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# Kirchhoff's voltage law

## Video transcript

now we're ready to start hooking up our components into circuits and one of the two things that are going to be very useful to us are Kirchhoff's laws and in this video we're going to talk about Kirchhoff's voltage law if we look at this circuit here this is a voltage source let's just say this is this is ten volts and we'll put a resistor connected to it and let's say the resistor is 200 ohms just for something to talk about one of the things I can do here is I can I can label this with voltages on the different nodes here's one node down here I'm going to arbitrarily call this zero volts and then if I go through this voltage source this node this node up here that is going to be at 10 volts 10 volts so here's a little bit of jargon we call this voltage here the voltage goes up as we go through the voltage source and that's called a voltage rise and over on this side if we are standing at this point in the circuit right here and we went from this node down to this node like that the voltage would go from 10 volts down to zero volts in this circuit and that's called a voltage drop that's just a little bit of slang or jargon that we use to talk about changes in voltage now I can make an observation about this if I if I look at this voltage rise here it's 10 volts and if I look at that voltage drop the drop is 10 volts I can say the drop is 10 volts or I can say the rise on this side is minus 10 volts a rise of minus 10 these two these two expressions mean exactly the same thing it meant that the voltage went from 10 volts to zero volts sort of going through this 200 ohm resistor so I write a little expression for this which is V rise minus v2 op equals what equals zero I went I went up 10 volts back down 10 volts I end up back at 0 volts that's this right here and this is a form of kirchoff's voltage law it says the voltage Rises minus the voltage drops is equal to zero so if we just plug our actual numbers in here what we just what we get is 10 minus 10 equals zero I'm going to draw this circuit again let's draw another version of this circuit and this time we'll have two resistors instead of one and we'll make it whoops we'll make it to 100 ohm resistors and let's go through and label these this is again 10 volts so this note is at zero volts this node is at 10 volts what's this note this note here is these are equal resistors so this is going to be at 5 volts that's this node voltage here with respect to here so that is 5 volts this is 5 volts and this is 10 volts so let's just do our tower visit again let's start here and count the rises and drops okay we go up 10 volts then we have a voltage drop of 5 and we have another voltage drop of 5 and then we get back to 0 we can write the sum of the Rises and the Falls just like we did before we can say 10 volts minus 5 minus 5 equals zero all right so I can generalize this we can say this in general we can do the summation that's the summation symbol of the V rise minus the sum of the V fall equals 0 this is a form of Kirchhoff's voltage law the sum of the voltage Rises minus the sum of the voltage Falls is always equal to 0 there's a more compact way to write this that I like better and that is we start at this corner we start at any corner of the of the circuit let's say let's say we start here we're going to go up 10 volts down 5 volts and down 5 volts so what we're adding is the voltage Rises we're adding all the voltage Rises rise plus 10 that's a rise of minus 5 and a rise of minus 5 so I can write this with just one summation symbol the voltages around the loop where I takes us all the way around the loop equals zero so this means I start hit any place on the circuit go around in some direction this way or this way up down down and I end up back at the same voltage I started at so let's put a box around that - this is kvl kirchoff's voltage law now I started over here in this corner but I could start anywhere if I started at the top and went around around clockwise if I started here say I would go minus 5 minus 5 plus 10 and I get the same answer I'd still get back to zero if I start here and I go around the other way same thing happens plus 5 rise plus 5 rise and this is a 10 volt drop so it works whichever way you go around the loop and it works for whatever whatever node you start at that's the essence of Kirchhoff's voltage law we're going to pair this with the current law Kirchhoff's current law and with those two that's our tools for doing circuit analysis