Hey guys. So in this video, I'm going to show you some awesome shortcuts that you can use in some cases when you have resistors in parallel. And this is going to keep you from having to do a lot of work with fractions. Let's check it out. All right, so if you have 2 resistors in parallel, there's a shortcut equation you can use. Now remember, the general equation is that the equivalent resistance in parallel is req=1r+1r1+1r2. This is if you have 2 resistors, this is the general equation. K? And I'm going to solve for requiv so that you never have to do this again. And you can just use a shortcut if you have 2 resistors, which is the most common thing you're going to get. So the first thing if you remember we have to do is get a common denominator. And to do that, you're just going to multiply r2 here and then multiply r1 here. So r1×r2. So if I do in the bottom, I also have to do it in the top r2×r1×r1. Let's extend the little fraction thing. So what happens now is I have r1×r2 at the bottom, so I have a common denominator so I can write r1×r2. And then at the top I have r2+r1, or I'm going to write it r1+r2. So it's in order. Are we done? No. Remember we have to flip the sides. So if I flip here, I get requiv=r1×r2,r1+r2. Now notice I'm drawing the r1 and r2 in the bottom really far apart and the reason I'm doing this is because one of the biggest problems with this equation is that people forget whether the times is on top or the plus is on top. You don't know what goes where, you might forget. The way I remember, which is silly but works is because this is a dot, it's a tiny dot. The r1 and r2 are really close together and this is a fat plus sign, which takes up a lot more space. The bottom variables are farther apart and the skinny top and fat bottom gives you sort of a triangle. K. Super silly but maybe hopefully it works for you. Whatever works. Right? So that's the equation. So whenever you have 2 resistors in parallel, you can just use that equation instead of playing with fractions. K? Now super important is that you cannot do this for 3 or more resistors. So I actually want you to draw write this here. This is wrong, but I want you to write it. Let's say you might wanna think that you can multiply r1,r2, why not just add an r3 here, and then at the bottom here, do a plus r3. Well, this is wrong. This does not work. So I want you to write it, scratch it out and say don't. K? Do not do this. This only works for 2 resistors. It does not work for more than 2. Okay? So let me give you a super quick example here. Let's say you have a 4 and a 6 and you want to combine them into a single resistor, you would just use this equation here and say that the equivalent resistance is 4×6 divided by 4+6. I'm setting up the parenthesis so I can put the numbers inside. 4, and 6, and this is 24 divided by 10, which is 2.4. Right? Much faster than play with fractions. So that's the first shortcut. The most important thing always is that you know the general equation because this is going to work for everything, but this shortcut is pretty handy as well. It's more important shortcut number 2, but shortcut number 2 is super simple. If you have resistors of the same resistance, you can also use a shortcut equation. So let's say I have a, let's make it creepy. 666. Let's say you have something like this. What's the equivalent resistance? Well, if you write the general equation, remember, you cannot write this equation right here, the one we just talked about because that works only for 2. But if you have this, you end up with something like this, 1r6+1r6+1r6. And the denominator is already the same, so you end up with 3r6 or r63, which is true. The fast way to have done this is to just say that the equivalent resistance 8, and 8, the equivalent resistance here is super easy to calculate. It's 2. Cool? So now I'm going to do an example that sort of merges all these ideas. You now know how to easily combine things that are the same and you know how to easily combine when they're the same resistance and you know how to easily combine if there's 2 of them using that first equation. Now you can actually use those two rules to your advantage. So if you get a question like this, this might look hairy, but it's actually really simple. So what we're going to do, notice we have a 9, a 9, and a 9. And even though they're not right next to each other, you could technically rearrange them to be right next to each other. And you can say, you know what? This 9 with this 9 and this 9 because they're the same, I can write the equivalent resistance of the 3 nines is just 93. I'm using this shortcut right here. There are 3 nines, so it's just 9 divided by 3, which is 3. K? You can do the same thing for the twelves. There's 2 twelves. So I can say the equivalent resistance of the twelves combined are going to be 122, just 6. So what I can do is all the reds become a simple, a single 3 and the and the blue becomes a 6. And now if I combine these 2 because I have 2 resistors that are parallel to each other. Right? Let's put the little connectors this way. So there's 2 resistors here, they are parallel to each other. I can use the first shortcut equation, which is you multiply at the top and then you add at the bottom. Remember the pyramid, right? It's multiply, and add. So this is going to be 3×6,3+6. 3×6, of course, is 18. 3+6 is 9. So the answer here is 2Ω. So notice how we're able to combine everything really, really quickly. 9,9,9,3,12 is a 6. Put them together and you get a 2Ω. Alright? That's it for this one. Let's keep going.