Hey, guys. So now that we've seen how to solve these complex circuits using Kirchhoff's rules, I want to show you a simple method you can use to 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'd be great to be able to quickly double check. So let's talk about them in this video. Alright. So once you know everything, you know all the voltages, all the currents, and all the resistances, 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 talk about this many times. If you have something like this and the voltage of the source is 9 volts, then the voltage of this resistor is 9 volts as well. And that's because they're sort of opposite to each other on the two branches, right? You can think of these as, this is one branch and this is another branch. So the voltages have to be the same on opposite sides. 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 9-volt battery this way and then a 9-volt battery this way, it's the same voltage, but this one's positive on the left and this one's positive on the right. 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 going to check if all the numbers match up. Now just to be clear, you're not going to 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. Alright. So we're going to check that all the voltages on all the branches add up. And a branch, remember, is all of this. But really, you just have to worry about the top part because there's only 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 does it have the same voltage as this branch? Cool? So let's look at all the voltages. This guy is 18. What about this guy here? This is a resistor. The voltage of a resistor, remember, comes from Ohm's law, v equals I r. So I can just multiply the I with the r. Same thing here. I can multiply the I against, with the r. So I times r, they're going to multiply. This is going to give you the voltage r times I. Okay. So let's multiply these numbers. This is 40. This here is 36 volts and this here is 24 volts. Okay? So now what we're going to do is we're going to put the polarities and I'm going to write it over here. So this 18 has a positive and a negative. Right? Remember the positive and negative on the resistor depends on the direction of the currents and if the current's coming this way, this is a positive and a negative. So if you go here to the side, I'm going to 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 volts this way. What do you think is that net voltage or the equivalent voltage of those 2? 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 equivalent voltage of 22 with the positive pointing to the right. 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 volts positive-negative, and this is 36. The current look at these 2 currents here. Look at these 2 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 a positive 36 volts negative. The 58 this way is going to overpower the 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 24 here and 2 here. The 24 wins, so it's 24 minus 2, they're also going opposite directions. It's 24 minus 2 so you end up with 22 here and here. Okay? I drew it this way but yeah, but I could also have drawn 22 this way, 22 this way, 22 this way. Maybe that's a little bit easier just to just to sort of for it to make sense. All these things have a polarity of 22 to the right, okay? Or the positive side is on the right side over here of the whole branch. That's it. That's all you got to do. So let's look at this one, and it might be a good idea for you to pause the video and do exactly what I did before and double check it. This might seem a little long because the first time I'm explaining, but once you get the hang of it, you can do it really quickly. Cool. So I'm going to keep rolling here, and I'm going to go as fast as I can to show you that this can be actually pretty fast. So if you do the calculator 6 times this to get the voltage, it's 4 volts. And if you multiply these two numbers to get the voltage, this is going to be 14 volts. Okay. This current is leaving. This current is leaving. So this current must be entering, which means this is positive, negative, positive, negative, positive, negative.
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Kirchhoff's Loop Rule
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