 We've already derived expressions for the current when you apply an alternating voltage across resistors, inductors, and capacitors. And an interesting thing we saw in these two circuits is that even though there are no resistors, the current is limited, meaning there is some opposition provided by inductors and capacitors as well. And the goal of this video is to figure out what exactly is that opposition, what do we call it, and how is it different than the regular resistance. And before we proceed, if these equations look new to you and wondering where did they come from, then don't worry, you can always go back and check out our previous videos on pure resistive, inductive, and capacitive circuits. We've talked about them in great detail and derived them. So feel free to always go back and check them out. So let's begin with an inductive circuit. How much opposition does an inductor provide to a current? For that, I look at this equation and I say, huh, I see i is equal to v0 divided by something. And that's something should represent my opposition because because if this number increases, the current will decrease. And so we give a name to this opposition. We won't call it resistance because resistance has a specific meaning. It's something else. And we call it reactance. Okay. And because this is due to inductor, we call it inductive reactants. So let me just write that down inductive reactance. And it's denoted by the symbol x capital X. And for inductor, we use an L over here. So the opposition brought by the inductor is the product of omega and L. And that product is called the inductive reactants. I want you to quickly think about what would be the unit of inductive reactants. Can you pause and think a little bit about that? Okay, one of the ways to do that is you can say, okay, I need the unit of omega and the unit of inductance multiply them. But a quicker way of doing this is we could say, hey, i is equal to v by something that something should have the units of resistance should have the units of ohms, right? Because this value will be v divided by i. And that should be ohms. So inductive reactants has the unit of ohms as the same unit as resistance, but it's not resistance. And we will see the difference in a second. Now let's do the same thing for our capacitor. In fact, again, I want you to pause the video and think about it. What is the opposition provided by the capacitor going to be? What will be the expression for capacitive reactants? You can try to do it in a similar manner. Can you pause and think about it? Okay. Now immediately you might say, hey, there's nothing in the denominator, right? So how can I come up with capacitive reactant? How can I come up with the opposition? Well, remember we have, along with v naught, we also have omega and c in the numerator. And you know, you can always take something in the numerator and put it in the denominator. There are ways to do that. So if you didn't write before, now would be a great idea. It's just a mathematical trick to see if you can figure out what the opposition is going to be. So here's how I think about it. If you have some x multiplied by v, I can always write that as v divided by one over x. That's the mathematical trick. I can do that, right? And therefore what I can do is I can write this as v naught divided by one divided by omega c. One divided by omega c. And now I can say, look, this represents the opposition because if this number increases, your current will decrease. And so this is also reactants. We call this capacitive reactants. Capacitive reactants. Same symbol x, but since it's capacitor, we'll put a c over there. And what would be the units of capacitive reactants? Again, it has to be ohms. So one of the things is inductive reactants is omega into L. But capacitive reactants, as you can see, is not omega into c. It's one over omega into c. One of the mistakes that I used to always make. Okay, now before you proceed, I want you to think a little bit about what is the major difference that you can find between reactants and resistance. Of course, there is symbol difference and all of that, but I'm looking for some really conceptual difference between them. So again, can you pause the video and think about what difference you see? Okay, the major difference that we are seeing is that reactants depend on the frequency of the voltage source, and resistance does not. So you see, resistor is saying, look, I don't care about the frequency of the voltage source. I really don't care. Doesn't matter what frequency it is, my opposition is going to stay the same. But that's not the same with reactants. If you look at, for example, inductive reactants, we see that as the frequency increases, even if I keep the height of the voltage same, but if I just increase the frequency, I will find that the opposition increases and therefore the current in the circuit drops. Why is that happening? Why does inductive reactants increase with frequency? Why does the opposition increase with frequency? Can you think a little bit about that? Well, think in terms of inertia. Remember how we thought of inductors as a box currently through an inductor as a box sliding over a plank that's going up and down and the speed of the maximum speed of the box would represent the maximum current over here. Now I want you to think about or visualize what would happen if the plank were to go up and down to the same height, but where to go faster? What would happen? Well, let's see. Okay, here it goes. Ooh, notice because it's going up and down very quickly, the box doesn't have any time to speed up and as a result, the maximum speed of the box becomes very, very low. The same thing is going to happen over here. As the voltage changes very quickly, the charges hardly get any time to accelerate and as a result, the maximum current becomes smaller and smaller and smaller and that's why with frequency inductive reactance increases. And so this has a nice application electronics. This means that the inductors do not allow high frequency current to pass through them because when the voltage changes very quickly, the opposition is very strong, but they do allow low frequency currents to pass through them. And that's why we say inductors are high frequency choke, the choke high frequency currents. And we also see that inductive reactance depends upon the inductance itself. Why is that? Well, that's because if the inductance itself increases, then the inertia of the circuit also increases. So the charges will take even more time to accelerate and as a result, the current will become smaller. Does that make sense? All right, now let's talk about the capacity reactance and you see it's exact opposite. Here you find that if you increase the frequency, the capacity reactance becomes smaller, opposition becomes smaller. Why is that? Now, one thing you might be wondering, why do I call this number the frequency? That's actually the angular frequency, even as 2 pi f. So if you change the frequency, automatically omega changes. Okay, so that is the direct relationship. That's why I just keep calling this frequency. It's actually the angular frequency. But anyways, why is this if you increase the frequency, the capacity reactance reduces. This is something we've talked about before in the previous video. But to quickly summarize what happens is if you change the voltage faster, you need the capacitor voltage to also change quickly. But the capacitor, that means the charging and the discharging needs to happen very quickly. And that means the currents need to be high enough. Does that make sense? So more the frequency, more faster charging and discharging needs to happen. And therefore you need a high current. And so the current increases and therefore we say the opposition becomes smaller. Okay. And similarly we find increasing the capacitance also reduces the opposition. Why is that? Well, because if you increase the capacitance, the capacitor now has more capacity to hold charges, meaning it makes it even harder to change the voltage. And therefore now to change the voltage, you require even higher currents. Does that make sense? And therefore increasing the capacitance increases the current. And therefore we say the capacity reactance becomes smaller. And you can summarize all of this in this short animation. If I have an inductive circuit and let's say this is the voltage, the pink one is the current. If I were to increase the frequency of the voltage, how does the current change? Well, of course, the current frequency will also increase. But because the inductive reactance increases, because the opposition increases, the height of the current becomes smaller. Opposition depends on the frequency, reactance depends on frequency. What happens in a capacitive circuit? Well, we can do the same thing. It's exact opposite. Now, here if you increase the frequency, of course, the current will also increase in frequency. But because now charging and discharging becomes faster, more current, here the current increases. So the capacitive reactance decreases. Again, reactance depends on the frequency. But what if you have a resistive circuit? In this case, what happens if you increase the frequency of the voltage? The current frequency increases, but the height does not change because the resistor says, Hey, my opposition does not depend upon frequencies, right? I do not, I do not discriminate against high, discriminate against high frequency or low frequency. And therefore here, the resistance doesn't change with frequency, but reactance is to major difference. The second major difference has something to do with energy and power. Resistors, when they limit the current, you might already know they convert energy into heat. We say power gets dissipated. Whereas when inductors or capacitors, when they limit the current, they do not convert the energy into heat. Instead, they store the energy temporarily and they transfer it back. And so resistors dissipate heat, whereas reactances don't. And of course, we'll talk more about power dissipation and all that in the future videos. Finally, there is yet another term called impedance, which also represents opposition to the current. Also having unit of ohm. So what is this now? Well, don't worry. It's nothing new. Just like how when you have a group of men and women, collectively they can be called humans. If you have circuits which have both resistances and reactances, the total opposition is often called impedance. So you can think of impedance as a general word we use to represent opposition. So in this circuit, impedance is just the resistance. In this circuit, impedance is just the inductive reactance. And in this circuit, impedance would just be the capacitive reactance. And so you might be now wondering what if you have circuits that contain, say, both resistor and an inductor? How would we calculate impedance of such circuits? It might be reasonable to think that we just add the resistance and the reactance over there because it's the total opposition. But turns out it doesn't work that way. You can't directly add it. And if you're wondering why we'll have to do a full-blown circuit analysis, which we will do in the future. I just don't want you to think that just because impedance is the total opposition, we just sum them up. That's not how it works. But what makes impedance interesting is because it has both the resistive component and the reactive components to it, it can have them. When you change the frequency, the resistive component wouldn't change, but the reactive components changes. So it's very interesting to see how impedance changes when the frequency changes. And we'll talk all about that in the future videos.