 Now, we're ready to look at parallel circuits and the equivalent resistance calculation. This one's a little bit more of a complicated formula. In this case, in order to find the equivalent resistance, you've got your 1 over R1 plus 1 over R2 plus however many resistors you have, but it's 1 over that value to give you the equivalent resistance. This is similar to the series capacitors, so if you haven't watched that, you might want to go back and watch that video as well because I highlighted some of the common student mistakes when they're actually working with this equation. And I want to remind you that this equation came about because what we actually had was that 1 over the equivalent resistance was 1 over R1 plus 1 over R2, again continuing the pattern as far out as you needed to. So let's take an example with just two resistors and show you how that calculation works out. So in this case, I've got a 42 ohm resistor and a 21 ohm resistor. When I did these same things in series, I just added the 42 in the 21 to give me 62. But in this case, I've got 1 over 41, 1 over 21, and then it's 1 over that answer, which gives me 14 ohms. And yeah, I picked these numbers just to give us something even that works out. More often, you're going to end up having numbers that are going to have decimals or fractions in them. Now this particular equation is nice because it can extend out to more than just two resistors. So for example, if I've got three resistors, you just have 1 over R1 plus 1 over R2 plus 1 over R3. And once you've done that, it's 1 over that value. Or if you plug it into your calculator, 1 over and make sure you have those outside parentheses so that everything else remains on the bottom. Now in this case, I'm going to do an example that's got some smaller resistances in there. 1 over 1 over 2 ohms plus 1 over 3 ohms plus 1 over 4 ohms. And if you plug that into your calculator, you get 0.923 ohms. Now again, I'm going to point out here that just like the series capacitors, the parallel resistors, the equivalent resistance is always going to give you a number, which is smaller than the smallest of all the capacitors. So in this case, with the 2, the 3, and the 4, the 2 was the smallest. And my answer has to be smaller than 2, which it is. In this case up here, I had the 42 and the 21, the 21 was the smallest. And my equivalent resistance, 14 ohms, is smaller than that smallest one. In series, because you're just adding them, you always get a larger value. But in parallel, you always get a smaller value. And you can think of it in the sense of because I've got parallel circuits, there's more paths that the current could flow, which decreases the overall resistance of the system because there's more paths to follow as opposed to having less paths to follow. Now the other way that we can work with this equation, just to give me some room here, is what if it's not the equivalent resistance that you're trying to find, but you're trying to find either R1 or R2. In that case, it's better to go back to this form of the equation. So for example, if I was trying to find R1, what I want to do is I want to actually subtract over the 1 minus R2 to the other side. And then algebra wise, R1 would be 1 over the equivalent resistance minus 1 over the second resistance. And that would give me my value for R1. You could do something similar if you were solving for R2 and didn't know it, but knew the equivalent resistance and the R1 value. If you have more questions about these parallel equivalent resistances, certainly feel free to make a comment or send me a question. Again make sure you're using your parentheses and after you finish your calculations, make sure your value makes sense that it's a smaller value for the equivalent resistance.