We've talked a lot about resistors in circuits. The next element that we need to include is capacitors. So what do capacitors do in circuits? Well, let's think about the battery again for a second. The battery has a positive side and a negative side. And the positive side is the long bar, the negative side is the short bar. Okay so if you take a double A battery, the one that says plus, that's the long bar. Let's hook up a capacitor here in this circuit. Remember, a capacitor we draw with two equal length lines, which is supposed to distinguish it from the battery. And that capacitor has a capacitance, C. If I put this capacitor in this circuit, it's going to charge up. Namely there is going to be some positive charge on one side and some negative charge on the other side. Which side should have the positive charge, the top side or the bottom side? The top side. The top side should be positively charged, the bottom should be negatively charged. How do you know that? Well, the battery has a whole bunch of positive charge on that side of the battery. And it's going to push away other positive charge through this wire and that positive charge is going to accumulate on the top of the capacitor. Likewise the negative side of the battery, which has a whole bunch of negative charge on it, is gonna push negative charge away. And end up on the bottom side of the capacitor. So that original statement that we said, "like charges repel." You can really discover a lot about circuits just remembering that. Like charges repel each other. So positive charge on this side of the battery is gonna push positive charge away from it onto the top of that capacitor. How much charge? How much charge is on the capacitor? Well, I don't know. You guys know? We have a relationship between charge and voltage, right? What's the relationship? Q equals CV. I know C, I would give that to you. It's a number like 5 microfarads or 10 picofarads. It's some set number that only depends on the geometry of the device. What it's made out of and the geometry of it. And now if I attach a voltage to it, the voltage, V, is the same voltage across that capacitor. Because everything else is connected by metal wires. So what's the charge on the capacitor? CV. This is the charge on one plate. Obviously the capacitor has equal and opposite charge on the other plate. So the net charge on the whole thing would be zero. But when we say what's the charge on the capacitor, we mean what's the charge on one side of it. What's that positive charge? It's Q. Okay. But let's try something a little more complicated now. Let's say we hook up two capacitors like this. We'll call this one C1 and we will call this one C2. I've just added a second capacitor onto the first one and it looks like we've done it in parallel. As opposed to series. What is the charge on Capacitor 1? Well, the voltage across it is still just V because those are wires connected right to the battery. So the charge is going to be C1 times V. The charge on C2 is going to be C2 times V because it also sees the same potential, right? It's also connected by metal wires to the battery and so the charge on it is just C2 times V. So, let's ask the question, what is the total charge that is stored on the positive plates of those capacitors? Well, we just add it up, right? Total Q is going to be Q1 plus Q2. Piece of cake. What is Q1? We said it's C1 V. What is Q2? It is C2 times V. And now I have a common V in both of those. So I can factor it out. And the total charge is just C1 plus C2 times V. And that thing we can call C sub p V. This refers to parallel. We've added these things in the parallel configuration and yet somehow their capacitance has added up. Which is very different than resistors, okay. When you add capacitors in parallel, you simply add their capacitances to calculate the equivalent capacitance of that circuit. Parallel capacitors add. Battery, V. And that whole thing simplified to our simple circuit. One battery, one capacitor. But this capacitor is in parallel and the rule for adding capacitors in parallel is you add up the capacitances. All right. By adding those two, we have in fact increased the capacitance. One way to think about this is it's just like you took these metal plates and you doubled their area. These were equal capacitances and I had two metal plates that were separated by that. And I brought them together, I would just double the area of the capacitor. And when you double the area of a capacitor, you double its capacitance. How much energy are we dealing with in this case? Well, remember energy is CV squared. One-half CV squared. It's the energy storage in a capacitor. So we have one-half CV squared in that one. We have one-half CV squared in the other one. We know that we can add those up because we have some common factors. C1 plus C2 all times V squared. But C1 plus C2 is the exact same as Cp. So this is one-half CpV squared. When you have a circuit like this and it charges up, the capacitor has energy in it of one-half CpV squared.