 In this video, let's see how to use Kirchhoff'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 Kirchhoff'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 we'll go through one specific example, we'll 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 gonna 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 gonna 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, 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 stands for voltage, right? 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 asked you to choose one coulomb. So whatever is the voltage, that itself becomes the potential energy for one coulomb. All right, so we are 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 gonna 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 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 write the number 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 reduced is 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 2I3. And so if it's over here VA, at this point, your voltage must be VA minus 2I3. I'm gonna write that down. Does that make sense? Think about it. You went down, you are VA over here, you decreased by 2I3, you got that from Ohm's law. Potential difference is 2I3. And now your new potential energy of that charge is VA minus 2I3. 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, you go 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, we'll do the same thing. 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 way, through a battery, current can go either ways. It can go up the potential or down the potential because a battery is like a pump. So 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 Kishav'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, 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 five volts. The battery voltage is given to me. Ooh, so can you tell me when I come over here, what's going to be my new voltage? All right, hopefully you've told. So it was VA minus 2I3 over here. And now when I come over here, it's going to add, you add five volts. So it's going to be VA minus 2I3 plus five. Okay, this is basically how you use the loop rule. Now, of course, in reality, when we are 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 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 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 have 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. The diagram is a little messy, but 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 three I two. So when I come over here, it'll be this number plus three I two. All right. And now here comes the moment of truth. We have reached our initial point 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, original 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 two I three, plus three I two, plus five minus one is plus one. So let me write plus one. And that equals zero. I get a zero. That equals zero. And this is how we build equations using Ke$hev'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 I two and I three are. And I'm done. And that's how you solve circuits. If there were more loops, then you'll get bigger equations with three or four unknowns. And you will 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 just happened? So look back to gravity. Since we landed at the same height, we can now say in this entire loop, whatever number of steps 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, how much ever 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 gained together, which we're 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.