 In this video, I want to go over the whole concept of resonance, especially in the series RLC circuit. Now, what resonance is, is when your XL is equal to your XC. So, when your XL equals your XC here. Now, let's have some numbers at this. It's a little easier to understand when we've got some numbers to talk about. So, I'm going to start out with 30 ohms of resistance. So, I've got that guy there. I've got a source voltage of 120 volts, 60 hertz. Now, this 60 hertz is extremely important, which we're going to see later on. Let's assign some, let's sort this thing totally into resonance. So, I'm going to assign some values here and here as well. So, just to make everything easy, I've made everything 30 ohms. So, my capacitive reactance is 30 ohms, and my inductive reactance is 30 ohms, as well as my resistance is 30 ohms. So, at this point, when I'm trying to figure stuff out, when I'm trying to figure the current out, we've got to remember. Let me just get my pen going here. Make sure I've got a good size sink. There we go. And we'll go with black. This guy here, it's reactance, the inductor, it's going up. So, it's heading that way, right? Because our resistance is heading this way if we draw it vectorially. And our capacitive reactance is going down. So, these two guys here, this inductive reactance and this capacitive reactance are working against each other. If they're of equal value, they end up canceling each other out, which means the only thing left in the circuit to oppose current is the resistance of the circuit. So, doing the math in my head, showing how smart I am, I can go 120 volts divided by 30 ohms, and I will get my current of 4 amps right there. So, that's that. That's how we work out of resonance circuit. Resonance is when this guy and this guy equal each other. Now, when we are at resonance, what we can do is we can say a couple things here. If we drew this out as a triangle, I'm going to draw a really bad triangle for you guys, but I do heart the triangle. So, if I drew this triangle out, this guy here, my X net, is this and this. Well, if these two guys cancel each other out, then all I get is, I got this inductive reactance going up, like right there, I got this going down. It becomes nothing, so I end up with nothing but a straight line. We can say at this point that my resistance is equal to my impedance. My resistance is equal to my impedance because I have no net reactance. R is equal to Z, which means that at this point, the only thing opposing current in this circuit is the resistance. So, at this point, we can say that our current is going to be at its maximum in a series circuit. We'll talk about parallel later on. So, these are two big truths when we're dealing with an RLC series resonance circuit. R is equal to Z and current is at its maximum in a series resonance circuit. Now, we're going to change things up a bit. As I said before, this frequency controls everything in this resonance. If you change this frequency, it's going to throw this whole circuit out of resonance. This and this will change. Let's take a look at why. We've got to look back at the formulas as to how we get XC and how we get XL. So, just a quick refresher, to get XL, we need 2 pi FL. To get XC, we need 1 over 2 pi FC. So, we see that with inductive reactance, your inductive reactance is directly proportional to the frequency. Your capacitive reactance is inversely proportional to the frequency. So, if I increase my frequency, this guy goes up, the XL. If I increase my frequency, the XC goes down. You start to see that it throws the whole thing out of resonance. Let's throw some numbers out just to see, just to prove the point. Okay, so what I've done is I've taken it and I've taken it from 160 Hz and I'm taking it up to 120. It does not affect this 30 ohms resistance, but what it's going to do is it's going to change these guys drastically. If I do this, 120, I've doubled my frequency. So, remember 2 pi FL means that we're going to double my inductive reactance. So, this guy now becomes 60 ohms. And this guy's not 30, let's take a look at him now. If we double our frequency, it's inversely proportional, which means we're going to cut this guy in half and it becomes 15 ohms. So, before what happened is this guy here and this guy here were the same value, so they cancelled each other out. They're not the same value anymore. This is 60 ohms, so it's going up. So, if I drew that out, this guy is going up 60, but this guy here is only going down 15. So, we're going to end up with a net reactance, not of zero. We're going to end up with a net reactance of 45. Let's take a look at our triangle. So, here's our impedance triangle. Before I still do, I have 30 ohms of resistance on the bottom. That hasn't changed, but look at this. My net reactance is now 45 ohms, which means I've got a triangle. Before, my R was equal to my Z. Well, now my Z is completely different. My Z is way higher, so I go 30 squared plus 45 squared equals 54 squared. That is my impedance. That's my opposition to current flow. It is different than my R now because our net reactance is different. So, let's take a look back at our circuit here. We've got 30 ohms of resistance, 15 ohms of capacitive reactance, and 60 ohms of inductive reactance, which gives us an impedance of 54 ohms. Now, remember, in the previous circuit, when everything was in resonance, we were at 4 amps, and I said that current was at its maximum in a series RLC circuit, Resonance Circuit. Now, we see that we have 54 ohms, so our current ends up being 2.2 ohms. 2.22 amps. So, we've dropped our current. That's what happens in a series Resonance Circuit when you change your frequency. It throws everything for a loop. That's basically the whole walkthrough. In the next video, I'm going to throw a second capacitor in there and ask you what size that capacitor is, but that's another discussion for another time.