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Direction of Current in Loop Equations

Patrick Ford
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Hey, guys. So in this video, we're going to keep talking about writing loop equations, except that I'm gonna add one complexity, which is the fact that you won't always know the direction of the current. Let's check it out. All right, so in the more complex circuits that were about to start seeing you are typically not going to know the direction of the currents. So what you're gonna have to do is you're going to have to assume the direction of the current. Okay, this is the word that you typically hear. But what this effectively means that you're guessing them. In other words, if you don't know if you have no way of knowing, you just pick one on. Did you solve the problem that way? Okay. And don't worry about picking the wrong one. It's going to be okay. I'll talk about that at the end. Okay, So before I talked about having their being these two steps, um, to write in these equations, but there's actually a new step here that you have to take before you could even get the steps one and two. And it is that you have to assume assume the direction of all currents unless it's given to you. Right. So if you don't know, you assume if you're given a direction, then you use that direction. Okay, so then you're going toe label positive and negative signs, and then you're going to cross elements in the chosen direction of the loop. First, let's talk about number one real quick, and we've done this before, but just as a refresher for every one of these elements, you wanna put pluses and minuses to the left and right or in the opposite ends of the elements. So plus or minus here plus remind us here, and we're gonna do this based on this rule here. So the battery is going to be positive on its longer terminal. So you put a little positive on the longer terminal, remember? I'm gonna positive here, which means you put a negative on the other side. So positive here. Negative on the other side. Okay. Same thing here, by the way. Positive. Here. Negative on this side. Positive. Here. Negative on this side. Okay, um, resistor is going to be positive where the current enters the resistor where the current enters the resistor. So this depends on the direction of the current. If you don't know the direction of the current, then you're going to use the assumed direction of the current. Okay, Alright, cool. So in this question here, before we get into number two, we're being asked to, um right loop equations. So we're gonna be following these steps over here to do that. Okay. And here it's asking to write a loop equation if the current is clockwise. So here current is clockwise means it goes this way. So the current is answering this resistor here, so I'm gonna put a positive, and then it's and then this one must be a negative. The current keeps going and it enters this resistor here. So this is the positive end, and this is the negative end. And then here we want the current to be counter clockwise, which means it is going this way and it's entering this resistor here. So that's positive. The other one's negative. And then it's entering this resistor here. So this is positive, and this is negative. Okay, So Step one is to label Thebe positive and negative signs. We got that done. And Step two is to cross elements in the chosen direction of loop. In other words, you're gonna go around the loop and then you're gonna sort of jump over each one of these elements. And as you do that, you're going to add the voltage if you're crossing from negative to positive and you're going to subtract the voltage if you're crossing from positive to negative. Okay, remember that. So now let's just do that. Let's pick. Let's pick a direction of the loop here. We're gonna loop this way for both of them, and we're gonna start right here. Okay? Right here and right here. That's my starting point. So if I'm going in this direction, remember, the direction of the loop is just the sequence in which you're going to sort of walk around this circuit. It's not the direction of the current necessarily. Okay, so it's just the sequence that you're going to add these things. So I'm gonna write that the sum of all voltages in this loop is a bunch of stuff equals zero. Okay. And what we have to do is write all these different things. They're gonna be four numbers here or four elements here, adding or subtracting. So the first one we get to use this to own resistor, and I'm going from positive to negative. I'm going from positive to negative. So I'm going to subtract that voltage. Remember, the voltage of a resistor comes from owns law V equals IR. So here I'm gonna right, we're going into the negative, So I'm gonna write Negative, I r. And the resistance here is to homes. So I could do this. I cannot plug anything for I because we're looking for the currents. Okay, we're looking for the currents through the whole thing. All right, Now we're gonna keep walking here. I'm gonna jump from a positive to a negative. Therefore, that voltage is also going to be subtracted. Negative four v. I'm gonna keep going, and we're gonna jump from a positive to a negative. This voltage is also going to be subtracted. Negative. Um, this is a resistor. So it's going to be I r. I is I and R is one. And then finally, I'm gonna get over here and jump over this guy from it's gonna go from negative to positive because I landed a positive. This is a positive 10 volts. Okay, Everything is equal to zero, and this is gonna allow us to solve. So have four votes in 10 volts or 10 volts, minus four votes. If I combine these two things is going to be six volts and then I have negative to actually know what Let's move these guys to the other side. So if you move negative one, I it's gonna be positive. One I and then this is too. I it's gonna become positive, too. I So this is obviously just three I, and at this point, I'm gonna be able to solve. For I I is just 6/3, which is two amps and we're done. That's it for part eight. Now, we're gonna do the same thing here for part B, right? That the sum of all voltages in this loop equals a bunch of stuff equals to zero, and then it's going to be it's gonna allow us to solve for I What I love free to do is positive video right now. Try to emulate the steps that I had in part a See if you can get something for part B. I'm gonna keep rolling here, but hopefully you gave this a shot. It's important that you're following, and then you're able to do this yourself. So we're going to start here and we chose to go in the same direction, so I'm actually going against currents. Now. I'm going to sort of walk around the circuit against the direction of current, which is totally okay, right? So I'm gonna go here. And I mean, the first thing I gotta jump over is this, and I'm jumping from a negative to a positive. So this is gonna be positive. Um, the voltage of that resistor and that the voltage of resistors ir So it's i times to This is a new problem, by the way. So I can't just use this to over this to as current, right? We gotta find the current in this one, and then we're gonna keep walking here and jump from a positive into a negative terminal. So this is gonna be negative four votes and we're gonna keep walking here and jump from a negative to a positive and because I'll end on a positive. This is gonna be positive Voltage of the resistor voltages of resistors R or is ir. So it's gonna I Times are, which is one. And finally we get over here and we're gonna jump from a negative to a positive and because I'm landing on a positive. This is positive. 10. Okay, this may even be already a little repetitive for some of you. Hopefully, which means you are getting it. That would be awesome. So here I can add up these eyes. I have one eye in two eyes. Um, it's a lot of ice, so this is gonna be three I and then 10 minus four is six plus plus six volts equals zero. So if I'm solving for I'm gonna move this six votes the other way. Three I equals six votes. Therefore, I am sorry. Negative six votes. Whoops. Almost messed up. And that means that I is negative. Two amps. Okay, negative. Two amps. Now notice that this here was a two amps positive, and this year was a two amps negative. Do you think that's a coincidence? It isn't. It's not a coincidence at all. Um, in fact, you should have expected that because these are exactly the same circuits that you would get the same current. This negative here. What's up with that guy. All that negative duck means he said you've chosen or the direction that was assumed for you. He didn't choose. He was chosen for you was wrong. So if you had chosen this direction, it just means that you chose the wrong direction. But the cool part is, the answer is still right. You just now know that it was actually the current was actually physically moving in the opposite direction. Okay, so the answer to what is the magnitude of the current? Well, the current is too amps. That's the magnitude of the current. But the direction of the currents we now know is opposite to what we were working with where we're going with the current being counterclockwise, and we know the direction of the current is actually clockwise. Okay, here, I got a positive, Which means the direction I was working with was actually correct direction. Cool. So you pick. You were either given a direction or you assume slash guest one. And if you and if you you know, if you pick the wrong one, it's okay. You're just gonna end up with a negative current at the end, the number will still be right, and you would just know. Oh, whoops. I guess. The wrong one. That's cool. Flip it. You don't have to resolve the problem again. You would just know that the direction of the current is opposite to the assumes one. Okay, I said that same thing a few times. Hopefully that sticks. Let's get going.