27. Resistors & DC Circuits

Kirchhoff's Loop Rule

# Intro to Kirchhoff's Loop Rule

Patrick Ford

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Hey, guys. So now we're going to start talking about Kirk AUVs loop rule, which is gonna be massively important when you start solving more complicated circuits. Now, we're gonna build this up a little bit of time over a few videos, and I'm gonna take a little bit slow, because I want you to have a strong foundation so that when you get to problem solving, it can be agrees. This can be a little Harry, so we're gonna build it up a little bit of the time. Let's check it out. All right, So, so far we've dealt Onley with resist what circuits that had a single source, like a single battery. Okay, but now we're going to start to get into circuits with multiple batteries, so we're gonna need new tools. And what we mean by new tools is new rules and new equations. Okay, so the new rule we're gonna use is Kirchoff loop rule, and it states that the sum of all voltages in a loop is simply zero. Okay, it's conceptually very simple, but it's pretty tricky to write equations. So once One way to summarize this entire thing here is just to say that the sum of all voltages in a loop is zero. This ruins also called Kirk AUVs or Kirk Shop's voltage law. Okay, voltage law. So loop rule because you're gonna be going in a loop, adding voltages or voltage law because you're adding voltages. Whatever you wanna call it, I want to point out that this rule actually works for any circuit. So we could have used this to solve some circuits earlier, but it's gonna be especially useful when you have multiple sources. It's too hard for the easy stuff, but it's necessary for the hard stuff. Got it. So let's see. So what we're gonna do is for each loop in a circuit, we're going to write one loop equation. So, for example, if you look here, these wires and all these elements form one loop, so we're gonna get one loop equation. So we're gonna focus on now is how to write this loop equation. Okay. What the equations will do is that we either add or subtract voltages off the batteries and the resisters. Okay, deed. We have a voltage of the battery here. Now the voltage of the resistor is simply I times are high times. Our eyes, the current and our is the resistance. And this comes from OEMs Law V equals IR. Okay, so that's the voltage of the resistor is gonna be. I are. So, for example, I have a current I hear. So it's going everywhere here. Okay? And what we're gonna do is we're gonna right the sum of all voltages, which, by the way, is going to equal zero. I'm going to write all the voltages here. I'm gonna list all the voltages. Okay, so I'm gonna pick a point here. Let's say we're gonna start here, and we're gonna make a loop all the way around. Um, this circuit here and I can go in any direction I can I can go this way or I can go the other way. I'm gonna go this way because it's the way that the currents going. So we're just gonna go with the currents. And so the first element that you run through here is our one. So what you're gonna do is gonna write. I are one. And then when you get to be too, you're going to just write plus V two and then you're gonna keep going here? Imagine you're moving along. You're going across this are too. So you're gonna write. Plus the current, which is I everywhere I are, too. And then you're gonna get over here, and you're gonna write plus V one. Now notice here that I said that the the equation is going to add or subtract voltages. And here I just added all of them, which is actually wrong. These voltages, they're going to be either adding or subtracting. And I don't know yet, we don't know yet which one. Okay, and that's what we're gonna talk about next. But I just want to give you a basic idea first, before we start that you're going to be adding these things and then setting them equal to zero. Now, are they going to be, um, adding or subtracting is what we're gonna talk about now, Okay, they're going to be added or subtracted, depending on two things on the direction of the current and on the direction of the loop. Okay, So direction of the current in this case was, um, was clockwise in the direction of the loop was also clockwise cool. Just to show you what I mean, by direction of current and direction of loop. So the first thing we're gonna do and we have to do this before we start writing the equation is we're going to use the direction of currents to put positive and negative signs on the ends of each resistor. Okay, so let me show you what I mean. Um, so here for a resistor, the positive sign, the positive end is where the current where the currents enters the resistor. So look at this diagram down here, the currents going this way, it enters the resistor here. So I'm gonna put a little positive on this side of the resistor, and therefore the negative goes on the other side. The current keeps going keeps going, and the current enters this resistor right here. So we put a positive here, make this negative, bigger and a negative here. Okay, so that's that first step. Got it for batteries. The positive end is always going to be, um, the positive terminal. So it actually does not depend on the direction of the current. So the positive terminal is a longer one here, so I'm just gonna put a positive on this side, so the other sides are negative. And I'm gonna put a positive on this side and this other sides of negative. Okay, so the first thing we do is we put these signs everywhere. Now what we're going to do is we're going to choose the direction of the loop. Remember, I mentioned when we started going around the circuit up there that I could have gone clockwise or counterclockwise. We're gonna choose the direction, and I'm gonna choose to loop this way. I'm gonna write loop here. And all that means is the sequence in which you're going to add things, right? So we're gonna start here and we're going to go this way. So the first element I'm going to cross is our one. Then I'm gonna cross V two and so on so forth. And it says here when crossing elements in this direction this is the direction of the loop. You're going thio, Add the voltage if you crossed that elements going from negative to positive. Okay, Once you get this, it's gonna be super simple, But I wanna move slowly here, so let's just see here. Um, if you're if you're going from negative to positive So if you follow the current here, you're going from positive to negative. That's the opposite here. Right? So if you add when you're going from negative to positive, this means you will subtract, subtract if you're going from positive to negative. Okay, so this are one here. The voltage of that are one will be subtracted. So I'm gonna write the some of our voltages is negative. I are one. Okay, now, let's go to the next element. I'm gonna keep going here, and I'm going from positive to negative again. So when I cross this, this battery, I'm going from positive to negative. So I'm going to subtract that voltage there. Okay, the to now, let's keep going. Now, I'm gonna go again from positive to negative. So because I'm going into the negative, I'm going to subtract the voltage of our two. And remember, the voltage of every resistor is always I are. So this is gonna be I are too. And finally I get to this last element here, and I'm going to cross it. And when I cross it right, imagine you're sort of charges going through. I'm going from negative to positive. Finally going to a positive. So this voltage will be a positive voltage when I listed here V one and this entire thing has to be set to zero. Okay, if you wanna make this a little neater, I could move some things around, notice that everyone's negative except view one so I can move everything to the other side, and it's gonna look like this View one equals B two. Plus, I want our I'm sorry, man. I Yeah, I r one plus, I are too. So that's the loop equation for this loop. Okay, So what I want to do now is I want to write a loop equation for the same circuit above which I drove down here. But now we want to go in the opposite direction of the loop. Let's go in the opposite direction of the loop. So I'm going to put my little starting point here, But now we're going to go this way. And what this means is that your first going to encounter this guy and jump through it? Okay, Now, remember, the first thing you do is you put these signs everywhere. Thes pluses and minuses. The battery is the easiest one to do because the big one is always Plus, this is always minus always plus always minus the resistor. The plus goes where the plus goes where the current enters the resistor. This is one of the most important things to remember. Okay, where the current enters the resistor So the current hasn't changed direction. So it enters here so positive to negative and the current keeps going to hear and then it enters your positive to negative. Now we're ready to start going around the loop Some of our voltages in this loop we're gonna start here. So the first element you jump across is the view one, and it's going from positive to negative. So it's gonna be negative. View one and then you keep going. You jumped are two from negative to positive. So it's gonna be positive. Voltage of the R two voltage of a resistor is I R. So I r. Two and then we're gonna keep going here, and we're gonna jump from negative to positive. So it's gonna be positive voltage of that battery, which is V two. And lastly, we're gonna get here and jump from negative to positive and because I'm going into a positive. It's going to be positive. The voltage of of our one, which is I r one. Don't forget at the end to set this entire thing to zero, okay? And you end up with this. Now, if I want to clean this up a little bit, I can move. The only guy that's negative here is V one, so I could move you one to the other side, and I get that V one equals V tube. Actually, I'm gonna right. I'm gonna right if you want on the left. Okay, I'm gonna write view one of the left view one equals. Imagine that all these guys go to the other side, and then you get rid of all the negatives. So you get something like this after a little bit of moving around. And the reason I wanted to put it here is because I wanted to show you this is the final equation, that this equation is exactly identical to this equation. And the point here that you absolutely have to remember is the direction of the loop does not matter. Okay? The direction of the loop does not matter in that it's going to give you the same equation whether you go clockwise or counterclockwise, So just pick one. Okay, Cool. So this is a quick introduction of how you write these loop equations. We're gonna do a little bit more to build up the concept so that you are a beast at this. Let's keep going.

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