 Now we can look at resistors in series. And we'll start by reminding ourselves of the basic resistor circuit, which has one battery and one resistor. And our resistor equation relates the voltage and current for that particular resistance. I can algebraically rearrange that equation to solve for either the voltage or the current using these equations. Now in a series circuit, it's defined by there's one path around the whole circuit. So in this case, it's one path going through resistor one and two and back through the battery. And there's just one single path with no splits anywhere on that path. So now let's look at the series current. If I look at the current going through that path, and then I think about what the current going through resistor one and resistor two is, I see that I have exactly the same current going through both resistor one and resistor two, meaning I have an equivalent current, which is equal to both current one and current two. For voltages, remember that a voltage is a potential difference. So for my battery, I'm going to have a high potential on the positive side of the battery. And that's going to be the same high potential all the way along this branch here up to R1. Similarly, I'm going to have a low potential everywhere over here on this side of the circuit. Now, what's the potential in between going to be? Well, it's going to be some middle value of the potential, something which is lower than the high value, but higher than the low value. If I think then about the voltage on resistor one, it's going to be the difference in the high and the mid potentials. Similarly, the voltage on resistor two is going to be the difference between the mid and the low potentials. While my equivalent potentials, equivalent voltage, is going to be the difference between the high and the low. And I can think of that as either being the voltage on the battery or overall going all the way across the resistors. I'm going from high to low. Now, working with those equations, what we see is that what we really have is that the voltage equivalent is equal to the sum of these two individual voltages. You can think of it this way. The battery increases the potential. And the combination of the two resistors decreases it a little bit and then a little bit more, but it has to add up to the total amount that my battery originally increased it. So now we come to series resistance. And we're going to use our previous equations we've just found to try and understand this. Starting with this voltage equation. Now, the voltages add up, but I can also remember that each individual voltage was related to the current and resistance through that particular device. And so I've got that for resistor one, resistor two, and the equivalent resistance for the whole circuit. Combining those, what I see is I can represent this equation in terms of current and resistance, but I also want to remember that my currents were all the same. That was something I found for series circuits. And that means up here, each individual current, well, I could divide through, and that would cancel out of every term, leaving me just my resistances. So in summary, if I have a series circuit, the currents are going to be equal to each other. The voltages will add up, and the resistances will just add up. What if I had more than just two resistors, though? Well, my currents are still all going to be equal to each other. The voltages are still going to add up, and the resistances are still going to add up completely. So that's your summary of the series resistors and their equations.