 Now we're going to look at parallel resistors. So we start with our basic resistor circuit, which has one battery and one resistor. And we remember that our definition of our resistance related the voltage to the current for a particular device. Now I could algebraically rearrange that equation to solve for either the voltage or the current in terms of the other two quantities. Now we can talk about a parallel circuit. And again, parallel means there's two paths around the circuit. In this case, one path goes through resistor 1. The other path goes through resistor 2. I could also think of this in terms of the path splitting and going two different directions and then coming back together. So now that we have this understanding of a parallel circuit, let's look at the parallel currents. And we're going to first look at this by defining current 1 and current 2 as the currents going through resistor 1 and 2. And the equivalent current being what's going through the branch that has the battery on it. Now as the battery starts to make that current flow, what we see is that current 1 and current 2 are moving together through the equivalent branch. And I could also think of this in terms of that equivalent current coming up, splitting off into 1 and 2, and then coming back together as the equivalent current. Either way I think of it, I should have that my equivalent current is equal to the sum of current 1 and current 2. Now let's talk about the voltages in parallel. Again, a voltage is a potential difference. And so that means my battery is going to have a high voltage on one side. But that same high voltage is going to be communicated along the wire to everything along this branch. So I have that same high potential at the top of both R1 and R2. And I'm going to have a low potential down on the bottom. And I have to have the same low potential over here, because it's all connected by wires. And if these are ideal wires, they'll all be at the same potential value. And so that means my voltage across resistor 1, which is the potential difference between the high potential and the low potential. Similarly, my voltage on resistor 2 is going to be the difference between my high and low potentials. Same thing for my equivalent. And that means for parallel, I've got the same voltage for my equivalent voltage, my voltage on 1 and 2 in terms of my two resistors. So now we get to parallel resistance. And we're going to use these previous equations we've come up with, starting with our current equations where the currents add up. Now going back to those original things, I recognize that I can express the current in terms of the voltage and resistance for the equivalent, resistor 1 or resistor 2. And plugging these three things into my equation up here, I see that I can express this in terms of the sum of the voltage over the resistance for 1 and 2, giving me the equivalent. But remember, we just found that the voltages were all the same. So that means in this equation, I could divide by the voltage and it would cancel out on each one of those terms, leaving me with just the inverses. Now that's a perfectly acceptable way of expressing the equivalent resistance. But we often go a step further and actually solve for the equivalent resistance by seeing it's the inverse of the sum of the inverses. So just to summarize again, in parallel for resistors, my currents add up, my voltages are the same, and the equivalent resistance follows the inverse law. If I had three or more resistors, the currents would still add up, my voltages would still be the same, and I would still work with the inverses. But now it's 1 over the sum of all the resistors added up. There are individual inverses. So those are our parallel resistor equations.