27. Resistors & DC Circuits

Kirchhoff's Loop Rule

# How to Check Your Work (Kirchhoff's Rules)

Patrick Ford

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Hey, guys. So now that we've seen how to solve these complex circuits using Kirchoff rules, I want to show you a simple method. You can use the double check your work, and the idea here is that solving these circuits is a long process. There's a lot of steps to it. So there's a lot of room for small mistakes, and it be great to be able to quickly double check. So let's talk about that in this video. All right? So once you know everything, you know, all the voltages, all the currents, and all the resistance is you can double check your work with a simple rule. And you actually already know this rule, which is that all branches must have the same magnitude of voltage. Same magnitude of voltage. Okay, so you might remember we talked about this many times. If you have something like this and this voltage of the source is nine volts, then the voltage of this resistor is nine volts as well. And that's because there's sort of opposite to each other on the two branches. Right? You can think of these as, um, this is one branch and this is another branch. So the voltages have to be the same on opposite sides. Um, now, the direction must always be the same as well. And direction is actually not the right word. The right word here is polarity, but it really just means direction. So what does that mean? So if you have a nine volt battery this way and then a nine volt battery this way, it's the same voltage. But this one is positive on the left, and this one is positive on the rights. So they have different directions. The directions have to match and the total magnitudes have to match. So let's do this real quick. We're gonna hear, check if all the numbers match up now, just to be clear, you're not gonna get a test question that says, here's a complete circuit. Is this right or not? Right. I haven't seen those in tests, but I'm giving you this just to sort of build up the skill that might be useful if you have enough time at the end of a test, right? So or if you're doing your homework. All right. So we're gonna check that all the voltages on all the bridges Add up on a branch, remember? Is all of this But really you just have to worry about the top part because there's Onley. You only have circuit elements up here. There's nothing on the sides. Same thing here. So does that branch have the same voltage here as this branch and doesn't have the same voltage as this branch? So let's look at all the voltage. Is this guy is 18? What about this guy here? This is a resistor. The voltage of a resistor, remember? Comes from owns law the equals ir So I can just multiply the i with er Same thing here I can multiply the i against with er so I times are there gonna multiply? This is gonna give you the voltage are times I Okay, so let's multiply these numbers. This is a 40. Um, this here is a 36 volts volts, and this here is a 24 votes. Okay, so now we're gonna do is we're gonna put the polarities and I'm gonna actually I'm gonna write it over here. So this 18 has a positive and a negative, right? Remember, the positive and negative on the resistor depends on direction. of the current. And if the currents coming this way, this is a positive and the negative. So if you go here to the side, I'm gonna write that you have 18 V positive and negative. And then here you have 40 V positive and negative, and you can think of it as 18 volts this way and 40 votes this way. What do you think? Is that net voltage or the equivalent voltage of those two? If you have, if they're going opposite directions, they're going to subtract the 40. The 40 wins over the 18. So it's 40 minus 18 40 minus 18 which is 22. So this guy is the winner, which means this entire branch has the equipment voltage off a 22 with the positive pointing to the rights. Okay, Now all the other branches have to have the same thing. Let's look here. This is positive and negative. So I got a 58 Volz positive, negative. And this is a 36. The current look at these two currents here. Look at these two currents. The third one, they're both going into here, so the other one has to be this way which means this is a positive and this is a negative. So here I have positive 36 volts. Negative. The 58 this way is going to overpower to 36. And then you do 58 minus 36. That's 22 as well. Awesome. So I have a 22 to the right. Cool. So so far it's matching up. And then here at the end, I have a 24 here and a two here. The 24 wins. So it's 24 minus two. They're also go in opposite directions. It's 24 minus two. So you end up with 22 here and here. Okay, I drew it this way, but But I could also have drawn 22 this way. 22. This way. 22. This way. Maybe that's a little bit easier, Thio. Sort of for it to make sense, all these things have a polarity of 22 to the right. Okay? Or the positive sightings. Eyes on the right side, over here, off the whole branch. That's it. That's all you gotta do. So let's look at this one. And it might You're gonna be afraid to positive video and do exactly what I did before and double check it. This might seem a little longer, because the first time explaining But once you get the hang of it, you can do it really quickly. So I'm gonna keep rolling here, and I'm gonna go as fast as I can to show you that this can be actually pretty fast. So if you do in a calculator six times this to get the voltage, it's four volts. And if you multiply these two numbers to get the voltage, by the way, this is a period, not a comma. Hopefully caught that This is gonna be 14 volts. Okay, the this current is leaving. This current is leaving. So this current must be entering, which means this is positive. Negative, Positive, negative. Positive, negative. Positive, negative, Positive, Negative. By the way, if you solve this yourself, you already would have all these little negatives and positives everywhere. Cool. So what we have here? I have a four to the rights, and then I have a 12 to the right, and to the right means it's going negative to positive. Okay, so this is obviously a 16 to the right here. I have four times Four. That's 16. And it's to the right. Cool. And then here I have 14 to the right, and then I have 32. Um was saying to the right, I don't know. I don't remember, but this is to the left. I might have said to the right if I did. I'm sorry. Um, so obviously the 30 wins 30 minus 14 is 16. So 16 to the left. Okay, that's it. All you gotta do is edible. The whole to just make sure that it works. By the way, if you had a resistor here, you could have just moved it over here so that you're comparing sort of rose or just columns. Right? So it's a little bit easier to visualize, but a resistor here, for example, is part of this entire branch. So you could have just moved it over here to make it easier to sort of see, you're comparing just the rows of voltage goal. That's it for this one. Hopefully make sense. Hopefully helps. Let's get going

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