Voltage divider

- [Voiceover] Now I'm gonna show you what a circuit, that's called a voltage divider. This is the name we give to a simple circuit of two series resistors. So, I'm just gonna draw two series resistors here. And it's a nickname, in the sense of, it's just a pattern that we see when we look at circuits. And, I'll show you what the pattern is. The pattern is, we have two resistors in series. It's no more than that. And we assume that there's a voltage over here. We hook up a voltage over here like this. So, that's called an input voltage. We'll call it 'VI', for 'V in'. And then, the midpoint of the two resistors, and typically the bottom, that's called the 'out'. So, we basically just have a pattern here with the series resistor, driven by some voltage from the ends of the two resistors. And we're curious about the voltage across one of them. So now we're gonna develop an expression for this. Let's also label our resistors. This will be 'R1'. And this will be 'R2'. That's how we tell our resistors apart. And we're gonna develop an expression for this. So, let's first put a current through here. We'll call that current 'i'. We'll make an assumption that this current here, is zero. There's no current going out of our little circuit here. And that means, of course, that this current here is also 'i'. So, it's continuous all the way down. And now we want to develop an expression that tells us what 'V out' is, in terms of these two resistors and the input voltage. So let's go over here and do that. First thing we're gonna write is, we know that, using Ohm's law, we can write an expression for these series resistors on this side here. Ohm's law, we'll put over here. 'V' equals 'iR'. In a specific case here, 'V in' equals 'i' times what? Times the series combination of 'R1' and 'R2'. And the series combination is the sum: 'R1' plus 'R2'. I'm gonna solve this for 'i'. 'i' equals 'V in' divided by 'R1' plus 'R2'. Alright, next step is gonna be, let's solve for-- let's write an expression that's related to 'V out'. And 'V out' only depends on 'R2' and this current here. So we can write 'V out' equals 'i' times 'R2'. And I'll solve this equation for 'i' the same way. Equals 'V zero' over 'R2' And now we have two expressions for 'i' in our circuit, because we made this assumption of zero current going out, those two 'i's' are the same. So, let's set those equal to each other and see what we get. 'i' is 'V zero' over 'R2', equals 'V1' over 'R1' plus 'R2'. So now I'm gonna take 'R2' and move it over to the other side of the equation. And we get 'V out' equals 'V1'. Sorry, 'V in' times 'R2' over 'R1' plus 'R2'. And this is called, this is called the voltage divider expression. Right here. It gives us an expression for 'V out', in terms of 'V in', and the ratio of resistors. Resistors are always positive numbers. And so this fraction is always less than one. Which means that 'V out' is always somewhat less than 'V in'. And it's adjustable, by adjusting the resistor values. It's a really handy circuit to have. Let's do some examples. We'll put that up in the corner so we can see it. Then real quick, I'm gonna build a voltage divider that we can practice on. Let's make this '2k' ohms, two thousand ohms. We'll make this 6000 ohms, or '6k' ohms. And we'll hook it up to an input source that looks like, let's say it's 6 volts. Like that. And we'll take an output off of this. Right here, is where the output of our voltage divider is. And we'll say that that is 'V out'. So let's solve this using the voltage divider expression. 'V out' equals 'V in', which is 6 volts. Times the ratio of resistors. 'R2' is '6k' ohms, divided by '2k' ohms, plus '6k' ohms. And notice this always happens, the 'k's' all cancel out. That's nice. And that equals six times, six over, two plus six is eight. And if I do my calculations right, 'V out' is 4.5 volts. So that's what a voltage divider is. And if you remember at the beginning, if you remember at the beginning, we made an assumption that this current going out here, was appr-- about zero. If that current is really small, you can use this voltage divider expression. Which as, we see up here, is the ratio of the bottom resistor to both resistors. That's how I remember it. It's the bottom resistor, over the two resistors added together. If you think the current is not very small, what you do is you go back and you do this analysis. You do the same analysis again but you account for the current that's in here. So that's the story on voltage dividers