Solving Resistor Circuits

by Patrick Ford
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Hey, guys. So in this video, we're gonna talk about how to solve more complicated circuit problems. Let's check it out. All right. So in some circuit problems, you'll be asked to find not just the equivalent resistance, but also the current I and the Voltage V of different resistors. All right, so let's see how we do that. But first, let me remind you that resistors can be connected in serious or in parallel. And if they're in serious, this is the equation you used to find the equivalent resistance. This is the equation for equipment resistance in parallel. Remember that in parallel there are also two shortcut equations you can use to shortcuts. So this is all news. What's new? Here is this stuff here, right? And when you have resistors in Siris, they will share current with each other. They will share current with each other. So, for example, if I have a one ohm resistor two and three, two homes, three homes. And if I know that this current here is two amps, then I know if I'm given the current here's two amps, then I know that this year has to be two amps and then I know that this year also has to be two amps because they're in Siris, the currents flowing this way. It has nowhere to go. So he has to just flow with a constant two imps. So they share currents with each other. Cool. Now you need to remember that. But you also have to remember that they share current with the equivalent resistor as well. So they share current with the equivalent resistor. What does that mean? Well, if I combine these, I just add them. So I have 12 and three. This is six own resistor. But this to here is not only the same for these guys, but it's also the same here. So I'm going to know that this has to be a to ome to AMP current going through this resistor. So not only is the current the same with each other when you're combining and serious, but also with the combines merged resistor. Okay, very important. One way to think about this is that these guys combine to form the equivalent resistor and the equivalent resistor will inherit inherit the current's because it's coming from a serious combination in parallel. It's not current. It's the voltage that will be the same. Okay, so the voltage will be the same with each other and also with the equipment resistor. So let's say this is a nine home resistor. Nine ohm resistor nine ohm resistor. You may remember from the shortcut that if I have 39 homes, the equipment resistance will just be nine homes divided by three. Because there three of them. So the equivalent resistance is three. That's new. That's old news. But let's say I know that this is, um let's say I know that this is five votes. Well, if this guy's five volts, it must follow that this guy right here is also five votes. And this guy here is also five votes because if they are in parallel, which they are, they have to share the same voltage with each other, and not only with with each other, but also with the merged equivalent resistor. So the voltage here would also be five volts. You can think that when you combine them in parallel, the equipment resistor will inherits in Herod's the voltage. Okay, these points are super important for you to remember. Please do not forget now that's important for you to solve the problems. Now, here's the three steps that you're gonna use in solving all of these problems. We're gonna be very methodical about this. Very systematic. Cool. The first one is you're gonna get You're gonna get some sort of weird resistor network here like this, and you're going to collapse combined, merge down toe one equivalent resistor. And we're gonna do this using the techniques we already talked about. So this is old news. Okay, This is old. You know how to do this? Then you're gonna find voltage and current on the equivalent resistor. Once you get down to one resistor, you're gonna be able to find the voltage in the current on it. And by the way, you're gonna do this. Using owns Law V equals IR, which combines current and voltage with resistance. Okay, this is old because we've seen vehicles ir, and it's also really easy. It's a very quick step. Now The hard part is step three where we're going to work backwards, noting voltage and current on the transistor. Now, don't worry about what that means yet I'm gonna show you and the best way to show you is just by doing an example. OK, so let's walk through this simple example here, and we're gonna use this thes steps, um, to find the current and voltage across each one of these resistors. Okay, so let's draw small here because we're gonna need a lot of space. So the first thing we're gonna do remember from the rules up there is that we're gonna get everything out to one resistor, and you know how to do this. The first place I'm going to start is by combining these two in parallel. Okay, I'm gonna combine these two in parallel, so I'm gonna draw the circuit here in black and then circuit here in black. I'm gonna leave some space there. This is the six home resistor, and this is the 10 volt battery right here on. This is the combination off the combination of the two with the one. I'm gonna do one of these and I'm gonna right here that this is a parallel merge. Okay, I got these two and I compress them, um, is a parallel Merge into the single resistor here. Let's, um if we want, we can calculate that. Let's do that real quick just to get it out of the way. So I'm gonna say that the equivalent resistor. Let's call this. Let's call this our one, which is a new resistor here. So we're gonna say that are one I'm going to use the shortcut equation because I have two resistors in parallel so I can use a shortcut equation. Right? And I'm gonna have, um it's a 200 once I'm gonna have 21212 times one is 21 plus years, three. So to over three, which is 30.67. So this resistor here is has a resistance off 6.7, owns 6.7 owns. Cool. Now I have two resistors Sound like it down to one. So I still have to merge these other two right here. And hopefully you can clearly see here that they are in Siris. Okay, so I'm gonna get a single Siri's resistor here that's hooked up to the 10 volt battery. Can you see that? 10 vote. Yes, you can. Andi, I have to combine those two there. So this was us combining these two resistors. Now let's combine these two resistors over here and I'm gonna call this Resistance R two and R two is just 6.7. Um, plus six. I'm sorry. I wrote 6.7. I hope you caught that. It's 0.67. Who hopefully didn't freak out. 0.67. Okay, I'm just gonna added to, so it's gonna be 6.67 right? Once you, Adam, you get 6.67 owns. This one is owns is Well, um cool. So this resistance right here is 6.67 I've completed step one, which is getting all the way down to, um, to one resistor this merge here. By the way. It was a Siri's merch. Okay, once you do that, Step two is right. V equals ir to find other things about that resistor that you may not know. Okay, so now we're gonna right the equals ir. And let's see, for this resistor here, we know the resistance. We know the voltage is a 10. Because if this is attend, then this has to be a 10. Writes the voltage battery there. So I confined the I. And by the way, this is almost always what's gonna happen. You're gonna know the V and you will just have found out the equivalent resistance. So you're gonna be able to find the current coming out of the battery. This is the current drawn, um, but the current drawn by the resisters of the battery. Cool. So I equals V over R. The voltage is 10 volts, and the resistance will be 6.67 homes. And if you do this, you get 1.5 amps, so your current is 1.5 amps. What this means is that 1.5 is the amount of currents that comes out of the battery or that is drawn out of the battery by the resistor. So I'm gonna right here that this is a current what, 1.5 amps, by the way, this current keeps going and it's the current that goes through this resistor right here. So I now know the the resistance of I know the resistance of this guy. I know that this guy has a voltage of 10 volts. It has to be the same, right? When you get down to one resistor, that resistor has the same voltage, the battery. And I know that this guy also has a current of 1.5 amps. Let me write it like this. Let me just write 10 votes and 1.5 camps. Quote I'm done with that resistor. So now you're gonna do is you're going to work backwards, Meaning you've compressed. And now you're gonna work backwards and go back to this to this circuit here and try to find as many Aziz much information as you can about every single one of these resistors. And the way we're going to do that is by remembering how we merged that in the first place. So I went I got to this circuit by going by doing a Siri's merge. So when I go back, I have to remember this was a serious merge because this resistor here, this green resistor came from these two resistors. And remember when you merge two resistors into an equivalent resistor and they were in Siris, they shared the same current. So what that means is that this current right here 1.5 is gonna be the current of these two guys here because that same current goes through both of them. Okay, so the current of the six is 1.5 amps, and the currents of the 0.67 is also 15 amps. Okay, Now, remember, you can use owns law, the equals IR. Any time you know, two out of these three, you can find a third one. So if we look at this resistor right here, this first one Okay, I know the resistance is, um six. I know the current is 1.5, so we're able to find its voltage. Okay, so let's just plug in the numbers. So the current is 1.5. The resistance is a six, and if you multiply, this is a nine. It's vote, vote. It's the voltage. So the answer is in the units of volts. Nine volts. So I'm gonna right here that this is nine volts. Okay, now, this is a little messy. You wanna make sure that you are as organized this possible, right? There's a lot of numbers. It's easy to get lost. You wanna make sure that you're as organized as possible, and as you're working your way back, you wanna make sure that you're getting all the information you should know The voltage, the current and the resistor for the resistance for everyone of these elements. Now, what about this red one over here? Okay. Again, we're gonna write V equals IR notice that I know that the resistance is 0.67. So I have that. I know the current is 1.5. So I have that. So I'm able to find again the voltage. Okay, The current is 1.5. The resistance is 0.67. And if you multiply this, you get 11 Vault's. Okay, So I know that this guy is one volts. The voltage across the this resistor here is one volts. Let me highlight all the information for that resistor. So it's all together without that 10 volts. That's the battery. Okay, this is all the information on the second on the resistor on the left. So now we're gonna go one step back. We're gonna go another step back here, and we're gonna go to this original drawing and notice that this six is the same as this six over here. They didn't change, so I could just transfer the information I can say. Okay, This six has a current of 1.5 amps, and he has a voltage of nine volts, Some done here. This is basically a big puzzle where you're trying to find out all the pieces of the puzzle. What about here? I know that guy. These guys, uh, resistance is, but I don't know I envy. Well, remember, what did they come from, Right. So or what do they merge into these two guys merged in parallel into this one. Resistors in parallel share the same voltage. Therefore, these two guys are going to have the same voltage as each other. But they're also going to have the same voltage as this one that they merged into. And that voltage we just found was one volt. Okay, so this is going to be one volt, and then this is going to be one Volz. Okay, again, whenever you have two of these things you can use owns law to find the third. So let's write ones Law two more times here, the equals IR. In this case, I know the resistance for both of them, and I just got the voltage for both of them. So we're gonna be able to solve for the currents because currents gonna be V over R the voltage. Let's do the top one first top. The voltage for the top one is one and the resistance is true. So the current is 10.5 amps. So I now know that this is 0.5 amps of current. I am done with this resistor because I know all three properties and the bottom one is gonna have a current I confined the current as well. So if I write, V equals ir once again, I know the resistance. And I know the voltage of this bottom resistor here. So I is going to be V over R and voltage is one. I'm just looking here, right? Notice how If you have all the numbers in the pictures, it's easier. It's more organized and you can just kind of follow what's going on there. And then the resistance is 11 over on is just one. So 1.0 amps. So this has a current of one amps or one amp. And this is all the information for that resistor. Okay, so we now know the current voltage and the resistance there were given. So now we know everything for all of these resistors. So if you wanna line it up? You can, sort of You could make a table and say resistance, Voltage and current. And the two own resistor here has a voltage of one volt and a current of five. The one ohm resistor here has a current off voltage of one and a current of one. And the six over here with six home resistor has a voltage of nine volts, and a currents of 1.5 amps were essentially done. I just want to show you one last thing. Notice how you have this 1.5 here, and that's the current going this way. 1.5. Notice that the current here is five. So this 1.5 amps splits this way as a 0.5 amps and notice that here it splits down as a one amp. And this is consistent with Kirk offs um, Junction rule or current law that says that the currents at a node the currents and equal the currents out 1.5 women 1.5 has to come out. The reason I'm telling you this is because once you knew this and once you knew one of these guys, you didn't really even have toe calculate this using vehicles. I are. You could have just known. Okay, well, 10.5 went here. I got one left. So there, this current here has to be one. So these are just some of the things that help you move a little bit faster. So this is long inherited the first time. We're gonna do quite a few of these examples in practice problems, so you can nail this. But you absolutely have to know how to do this in highly recommend that you're very organized and systematic so that you don't get lost. Cool. Let's do some more.