If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Kirchhoff's voltage law (conceptual)

Kirchhoff voltage law states the sum of all the changes in voltage, around a closed-loop, must be zero. Created by Mahesh Shenoy.

Want to join the conversation?

No posts yet.

Video transcript

in this video let's see how to use kershaw's voltage law in solving circuits that cannot be reduced by using series or parallel formula now just as a refresher in the previous video we introduced these laws and we saw they're both conservation principles and we also focused on kirchoff's current law so if you need a refresher feel free to go back and check that out but anyways in this video we are going to focus on kvl it has this reputation of being a little confusing especially when it comes to science and so i'm going to try and make this as conceptual as possible and you will see with practice you don't even need to remember sign conventions or whatever that is okay concepts are what that matters all right so kvl kirchhoff's voltage law is basically energy conservation comes from energy conservation energy can neither be created nor destroyed and just like how kcl was used for a node or junction kvl is used for closed loops kvl is used for closed let me just write closed loops so what does it say well let me first tell you what it says and then i'll clarify what it means so it says that if you go around any closed loop like for example in this circuit you can find one closed loop over here you can find another closed loop over here you can also find another the third closed loop over here so the kvl says if you go around any closed loops then the sum of all the changes in the voltage the sum of all changes let me just write that down somewhere below okay the sum of all changes in voltage changes in voltage that has to equal zero this has to be true for any loop and now i know that at first this does not make much sense and so um we'll go through one specific example we will focus on one particular loop and by the end of the video this will make complete sense to you okay so let's start by focusing on one of these loops so let's start by looking at this one so let me help you focus by getting rid of the bottom one now imagine you have a charge of one coulomb in your pocket and you're going to walk across this entire loop so let's imagine you start somewhere so let's say you start at this point over here and the whole idea is as you walk across this we're going to keep track of the changes in the potential energy of that charge that's why i asked you to keep that charge in your pocket okay so right now you you know at this point your charge has some potential energy this is very similar to how we will think about it this is very similar to if you stand somewhere anywhere on our planet you will have some potential energy that it depends on your height this is gravitational potential energy this is electric potential energy so at this point let's say your charge has some potential energy we'll call va and if you're wondering why do we use v for potential energy is v v stands for voltage right it's it's it's different right well remember just to remind you something which you've seen before potential energy per coulomb is what we call voltage so for example if your charge has 10 joules of potential energy we will say the voltage is 10 volts and that's why i ask you to choose one coulomb so whatever is the voltage that itself becomes the potential energy for one coulomb all right so we're over here we have va amount of potential energy now let's walk across and see what happens to that potential energy so as i start walking over here in this wire we're going to assume there has no resistance wires have no resistance so there is no potential difference over here so there's no energy loss energy changes and so as i move ahead over here the potential stays the same it's kind of like saying you're moving on a flat land your potential energy doesn't change there all right now when i come across a resistor that's where i have a potential difference that's where my potential changes the first thing i want to know is whether i'm going up in potential or am i going down in potential now think of resistors as slides if you have a slide a ball will always roll down right so over here i will look at the direction of the current i know that through a resistance through a resistor my current will always go down and since my current is going to the right i now know that this must be high and this must be low i must be going down so i immediately know that this end of the resistor is at a higher voltage so this is let me just rather know here it has a higher voltage this end and this end should be at a lower voltage and so when i go from here to here notice i'm going down in voltage it's as if if we thought in terms of gravity it's as if you are walking down and notice your potential energy has now reduced and so when you come over here you will now have potential energy of va minus something does that make sense because you have reduced by how much has it reduces the question well for that we need to know how much is the difference in the potential energy and for that we can use ohm's law ohm's law says potential difference equals ir and i is i3 r is 2 and so over here the voltage must be have reduced by 2 i3 and so if it's over here va at this point your voltage must be va minus 2i3 let me write that down does that make sense think about it you went down you are va over here you decreased by 2 i3 you got that from ohm's law potential difference is 2 i 3 and now your new potential energy of that charge is va minus 2 i 3 notice we didn't have to remember any sign convention i didn't have to think that you know you go in the direction of the current it's positive or you opposite direction of the current it's positive i don't have to worry about that if you do this conceptually if you think in terms of energy i mean if you go down in potential it's negative if you go up in potential your energy increases so you add it okay let's continue now i'm over here as i walk across this wire no potential changes like walking on the flat land and then i encounter a battery and again i have to ask myself am i going up in potential or down in potential and at first you might think you know you will do the same thing and the current is flowing to the right current always flows down so high to low right well this is where you need to be careful a battery is an active device and what that means is a battery can use energy to pump charges so think of battery as an elevator okay just like an elevator can go both up and down the direction of the motion doesn't tell you which direction up is or which direction down is because in an elevator it can go both up and down in a similar in a similar way through a battery current can go either ways it can go up the potential or down the potential curve because a battery is like a pump so current i current can flow in any direction the current will not tell you which direction is up or down and i think this is the most important thing for do remember over here if you get this right then you will get the whole kisha's voltage law right so when it comes to battery how do i know whether i'm going from high to low or low to high so for that i just look at the terminals of the battery this is the negative terminal of the battery and negative means low so this end this end is at a lower voltage this end is at a higher voltage and so when i go from here to here notice i'm going up in potential so again if it was like a battery uh sorry again if it was like gravity then it's as if now i am going up in potential so whatever voltage i had over here it adds up it increases and increases by how much it increases by 5 volts the battery voltage is given to me oh so can you tell me when i come over here what's going to be my new voltage all right hopefully you have told so it was va minus 2 y 3 2 over here and now when i come over here it's going to add you add 5 volts so it's going to be va minus 2 i 3 plus 5 okay this is basically how you use the loop rule now of course in reality when you're solving problems we write this we don't write this over and over again over here because it gets messy we usually write it at the side but it's the same thing i wanted to you know explain to you conceptually what's going on and that's the main reason why i'm writing it this way so now would be a great time for you to pause the video and see if you can continue this and you keep walking over here and over here and and and figure out what will be the voltage at this point and at this point pause the video and see if you can try all right hopefully you've tried so as we walk through this battery notice we're going from high to low that means i'm going down the potential so over here the way i try to show it is just like you know how i came around over here imagine i came around like this um diagram is a little messy but you know hopefully it gives you the picture so i'm now going down this battery and so when i go from here to here voltage decreases by four volt and so when i come over here i would have previous whatever i had minus four hopefully you're able to get that and then finally when i go from here to here i'm now going through a resistor a passive device and i see that the current is flowing in this direction so i know the current always flows down in a resistor like a slide and so this must be the high point and this must be the low point current always flows from high to low and so when i'm going to the left notice i'm going this way i'm going this way i'm going from low to high i'm going up the potential so it's as if when i'm over here i'm now going up the potential i'm going up over here and so when i come over here i will have to add some number to it and how much do i have to add well that can be given by ohm's law i have to add 3 i2 so when i come over here it will be this number plus 3 i2 all right and now here comes the moment of truth we have reached our initial point the where we started remember all these have the same potentials which means this has to equal this we have come back to the original point it's like saying if this whole circuit loops back on itself we have now come to our original height whatever height we started with we have come to the original height and so similarly we have now come back to the original potential energy for the zero potential and so they have to be equal to each other and so if we equate them we get our equation so what will our equation be our equation will be this equals this same thing i'm writing over here this should equal va and notice now what i can do i can cancel this va and i get my first equation so i get minus 2i3 plus 3i2 plus 5 minus 1 is plus 1. so let me write plus 1. and that equals zero i get a zero that equals zero and this is how we build equations using kirchhoff's voltage law and you might say what do i do with the equations well now i can do the same thing for a second loop and i'll get another equation and with two equations and two unknowns i can now calculate what i2 and i3 are and i'm done and that's how you solve circuits if there are more loops then you'll get bigger equations with three or four unknowns and you'll have to get more equations but after this point it's basically algebra it can be solved so at this point you might ask okay where does energy conservation come over here what what just happened so look back to gravity see since we landed at the same height we can now say in this entire loop whatever number of steps i took i went down in total i must have climbed the same number of steps up in total if i went 10 meters down i must have climbed back 10 meters otherwise i wouldn't have come back to the same height and so it follows immediately that whatever was your you know how much every potential energy you lost same potential energy you must have gained otherwise you couldn't have come back so in total what was the net change in potential energy zero whatever you lost you gained same thing applies over here when i went over this entire loop whatever potential energy i gained should equal the potential energy i lost then and only then i can come back to the initial potential energy and so this is that total potential energy that you lost and gain together which we are equating to zero and that's basically what kirchhoff's voltage law is saying whatever potential energy you gained you must equal it to the potential energy you lost in a closed loop energy conservation