 See, whether you call it alternating current or alternating voltage does not matter the one in the same thing. What does alternating means? What does it mean? It changes. So, tell me which one are the alternating voltages or alternating currents? One a, b, c, d, which one are the alternating currents? Is it alternating? They definitely not. This is yes or no? Why? It is not changing. It is changing, but it is not becoming negative. It is not changing the direction. So, it is not alternating. It is a direct current. These are changing the direction. There is a positive current. After some time, there is a negative current. And in our syllabus, we are specifically focusing on this kind of AC, which is sinusoidal curve. When I say sinusoidal, cos is same as sinusoidal, like sin theta plus pi by 2 is cos only. So, it is one in the same thing. They behave similarly. So, we are dealing with this curve in this chapter. Why? Because this is what we are creating. In AC generator chapter, there is a sin term coming in or not. emf was equal to nab omega sin omega t. This is what is getting generated out of that rotating this thing. So, this automatically comes naturally. So, our focus is this type of voltage. See, this is the first time you guys are learning about alternating current. So, we will be first talking about the basic elements. Like for example, a basic circuit with AC, like only resistance connected to AC first. Then we will connect only inductor, then only capacitance. We will find out the current, voltage, power in all these circuits. And then we will talk about what if we connect them together, what will happen? How we will find out power, current and voltage, all that. And once we are done with everything, then we will talk about few practical stuff. Like how can you utilize alternating current to create something which we have learned in current electricity, potentiometer, midstone bridge. First we learn the basics, then instruments, similarly here. But the basic of alternating current starts from the very very basic, because you are learning alternating current for the first time. So, the first circuit that we are going to study is resistance circuit, only R. So, if you connect a resistance of value R with an AC voltage source, AC voltage source is denoted by this. This is AC and this is DC, this is AC. Let us say AC voltage source is this, V naught sin omega t. First you tell me, what is the average voltage? How much is the average voltage? This is the sign for average. How much is the average voltage? So, average voltage is how much? Average of sine graph is what? It is 0, it is equally above and equally below. So, average of voltage is 0. Current is how much? If you apply Kirchhoff's this thing, you will get current is equal to V naught by R sin omega t. Simply even current also changes with time. So, what is the average value of current? 0. So, how different it is with 0 voltage and 0 current? There is a lot of difference. So, average is not giving a true picture of what is happening. Average of 0 is also 0. This is what current which continuously changes and V naught sin omega t is voltage that is continuously changing. But if I ask you what is on and average, what is the voltage in AC? If you say 0, that does not make any sense. Because if you say on and average is 0, it should not give you a feel that there is no voltage. So, the way you take the average is completely different when such thing happens. What you do? You square it so that negative also becomes positive. You square it, then you take average of all the squares and then you take the square root. So, it becomes root means square. So, we will be taking root mean square root of all the means of the square. So, now let us try to find out V rms. Rms means root mean square. This will be equal to what? The mean of V square sin square omega t under root. Try to get the value of this. Use the fact that average of cos omega t is 0, cos 2 omega t is also 0, average of that. Use it and try to get the value. The average of V naught square is V naught square. So, V naught will come out of this square root. You have to take average of sin square omega t. What is sin square omega t equals to 1 plus or 1 minus? 1 minus cos 2 omega t divided by 2, the average of that. So, this will be root over average of 1 by 2 is 1 by 2. It is a constant minus average of cos 2 omega t divided by 2. How much is this? 0. So, you will get V naught by root 2 and as a fact also if you remember average of sin square is 1 by 2, average of cos square is 1 by 2. Now, it makes sense that on an average, if you take root mean square the voltage is V naught by root 2. So, now it is different from 0. So, there is something. V rms is V naught by root 2. What is I rms? I naught by root 2 which is what? V naught by r root 2. So, we have found average of voltage and current, but this is just average. Actual current is this and actual voltage is this. Now, can you find out how much is the power dissipated in the resistance? Power dissipated. How we find power? I square r. No. V naught square r sin square omega t. This is what you will get power. Isn't it? This is I. I square r is that. So, power dissipating the resistance depends on time. So, we will try to find out average power now, but you should remember one thing is if average power is coming out to be 0, you do not take rms of the average power because power represents energy. It has some physical significance. So, we do not take rms value of power. We just take average of power. So, what is average of power over here? V naught square by r into average of sin square omega t. What is the average of sin square omega t? 1 by 2. So, this will be equal to V naught square by 2 r. Now, if you try to write down in terms of rms values, you can say that it is V rms into I rms or it can be written as I rms square into r. So, when you use rms values, the formulas are very similar to what you have in direct current. So, this is the first basic circuit plot of the graph. In this graph, plot current, voltage and power. The voltage will be simply like this. This is voltage. The current will be what? If you assume resistance to be more than 1, V naught by r will be less than V naught. So, we will lag behind. No, no, no. They are both sin. No, but the graph will be the same, but it will be like this. If r is more than 1, when voltage is maximum, current will be maximum. When voltage is 0, current is 0. What about power? Power is this. It will go like this and it will just hop over. It will remain in the positive pattern. This is the most simple circuit for AC. Just resistance is connected. Write down a question. A light bulb rated 1000 watt for 220 volt. I am talking about AC. When I say 220 volt and I do not say anything else, what does it mean? What voltage is this? rms. Otherwise, I have to specify that this is peak value or whatever it is. If this is rms value, this is divided by 2. You have to find out resistance of the bulb, peak voltage of the peak voltage and I rms. What is power? Power is average power. There is no meaning rms power. Power is i rms square into r. This is also equal to v rms i rms and that is also equal to v rms square by r. Resistance is 484. R is equal to 0.454. When you substitute values over here, you get resistance as 484 ohms. Peak voltage is how much? This rms voltage multiplied by root 2 because peak voltage divided by root 2 is rms voltage. Resistance is 484, peak voltage is 311 and current is 0.45. 1 divided by root 2 is 0.7. You remember that 1 divided by root 2 is 0.7, root 2 you know and root 3 divided by root 2 is 0.866. This thing you must do is 0.866. 1.7 divided by 2. This thing should be on your fingertips. You should not be like, okay, let me divide with root 2. No, multiply with 0.7. Okay, so should we proceed?