V actually now represents the voltage. And I know that just sucks because we spent a whole lot of time talking about how we differentiate the potential, which is V and the voltage, which is Delta V. But as we start talking about circuits, people are your textbooks and your professor is not gonna have Delta V anymore. They're just gonna have V for voltage. It's just it's really crappy notation. But this is how everybody does it, So you might as well just get used to it. We'll talk about these as voltages now, and the C variable right here represents something called the capacitance. And the capacitance we can see from this equation is just Q divided by V. The units for this capacitance are in F and News, recalled Farage's. And basically what this capacities represents or what it measures is it measures the strength of the capacitor. And what I mean by that is we can see how, in this capacity formula you have charge, divided by a potential. So what happens is if you have a larger or stronger capacitor with a larger capacitance, it's going to store a larger amount of charge for the same potential difference for the same amount of voltage. So, for instance, you have five volts and you have 10 columns across those capacitors. Then the capacitance is gonna be something. But if you had 20 cool OEMs across the same voltage, the capacitor would be their capacities would be even higher than that. Okay, so these are a couple equations that we're gonna use for capacities and capacitance. Let's go ahead and check out how we use them in this example right here. So what's the charge on the capacitor in this following figure? So remember that this is actually the battery. So this is actually the battery over here with one where you have a longer and smaller terminal or a little horizontal line and This is the capacitor over here. We can also just tell by the units where now this nine volts right here actually represents the voltage, which is the potential difference. So this is actually V our voltage. And this represents the capacitance right here. So we're asked to find out what the charge on this capacitor is. In other words, were asked for Q. So what's our equation? Relating all of these things. They charge the capacitance and the voltage we have Q equals C times V. In other words, Q is equal to the capacitance. Three ferrets times the potential difference. Now, how do we figure out what the potential difference across this capacitor is? Will remember that in circuits where you have one battery and one capacitor, the voltage across the battery is always gonna be the voltage across the capacitor. So that means we actually do know what the voltage and the capacities for both of these, for both of this equation is, it's just gonna be three times nine volts, and that's equal to 27. Cool OEMs. And that's our answer. Okay, let me know if you guys have any questions with this and let's keep going