In this simulation of this lesson, we're going to do a transy analysis of LC separate, which is a dynamic second order separates. So first thing we're going to do is click here, new schematic and draw arrows here. So I've chosen series RLC circuits. So, inductor, capacitor, ground and then we put a voltage source like this pesky on other grounds the wire ASCII And then we're going to put some values for capacitor and inductor, let's say five micro. Remember it's written five micro c but not five week or crew limbs call its fire maker products, its international system units. So and here, one Meili.

Actually it's 1 million any but it's written on now, but don't worry. That's the way this program works. And then we're going to add a five volts DC value, voltage sauce And next we're going to do is simulate a simulation comment. We're going to put transients of two millisecond Okay. And then whatever venture to do run it all it's very important for Reacher choose an initial value of air. So cancel and let's choose like 100 ohms and then simulate it.

We have a blood vein here. And then what are we going to do is plot the current we have center. Another thing in other important thing to do is to plot the this voltage and then at block pain at trace Add the label to ease our life. Three ng we put it here and then run again. But the NG it's called started five volts, five dot 000. And we should note that Phantom pair, it's a very, very small current.

So this current is virtually zero should be taken as virtually zero. But what's happening here? Why isn't the capacitor present in some charging process? Well, also we set the voltage SOS is way We're telling the simulator that the voltage source is being five volts sees always. It's never been an beginning for others voltage SOS. So the capacitor is always being five volts charged.

So what are we going to do about this? We're going to change it, click here and click Advanced. And then we're going to get rid of this five volts, and they post here and each of Alou zero because the secret should start odds 00 current zero charge and so on. Regardless of butts v on us five volts and then Dion The time in which this voltage is uses 20 milli seconds per yards, 14 minutes and zere. Okay, let's move it through here. So it doesn't stay on top on all this correctors of the labels, and then we're going to simulate it again.

So the result was very different than what's happening here. We can see that the input voltage, it takes a very big time to reach the five volts. So it isn't what we want So let's but not zero here us rise time but a very small value like zero dot zero to micro click OK and then see what the result so in this case we see that we've got a virtually instantaneous change in input voltage, it was zero voltage and then switch it on the separates five volts mean five volts the current on the capacitor the behavior is like this. It reaches a peak here and decreases because the steady state of the secret is the capacitor charged and no more current flows into it because it's Red being charged. So, and this case with 100 arms is called the overdamped case effect as this is a second all the secrets these is second order dynamic circuits and it is a linear circuit This is governed by a second order ordinary differential equation and which equation is it is it these one these equation relevance or system let let us see hi Is the letter we use to represent the currents that's runs through their resistor that inductor and a capacitor.

We have a second order differential equation, R is this restore out these inductor, see this capacitor. And the solution to this differential equation depends on these values. In which case, it depends on the delta of these equation, these these paramita because we're going to solve these through the differential equation, and then we calculate it and dependent on the signal of it. Delta is positive delta is zero or delta is negative, we have free different behaviors for the secrets for delta positive, we have a over that but circuits for delta negative we have under them but separates the diff difference between over them but secrets and then under that butts here grades is very clear, as we shall see. And then between the two very distinct distinguishing cases, we have the critical adaptive case, which is chance, essentially, when we have delta equals zero. And for this secret we've chosen l as one Meeker Annie.

See us five Meeker and Which is that turning turning points for air for Lu, it is exactly this for air the turning point where there is the square square roots off a tangent which is approximately 28 dot 28 forms. So, below trans eight dot 28 ohms their response is under Duncan, we shall see what it means eco try to translate the response is critically damped. It's the response that lies between the two very distinguished responses and then which is our initial case, air greater than 2022. We have an offer that separate again We haven't 100 ohms so we're we are in the overcompensate so let's analyze what happens when we have all of our lose we have a hundreds and their response is like this for the currents so it is that over them but the case and then what they're going to do decrease these resistance value to say 30 it's very close he had to sign a document.

So watch it. What should we see? Quick there any man? Oh, it is faster as we can see You're free 10 back to 100 ohms and simulate it again. That's but voltage V. Yeah. That the current is between 45 milliamps and 50 milliamps.

And then when we decrease that resistance to your 30 we're going to see is a increase in the peak. And then we're going to we're going to decrease it even more. So let's put it exactly 28 dot 28 Okay. Now we have the critically damped case, the case that lies between the underdog but the ends of adopt now we're going to see that on the dumbfuck case we're free but a value very, very below 20 a document eight, like 15 let's see what happens okay. And then that simulated oh we see an oscillatory bata the currents goes up and then goes down goes below zero and goes above and eventually in a very long time it reaches virtually zero. So, what in the reaches first speak about between 120 milliamps and 200 milliamps before zero dot two milliseconds.

Let's see, if we reduce it to five. Let's see, zero dot two milliseconds 180 to 140 and 280. Between these values and an oscillatory pattern, the timing of hostility by that didn't change very much, but we now we can see, greater number greater number of oscillations. In the former case, we had 15. We didn't see so many oscillations because they died off so quick. So that's the very deep Difference between the over them but the farther me the sub them under damped case and over them but the case this is the under damped case because our resistance is less than 2828 and so this occurrence presents an oscillatory pattern and then if we had a very large resistance very large I mean great to downtrend a document a eight we should have a peak and highs low decreasing currents, choosier.

Let's see. very extreme value like free hundreds. Okay. Oh We see that in this case over them, but the resistance we've put here is way greater than then 28 or 28 omega. So, we see that it reaches the peak and then it decreases very slowly. So, in this lesson, we have seen the simulation of a second order series particularly of RC circuits, which is a second second order linear dynamic circuit, and we saw the difference between the three cases which is defined by the value of delta which is it and which gives us free the friends behaviors.

And so, I see See you again. The next lesson