Hey, guys. So let's take a look at this problem. We have an LC circuit with some inductance and a capacitance. It begins with the capacitor fully charged. And we're supposed to figure out how many seconds it takes for a fully charged plate to transfer all of its charge to the other plate. Now, that's a lot to unpack there. So what I'm going to do is we're going to begin with just a simple diagram of an LC circuit. Hopefully, I do this right. So I've got the inductor like this, and it goes around, and then you have a capacitor like this. Now, remember from our previous video that we talked about if we have a sort of charged capacitor like this with all the charges, the cycle has to reverse direction piles up on the other side. And then the cycle has to reverse direction and do the same thing over again, but backwards. So in other words, all the charge has to go from here. It escapes through this plate, and it basically piles it back to where it started from, and then the whole thing repeats over and over again.

So what this is saying is how long does it take for a charged plate to transfer all of its charge to the other side of the circuit, or the other side of the capacitor. So what that really means is that it's actually just looking for half of the cycle. So that means in terms of the period, that's the variable t, that's going to be t2. So really what we're looking for in this case is what is the half-period in seconds? That's really what we're looking for, but in order to do that, in order to figure that out, we just have to figure out what the period is in general. So let's remember if we can Let's remember our formulas for the period, the frequency, and the angular frequency for an oscillating system. We have that the period and the frequency are inverses of each other, so t=1f. And we also have that the angular frequency could be related to the linear frequency by this equation right here. So if I want to figure out what the period is, I have to relate that to the frequency, but I don't know what the frequency is, so I have to relate it to the angular frequency. And that I actually can figure out because remember that the angular frequency omega can also be related to the inductance and the capacitance of the equation, right, of the circuit. So let's go ahead and do that. Let's see. The t is going to be Let's see. If I wanted the frequency, that's actually going to be omega over 2 pi. If I just move this to the other side, it's going to be equal to the frequency. So what I have is that t is actually equal to 2πω. So that means, finally, that tover 2 is just going to be πω. So write one half of this, it's just going to be 1 half of this, so the 2 just cancels out. And we just get πω. So finally, what I can do is I can actually just take this formula right here, which is the square root of 1 over LC, and I can actually plug it back in for the denominator in this equation. And what I get is that t/2 is equal to π×L×C. So what happens is when you take the inverse of this, and this is in the denominator, basically what happens is we're taking π/L×C, and so LC just goes up on the top. Right? Got it. So I just wanted to sort of walk us through that because it's been a while since we used these kinds of equations. So really, this is actually just going to be the half-period. That's all we have to do. So that means that t, which is equal to the half period, is just going to be π×0.05×0.05. So we have L is equal to 0.05. We have the capacitance that's equal to 50 millifarads, which is actually 0.05 as well. So that means we're just going to have 0.05 here also. And we just get that the half period is just going to be equal to 0.157 seconds, and that's our answer. That's how long it takes in this circuit for the charge to transfer to the other side. That's half the cycle. It would take another 0.157 seconds to go back and then basically begin the whole thing over again. Okay, guys. That's it for this one. Let me know if you have any questions.