yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

LC natural response intuition 1


3m read
·Nov 11, 2024

We're going to talk about the natural response of an LC circuit, inductor-capacitor circuit, and this is an interesting one. This is a circuit that has two energy storage elements. In the past videos, we've done one energy storage element, either a C or an L, and this time we're going to put them together and see what they do as a pair.

There's no resistor in this circuit, so this is interesting because we have two energy storage elements. Well, what does that mean? That means for a capacitor, there's some charge stored on the capacitor, and that typically means that there's an excessive charge on one of the plates. So in this case, there's an excess of positive charge on the top plate, or you could say it the same way: there's a lack of negative charge. There's some negative charge missing from the top plate, and there's some extra negative charge on the bottom plate. So that's what we mean by a capacitor storing charge.

So, how does an inductor store energy? Well, that stores its energy in a magnetic field that's out in the space around the inductor. So when we have a current flowing in the inductor, its energy is stored in a magnetic field like that. So that's what we mean by two energy storage elements.

Now, one thing we know about the Q in a capacitor is Q equals CV. So if there's some Q here, that means there's some voltage here. So this is the voltage we're going to track in this circuit; that's the voltage between these two nodes here. And because there's an inductor, one of the interesting things is the current in the inductor. So I'm going to draw the current arrow this way, and one thing I want to point out is if I define the inductor current going down through the inductor, that same current is going up through the capacitor.

So our challenge when we want to know what the natural response of this is, is we put in some energy, and in this case, we'll put in some Q on the capacitor and we'll let I start at zero. Then we step back and we watch what this circuit does, and what that means is we figure out what the voltage is as a function of time and the current as a function of time, and both of those things together are the natural response of an LC circuit.

So in this video, what I want to do is predict the shape. We're going to predict V and I; we're just going to do this intuitively, and then in the next sequence of videos, we'll work it out exactly with mathematical precision what this natural response looks like. Then we'll look to see if the mathematics matches our intuition. A good way to make this prediction is we're going to follow and track what happens to this charge here as this circuit relaxes in its natural response.

So, first thing, let's just write some equations, the element equations for the L and the C. We know for an inductor, V = L * Di/Dt, so voltage is proportional to the value of the inductor times the slope of the current or the rate of change of the current. For a capacitor, we know that I = C * DV/Dt. One thing we know is that both of these equations are true all the time, so that's going to help us out.

The way we look at this intuitively is we're going to track the charge, and we're going to look at what happens in this circuit moment to moment as that charge moves around. So, what I'm going to do, just to get a setup here, I'm going to take out a little chunk of this circuit here and then put in a switch like that. So here's a switch, and that switch is going to close at time equals zero.

So before the switch closes, we're going to put some charge on this capacitor. There's going to be a voltage on the capacitor; the capacitor will have a voltage of VN. So that means that V of time less than zero equals V KN; we'll just call it V KN. And what else do we know? Well, the switch is open, so that means that the current through this loop, the current in our circuit, is zero. So we can write I(T < 0) = 0.

So there are two things we know about the circuit. Now we're ready to close the switch, and we're going to take a break right now, and I'll see you in the next video.

More Articles

View All
The Importance of Art Education | StarTalk
There’s a big issue, uh, probably in other places in the world, but we feel it a lot here in the States. The funding for Arts education is always under stress, and the school boards are wondering: Do we cut the art? Do we keep the science? And there’s ten…
Office Hours with Kevin & Qasar
All right, hi everyone, my name is Kevin Hail. I’m a partner at Y Combinator. Um, I went through YC myself back in 2006. I co-founded a company called WFU Online Form Builder. Um, ran that company for about 5 years and it was acquired by SurveyMonkey back…
Allies & enemies are lining up
What about this idea that could the world just bifurcate? Um, where you have more than like countries that align more like the U.S. and U.S. values versus, you know, thinking like China, Russia? Um, first of all, it’s happening. Um, and by the way, I wou…
Think on it | Barkskins
Mathilde: One only has to say the word “English,” and they come running like sick black dogs at low tide. Captain: Well, I heard about your selfless heroics with the Iroquois and the tragedy with the priests. Well, I suppose there’s nothing more that nee…
THE FEDERAL RESERVE JUST FLIPPED | Major Changes Explained
What’s up guys, it’s Graham here. So this is big. After more than a year of patiently waiting, the Federal Reserve has just officially paused their rate hikes for the first time since March of 2022, marking the beginning of a brand new market cycle that’s…
The Value of Rooftop Farming for the Community | Farm Dreams
Things are living, and things are growing on the roof, so they’re always living and growing. The flowers look amazing! Oh man, and you know the flowers are bringing the pollinators. Yes, we got the butterflies coming; we got the birds coming. So it’s goin…