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# Voltage divider

## Video transcript

now I'm going to show you a circuit that's called a voltage divider this is a name we give to a simple circuit of two series resistors so I'm just going to 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 that's called an input voltage we'll call it V I for V in and then the midpoint of the two resistors and typically the bottom that's called V out so we basically just have a pattern here with a series resistor driven by some voltage from the ends of the two resistors and were curious about the voltage across one of them so now we're going to develop an expression for this let's also let's also label our resistors this will be R 1 and this will be R 2 that's how we tell our resistors apart and we're going to develop an expression for this so let's first put a current through here we'll call that current I will make an assumption that this current here is 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 let's go over here and do that first thing we're going to 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 I R in the specific case here VN equals I times what times the series combination of r1 and r2 and the series combination is the some r1 plus r2 I'm going to solve this for I I equals V n divided by r1 plus r2 all right next step is going to 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-0 over r2 and now we have two expressions for I in our circuit because we made this assumption of 0 current going out those two eyes are the same so let's set those equal to each other and see what we get I is B 0 over r2 equals v1 over r1 plus r2 so now I'm going to take our two and move it over to the other side of the equation and we get V out equals V 1 sorry V V in times r2 over r1 plus r2 and this is called this is called the voltage divider expression right here it gives us a expression for V out in terms of V N and the ratio of resistors resistors are always positive numbers and so this fraction is always a less than 1 which means that V out is always somewhat less than V n 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 kind of real quick I'm going to build a voltage divider that we can practice on let's make this 2 K ohms 2000 ohms will make this 6,000 ohms or 6 K 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 V out so let's solve this using the voltage divider expression V out equals V n which is 6 volts times a ratio of resistors and the reason R 2 is 6 K ohms divided by 2 K ohms plus 6 K ohms and notice this always happens the case I'll cancel out that's nice and that equals 6 times 6 over 2 plus 6 is 8 and if I do my calculations write V out is 4.5 volts so that's what a voltage divider is and as if you remember at the beginning if you remember at the beginning we made an assumption that this current going out here 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 that you do the same analysis again but you account for the current that's in here so that's the story on voltage dividers