Reactance, resistance, & impedance (what's the difference?)

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 if 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 they 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 capacitor 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 i see i is equal to v naught divided by something and that 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 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 reactance 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 provided by the inductor is the product of omega and l and that product is called the inductive reactance i want you to quickly think about what will be the unit of inductive reactance 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 you 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 reactance has the unit of ohms has the same unit as a 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 reactance 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 reactor 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 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 their opposition is going to be so here's how i can think about it if you have some x multiplied by v i can always write that as v divided by 1 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 1 divided by omega c 1 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 reactance capacitive reactance 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 reactance is omega into l but capacity of reactants as you can see is not only going to say it's 1 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 in 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 reactances 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 reactances if you look at for example inductive reactance 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 reactance 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 current in end 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 planck would go up and down to the same height but where to go faster what would happen well let's see okay here it goes oh 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 in 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 they 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 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 reactants 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 know you might be wondering why do i call this number the frequency that's actually the angular frequency given as 2 pi f so if you change the frequency automatically omega changes okay so that is a 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 the faster charging and discharging needs to happen and therefore you need a high current as 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 have 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 okay 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 reactants 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 discriminate against high frequency or low frequency and therefore here the resistance doesn't change with frequency but reactance is two 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 om 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 capacity of reactants 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 though 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 can have it can have them uh when you change the frequency the resistive component wouldn't change but the reactive components changes so it's very interesting to see how you know impedance changes when the frequency changes and we'll talk all about that in the future videos