An L-R-C series circuit has L = 0.600 H and C = 3.00 mF. (b) What value of R gives critical damping?

Video transcript

Welcome back, everybody. We are making observations about an L R C circuit that is built in series. We're told that it's constructed with an induct er that has an inductive of 0.8 Hertz and a capacitor with capacitance of four micro fare adds. Now, we are tasked with finding what will be the resistance of a resistor that will cause critical damping to the system. Well, when we have critical damping to the system, we can make this equality right here. That one over R inducted as times are capacitance is equal to our resistance divided by two times the inductive squared. So let's go ahead and solve for our resistance variable right here in order to then plug in the other values to fine our R C. So in order to get rid of the power, I'm first going to take the square root of both sides and we can acknowledge that that gets rid of this power over here as well, then I will multiply both sides by two L. And you'll see that this cancels out these terms right here. So we are left with that, our resistance is equal to two L which square to one is just one. So I can multiply this into the fraction divided by the square root of L C L C. But I'm gonna make this a little bit easier. I'm gonna use a little trick here. I'm gonna square both sides again. And this gives us that our resistance squared is equal to four times L squared divided by L C. And you'll see here that I can cancel out the induct. It's on the bottom with the power on top one. Once more, I will take the square root of both sides getting rid of the power simply giving us two because square root of four is two. So I can pull that out from under the radical times the square root of our conductance divided by our capacity. It's much easier to calculate here. Let's go and plug in our values. We have to times 0.8 divided by four micro fare adds, but we need this in fair ads. So I'm gonna multiply this by 10 to the negative six. And when you plug this into our calculator, we get a final critical resistance of Omega's corresponding to our answer. Choice of a. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.