[Vật lý 12] Điện xoay chiều - Phương Pháp Số Phức - Thầy Vũ Ngọc Anh

Hello everyone, today I will show you a video about a very good way to solve the equation of rotation, which is the equation of magnitude. This method, for those of you who have studied before, you will be very respectful and very interested in learning about this method. Because in this method, we only have to press the button and solve it quickly. But you have to understand, what can be pressed, what can be solved quickly, it is the easy ones, not the difficult ones. So this method will speed up the process of solving the equation, but you have to understand the nature and the root of the problem. But you just press the button and solve it quickly, sometimes it becomes a double-edged sword. It makes you depend on the computer and you don't understand the nature. So you can't do really difficult equations. So this method is just a way for us to read more, to understand more, not to glorify it or praise it because it is very easy and basic. First, we will go to the equation of magnitude. As you can see here, many of you may not have learned the equation of magnitude. I will simplify it later. The equation of magnitude will be expressed on an equation of magnitude. And it has a real equation. Real equation is the real numbers. For example, 1, 1.1, 1.2, like that. Our imaginary equation is connected to the imaginary unit, which is Y. It is very imaginary because our Y is minus 1. For those of you who learn the equation of magnitude will understand this. So you see, we have two equations, right? The vertical axis and the horizontal axis. We will attach these two axes to our vector equation. I know, in the vector equation, how do you do it? U, R is horizontal. You will understand that R is also horizontal like U. Because U is like Z, you understand that. So you see, the real value of R is 50 ohms. So if you express it in the equation of magnitude, our R is also equal to 50. Because it is connected to the real unit. So it is 50. This is the real part. Next is ZL. ZL has a real value of 50 ohms. But when expressed in the equation of magnitude, what is the value? You see, UL is up. It is the same as the real part. But our real part has the unit of Y. So our ZL is expressed in the equation of magnitude. It will be here. ZL square has a cross on the top. It is 50 plus the unit of Y. Do you understand? It adds the unit of the real part. This is the expression in the equation of magnitude. That is, it has a square. Do you understand? Next is ZC. If expressed in the equation of magnitude, what is the value? We know that UC is down. Right? UC is down. Do you understand? It is the opposite of the square of the real part. So it definitely has the unit of Y. Right? It has the value of Y. Right? So it is 100Y. Do you understand? This is the expression in the equation of magnitude. ZL square and ZC square. Now you see, our square has R, ZL and ZC. So we will calculate the total of the whole square. Do you understand? The total of the whole square is Z. It is the unit of R square plus ZL minus ZC square. How much is it? 50 times 2. Do you understand? 50 times 2 Ohm. Right? This is the expression. You know, the unit of R square plus ZL minus ZC square. Right? But what if we express it in the form of Z square? You see, R is the unit of the square. This is 50. This is also 50. ZL is the unit of the square. Right? This is 50. This must be 50Y. Plus 50Y. But how will our Z express? Will our Z be the unit of the square or the unit of the square? Do you understand? So I start to look at this. Our Z square, you will have to learn the formula later. Z square is equal to R square. There. Plus ZL square. Z square plus ZC square. See? Our square is made up of 3 parts R, L, C. So Z square is equal to R square plus ZL square plus ZC square. And when you add it up, how much will it be? It will be 50. There. Minus 50Y. Right? 50 minus 50Y. What does it mean? Take a look. Here, our Z square is 50 minus 50Y. It has both the real part and the imaginary part here. Right? So if you express it to the square, what will it look like? Take a look. Our real part. See? Our imaginary part. There. The imaginary part is the unit of Y. The real part is not the unit of Y. It is the real number. Right? Look. The real part is 50. See? Our real part is 50 here. See? The imaginary part is minus 50Y. It must be below. Right? Minus 50. See? So our Z square is at this magnitude. See? Here. Is it correct? The magnitude is here. 50 minus 50Y. So the modulus of Z, right? That is the length of this vector, from O to this point. See? The modulus of Z, the length of this vector. Take a look. It has a value. How much is it? It has a value of 50.2. 50.2. It is the length of a rectangle. Right? Or the length of a rectangle in a square. See? 50.2. And this is the modulus of Z. Take a look. The modulus of Z is represented in two ways. The first way is 50 minus 50Y. But it is also equal to 50.2. See? The root. Minus Pi over 4. See? To convert from here to here, you can look at this figure. Right? 50.2 is the length of a rectangle. Right? The root. Minus Pi over 4. See? To convert from here to here, you can look at this figure. Right? 50.2 is the length of a rectangle. Right? The root. Minus Pi over 4. This is the modulus of Z. Right? This is the length of a rectangle. To convert from here to here, you can look at this figure. 50.2. This is the modulus of Z. Right? The root. Minus Pi over 4. How many degrees minus? Minus 45 degrees. The minus sign represents that Z is at the bottom of the range. See? At the bottom of the range. And this angle. I know that. It is the angle of inclination with angle of incline. It is 45 degrees. But because it is at the bottom, it is minus 45 degrees or minus Pi over 4. Moreover, you do not want to use this figure to use the drawing to move from here to here then you have another way that is to press the button press the button step 1 you turn on the mode 1, 2 to bring back to the complex mode done? step 2 is you enter the other formula step 2 you enter this formula minus 50i where is the i button? the n, g button that is step 2 step 3 you press shift 2, 3 shift 2 done, 3 shift 2, 3 that is, the machine will show the mode return to r, angle theta that is, return to the mode or for those of you who have a 580 press option option that is, select press down option down then 1 this is the old machine, this is the new machine 580 570 then you press equal press equal it will show the value it will show 50i 1, 2, 3, 4 1 is you combine according to the axis 2 is you will press the machine to move from here to here when you perform z-fuck what is it? when you perform z-fuck is 50 minus 50i do you press the computer? it will know 2 things 1 is I have its module is 50.2, that is, the real value of z is 50.2 and you know that its angle is pi over 4 that is, z is like u vector z is like vector u and this axis is the electric line because the real axis is horizontal, the electric line axis is also horizontal so you look at this pi over 4 I know right away that u is less than i one angle is 45 degrees this is how to show the reversals of the real value to the fuck value you can press the steps like this and we will go to a specific example do you see the following sentence? put the voltage u equal to u plus 2 omega t and RLC connected to R100 ohm ZL200 ohm and ZC100 ohm find z, that is, the resistance of the whole circuit and the frequency between the voltage and the current in the circuit this will do for you in 2 ways way 1 is I press the normal way you will have z the whole circuit that is, the resistance of R plus ZL minus ZC all of them is equal to 100 ohm is it done? Next, the frequency between u and i you can do it in 2 ways one is using cos phi or using tan phi I will use tan phi cos phi is the opposite of ZL minus ZC divided by R and tan phi is 1 and phi is 45 degrees specifically, what is faster? ZL is bigger than ZC so the circuit has a resistance then u will be faster than i right? way 2 is you do it in the fuck way this is the real value the module of fuck z it is z fuck divided by R fuck plus ZL fuck it is represented in 2 different ways to press this, you need to put the computer in complex mode 1, 2 R fuck is 100 ZL fuck is 200i ZC fuck is minus 100i because uc is going down so ZC fuck will be minus 100i always use negative sign and u add it all it will be 100 plus 100i right? press i is nr ok after u have z fuck u will press the computer 1 is shift 23 equal or option 1 equal to get the fuck z it is represented in another way this is the real value this is the fuck value this is the real value this is the fuck value this is the module this is the real value of z this is the vector length is 120 pi over 4 is the angle between u and i if it is negative, u will be more far if it is positive, u will be more far u is earlier than i angle is 45 degree this is the fuck function there are 2 ways to perform z 1. play with the angle 2. play with the angle 25.2 That's right, it will be relatively fast. Let's sum it up. 71.5 times 24.8 degrees. This is the result of the equation. That's our total U. The formula of total U is this. Total U has a magnitude. U0 is 71.5 volts. The initial phase is 24.8 degrees. But this equation has another meaning. What if I want you to find the magnitude between U and Y? This is difficult. The magnitude of U is 24.8 degrees. Now I need to find the magnitude between U and Y. I need to know the magnitude of Y. Where is the magnitude of Y? There is no magnitude of Y. Where is the magnitude of Y? In fact, the magnitude of Y lies in the magnitude of UL. Because UL is the magnitude of P over 2 compared to Y. So you will take the equation of ULX minus the equation of UX. This is the equation of UL. Let's do it. 90 times 30 minus 22.5 times 3. Subtract 23. Is it ok? Here. It is 59.5 times 49 degrees. This is the equation of UL. 59.5 times 49 degrees. The magnitude of UL is 49 degrees. So what is the magnitude of Y? The magnitude of Y is less than the magnitude of UL which is 90 degrees. 49 minus 90. The magnitude of Y is 41 degrees. Is it ok? Is there the magnitude of U and Y? Find the magnitude of U and Y. Delta Phi is the magnitude of U and Y. How many degrees? 24.8 plus 41. Subtract this. It is 24.8 plus 41 degrees. It is 65.8 degrees. This is the magnitude of U and Y. Subtract this. It is the magnitude of U and Y. It is done. This question is quite difficult. Many of you don't know how to find the magnitude of Y. At first, there is no Y. But the magnitude of Y is less than the magnitude of UL which is 90 degrees. This is the detail of this equation. It is done.