 So now let's take a look at series capacitors. But before we get to series, let's do a quick reminder of our basic capacitor circuit. So in this, I've got one voltage source, a battery, and one capacitor. And my basic equation here is going to relate the capacitance to the amount of charge stored on that capacitor given a particular voltage or potential difference. I can rearrange that equation to solve for either the voltage or the charge by using some simple algebra. Now we get to a series circuit. Here's a basic diagram of a series circuit. And the description really has to come with having one path around the whole circuit. So if I start at the battery and go around, I go through each one of the capacitors and then back to the battery. And there are no splits anywhere around that path. And that's the most important thing about a series circuit. So let's take that series circuit and that concept and start looking at what's going to happen to the charge. Well, what you see is that this voltage source actually starts moving charge. And it separates it so that I end up having negative charge, my extra electrons, over here on this side. And positive charge over here on this side. But that's positive Q over on C1 and minus Q over here on C2. The battery doesn't directly move any charge between those two capacitors. But the buildup of that charge is going to cause the charge in that wire to separate, such that I end up with a minus Q over here to balance out my plus Q and a plus Q over here to balance out my minus Q. So my Q1, the charge stored on capacitor 1 and my Q2, the charge stored on capacitor 2, are actually going to have to be the exact same Q. And that's the equivalent which was moved by the battery. Now, I can also think of this Q equivalent as looking at the charge plus Q over here compared to the minus Q over here. And again, those are the same. Well, now we need to look at voltages. Now, we should be very careful with our terminology here because a voltage is really a potential difference. So we want to look at the voltages, but we also want to look at the potentials. And a voltage source sets up a high potential on one side, on the positive side. And that high potential is going to be the same all the way along that wire, assuming it's an ideal wire, such that I have the same high potential over here on this side. Similarly, I've got a low potential side of my voltage source. And that's going to give me a low potential over here on this side by C2. Now, for a capacitor, when I've got my positive and negative charges, I'm going to have to have a higher potential on this side than I do on the negative side. And for C2, I'm going to have to have a higher potential on the positive side than I have over here on the negative side. So that means this wire here in the middle has to have some middle potential value. Coming back to voltages, my voltage on capacitor 1 is going to be the difference between the high and mid potential values. And my voltage over here on C2 is going to be the difference between the mid and the low potential. Now, if I work with these equations, what I'm going to see is that my equivalent potential is going to be the difference between the high potential and the low potential. And in this case, that also happens to be the potential of my voltage source. So the way we can end up writing this out is that the equivalent voltage is equal to the voltage on cross component 1 and the voltage on component 2. And these voltages, again, are a change in potential. So you could think about this as the battery increases the potential, but then the potential drops part way over capacitor 1 and part way over capacitor 2. And the total amount it drops has got to be the same as how much it went up at the voltage source. Now, we're going to take a look at our previous equations to look at the capacitance. So if I start off with my equation here for the voltage, that the two individual voltages have to add up to the equivalent voltage. And I start replacing things. And you see, this potential difference across capacitor 1, voltage 1, is going to be Q1 over C1. Similar sort of thing with the potential difference across capacitor 2. And I could define my equivalent voltage in terms of the equivalent charge and the equivalent capacitance. So I can take these three quantities and plug them into that equation and get something which looks like this. Now I make use of my charge equation, which tells me that the three charges are the same. And that means in this equation, my three charges can actually cancel out, leaving me with just 1 over the equivalent capacitance, equals 1 over C1 plus 1 over C2. Some textbooks will use that as my standard capacitance equation. And some will take it a step further to say, if I actually want to solve for my equivalent capacitance, I have this inverse relationship where it's 1 over the total quantity of 1 over C1 plus 1 over C2. Now just to summarize then, we've got equations for charge, voltage, and capacitance. And for capacitance, I just have two equivalent ways of writing out that fraction. What if I've got three or more capacitors in a series circuit? Well, for charge, they're still just all equal to each other. For voltage, now I add up that voltage on each component, no matter how many components I have. And the total of those potential changes has to be my voltage equivalent. And if I'm working with the equivalent capacitance, I just add an extra 1 over C3 or 1 over C4 or 1 over C5 for however many capacitors I have. And if I look at it in terms of the equivalent capacitance in this form, I still have 1 over. But now the stuff on the bottom has just gotten longer as I've added the extra capacitors. So that's your series capacitors.