 In this video I wanted to introduce to you a new piece of terminology called series. There are two ways. If I had two resistors, there's two ways that I could arrange them. The first is in series, and it would look like this. The second way that I could arrange two resistors is in parallel. That looks like this. It so happens there's a trick you can use to find the total resistance whenever you have two resistors that are in series, or two resistors that are in parallel. So I'm going to start off by showing you two resistors in series. So in order to find this total resistance of these two resistors, what I'm going to do is assume that they are attached to some sort of arbitrary voltage source. So it could be any voltage. The total resistance will satisfy Ohm's law, the formula that V equals IR. So the question is, what is our total in this case? Well, to do this I'm going to have to use my loop rule and my node rule. So let's start out using the loop rule. So remember, the loop rule tells me that the total voltage drop across this circuit here must be equal to the voltage gain across the battery. So that means that the voltage gain is equal to V, the total voltage drop is going to be equal to the voltage drop across resistor one plus the voltage drop across resistor two. And then using Ohm's law, I get, to get any further, I'm going to have to use the node rule. So the node rule tells me that the current flowing into this junction here is equal to the current flowing out. So I've asked to consider this point here, the current flowing into this point is equal to the current flowing out. This means the current flowing through resistor one is equal to the current flowing through resistor two. So mathematically, I can write, this means if I1 is going to equal to I2, so in this case I'm just going to call this I. So if I substitute this into the formula above, now let's compare these two formulas. So I've got formula number one at the top and formula number two down the bottom. So I've both got the voltage is equal to the current times the total resistance and the voltage is equal to the current times R1 plus R2. This proves that for two resistors in series, the total resistance is equal to R1 plus R2. Now it so happens that if you have more than two resistors, but they are all in series, you can still use this formula. It's simply that the total resistance is equal to the sum of the individual resistances. So you just add R3 plus R4 and so on. So we've just arrived to formula that allows us to determine the total resistance of any number of resistors in series. If we wanted to write this a little bit more rigorously, we could write that the total resistance is equal to the sum of all the individual resistances. Please note that this only works when resistors are in series. If the resistors are in parallel, then there's another trick that we're going to have to use and I'll show you this in the next video.