Hello folks, in this video we're going to take a look at the voltage divider rule. Very useful little rule when we're dealing with series connection of resistors. Consider the following problem. We have a voltage source and it's connected up to a string of resistors. I'll use three, but this could be two or 17 for that matter. And I'm just going to label these our one or two or three. I'm also going to put some points down here, point A, point B, point C. I'm interested in finding the voltage across various resistors and resistor combinations. The way we would ordinarily do that is we would figure out the total resistance. The total resistance here would just be R1 plus R2 plus R3 for however many resistors you have. We would divide that into the voltage that would get us the current. The source current coming out of here would wind up equaling E divided by RT. As the current flows down through the resistors, we get a drop plus to minus R1 plus to minus R2 plus to minus R3. So far nothing new. We use that current to find a particular voltage. If I'm interested in finding the voltage across R1, I'll just say, well, it's I times R1. Whatever that works out to. If I want to get something like voltage B, that's B to ground. Remember, single subscript means the second assumed subscript over here is ground. So that would be from here to here. We would take the current, pass it through R2 and R3, and we would sum up those two potentials. That would give us VB. So as a formula, we could just say, well, it's I times R2 plus R3. It's not particularly difficult, but there actually is a shortcut. And this is the voltage divider rule. So this voltage divides up according to the size of the resistors. I maybe didn't think about it this way, but because the current is a constant, the bigger the resistor, the larger the voltage. So the voltage divides up in proportion to the size of the resistors. Okay. So what's the shortcut? Well, looks kind of like this. I'm interested in the voltage across some resistor or parts of resistors, right? You know, like R2 and R3, or R1 and R2, or whatever. So I'm just going to refer to that as RX, some voltage of resistor X, right, where X could be multiple things together. So looking at what I do over here, that voltage is basically equal to the current times said resistance RX, right? Then we have to find out what I is. So I is E over our total. And, you know, we know our total is the sum of all the resistors for however many we have. Then I turn around, last stop, and we say, all right, so V of RX must equal this current times that calculated resistance, and we're done. Well, if you think about it for a sec, just take this and substitute it in. And what we're saying is V of RX is E times our X over our total. I don't actually have to find the current. This is saying, look, this is the proportion of the resistance, right? This is the percentage of RX out of the total, and that same proportion, that same percentage, is what we get out of the voltage. So let's throw some numbers in here just to illustrate, all right? Suppose I put in a 40 volt power supply, and then the resistors are going to be a 4K for R1, a 10K for R2, and then a 6K for R3. Now, before we go any further, I'll just calculate the value of RT. That's going to be a 4K plus a 10K plus a 6K, all right? So that's 20K for that whole thing. And, you know, the original way we would have done this is to say, well, I've got 40 volts divided by 20K. That's 2 milliamps, so I'll take my 2 milliamps and multiply out. I get my individual voltages. Now what I'm saying is, look, if I want to find the voltage across resistor 1, then the amount of this resistance out of the total, that percentage is the same as the percentage of the total voltage source. So I'm just going to take the total voltage and multiply it by that ratio, R1 over RT. In other words, R1 is 4K over the total, which we found to be 20K. All right, so, you know, a 50-40 volts is 8 volts. I don't have to find the current. I could have, right? Like I said, 40 over 20 is 2 mills, 2 mills times 4K, is 8 volts. But this way, I just go direct. You just look at the percentages, you look at the ratio, you're done. No current needed. You don't have to calculate the current. Now, suppose I want to find something a little different. Like I want to find VB, right? The voltage from here to here, the sky down here. We do the same thing. What's the total applied voltage to this string for VV? What's the resistance I'm interested in? In other words, look, I want to find the voltage from B to ground, so what's the resistance from B to ground? All right? Go from B to ground. What do you see? A 10 and a 6. So that's 16K. And then divide that by the total resistance, the 20K. So you run through that, and you wind up with 32 volts. That's simple. And this will always work with these series combinations. Right? The bigger the resistor is, the more voltage you get. And it's really just that straightforward. One resistor, two resistors, five resistors, you know, as I said, you could do it for a single resistor, you could do it for two resistors next to each other, you know, five out of seven, whatever the heck it is. And it actually works as you'll see. It works on sub circuits. We can have circuits where maybe the entire circuit isn't a series circuit. Maybe it's a much more complicated kind of circuit. But a part of it is series. Well, that part we can still use this rule. I can still use the voltage divider rule. All right? So it's great. Works for any number of resistors. All you have to know really two things. What's the voltage applied to the total string? What's the resistance of the total string? And then you just make the ratio and off you go. It doesn't have to look like this. All right? You could have something that looks like this. Again, I'm just going to use a voltage source off the side here. You could have something like this. And you're going to say, oh, I want to find the voltage from this point to this point. Right? So let's, again, I just call this a, b, c, d. And just to keep it generic, I'm going to call it R1, R2, R3, R4. Well, you know, we already know that our T is R1 plus R2 plus R3 plus R4. No magic there. Well, if I want the voltage from b to c, at least the magnitude of it, all I have to do is say, excuse me, that's c. Let's do d is more interesting. We'll do vbd. So from here, over to here. All right? So I'd put like a red lead and a black lead here on my meters. Take the total voltage applied to that string, e, multiply it by the resistor of interest or resistors of interest, which would be R2 plus R3. And then divide it by the total resistance that is fed by that voltage source, RT. You know, this thing over here. Grind it through, mock, you're done. Right? It's a piece of cake. Easy as pie. Suddenly, I'm hungry. See you later.