 So in this video, I'm going to derive the formula for how we can find the total resistance for resistors that aren't in parallel. So to remind you, this is what it looks like when resistors are in parallel. And just like last time, I'm going to assume that these two resistors together are attached to some arbitrary voltage source. The total resistance will satisfy Ohm's law. The V is equal to the voltage across the whole circuit is going to be equal to the current flowing through the circuit times the total resistance. But with this particular circuit, I'm going to need to be careful because there are two branches. See how at this point here, the circuit branches out to two points. And so some current will go this way and some current will go down this way. So when I write I, I need to be very specific about which current I'm talking about. So for this particular formula, I'm going to write I-Total or I-T, where I-T is the total current in the circuit. And I could say that that's going to be the current flowing through this point here, just to be absolutely clear. What I'll also do is I'll call the current flowing through this point here in the circuit I1, and I'll call the current flowing through this point in the circuit I2. So let's use the node rule and examine this point here that I've highlighted in yellow. So the total current flowing into this particular point in the circuit must be equal to the current flowing out. So that tells me that the total current I-T is equal to I1 plus I2. But to make more progress, I'm also going to have to consider the loop rule. Let's consider this loop here, which I'm going to highlight in green. So I'm considering a loop that starts at the battery, goes all the way along here, then goes down, goes past resistor two, then comes all the way back to the battery again. So for that particular loop, I can see that the voltage must be equal to the voltage drop across this arm here. So it's going to be equal to R2 times the current going through R2. Now let's consider another loop. I'm going to consider the loop here that starts at this point in the circuit, goes up, then comes through the top part of the circuit back down to my original point. So in this loop, I have the total voltage. So for this loop, I have the voltage going across this battery here is going to be equal to the voltage lost across resistor one, which using Ohm's law is equal to R1 times I1. So now I have four equations, which I'm going to number. Now by rearranging equation one, equation three, and equation four, I can solve for the current in each case, and that will give me these different numbers here. Now if I substitute each of these I's into equation two at the top, I get, then if I divide both sides of the equations by V, I get, so we've derived a formula for two resistors that are in parallel. It so happens you can generalize this formula for any number of resistors, it takes the form one over the total resistance is equal to one over R1 plus one over R2 plus one over R3 plus one over R4 and so on. Now note this formula only works for resistors that are in parallel. But we've derived a formula that's going to allow us to make useful calculations in circuits that involve resistors in parallel.