Inductors in Circuits

by Patrick Ford
94 views
3
Was this helpful ?
0
Hey, guys. So we saw how in the last couple videos how a coil of wire that has changed in a current can actually induce an E. M. F on itself that was self inducted its But sometimes you need to know how these coils of wire behave in circuits. So we're gonna go and take a look at this video. All right, So basically, if you place a coil of wire inside of a circuit, it's known as an induct er. So it's kind of like how we talked about capacitance, and then we talked about capacitors and circuits. Then we talk about resistance and then resistors in circuits here. We talked about induct INTs. Now we're gonna talk about conductors and how they behave in circuits. So there's two common symbols or you're going to see in your classroom in your textbooks. You're gonna see this little bumpy guy right here on. Then you're going to see this little loopy one. I actually kind of prefer the loopy one. Just because I can't draw this that well. So for the rest of this video, I'm gonna use these loops right here in the context of induct er's. Alright, so just be aware that you could see both of those symbols there. It's the same thing, all right, So because these conductors are circuit elements and we use them in circuits, we need to be able to use kerchiefs rules as we go around them in a circuit writes. We need to be able to use the loop rule on DFI. Get what the voltages are now the first things. First, we have to remember that induct er's Onley do something if the current is changing. We saw that for a coil of wire. The induct into the self inducted is given by this little letter L It was negative. L Times Delta I over Delta t so that relates the current changing to the self induced E M f. So what happens is if we have this diagram here and the current is constant, then that means that the change in current over changing time is equal to zero, and there's gonna be no e m f. So these induct er right here isn't doing anything because there is no change in current. So it's on Lee that when you have either in increasing or decreasing current in a circuit, you're gonna get some kind of e m f So we hav e m f here and we have e m f here. But what happens is that it's not just enough to know the magnitude of the e m f. We also need to know the direction and whether it's positive or negative in order to use kerchiefs rules. So we got a battery right here, and we've got a current It's gonna go in this direction like this. So this is gonna be our direction. And whenever we do kerchiefs rules, we have to basically pick up points like this, and then we have to go around in a loop and then add up all the voltage is the problem is is that I don't know whether the voltage across this in doctor is gonna be positive or negative, and the same thing goes over here for this diagram as well. So in order to do that, I need to use lenses law to figure out what the direction is of the induced e m f of the conductor. So let's take a look at this right. You have a coil of wire and it's gonna generate a magnetic field in this direction. And what happens is that magnetic that magnetic field is proportional to the current. So if the current is increasing, then the strength of the magnetic field is getting stronger. And so what happens is lenses law, which gives us which is given by this minus sign in this equation right here tells us that the induced EMF is going to be the opposite of whatever the system is doing. So that means if I were to try to figure out what the induced E. M. F is on the circuit, it's gonna be the opposite of whatever it wants to dio. So if it's going in this direction and it's increasing, the induced e m f is gonna go this way. Now let's take a look at this example where the only thing that's different is that the current now is decreasing, so it still goes in this direction and our loop is still going to be in this direction. But now it happens. Is that r E M f induced? If the current is decreasing, it actually wants to reinforce the weakening magnetic field. So the induced EMF is actually gonna points along that direction. Okay, so it's not about where the direction of the current is. It's about where the current is, whether the current is pointing and whether it's getting stronger or weaker. Now. The thing is, is that if the direction of your induced CMF and this is the most important part here, if the direction of your induced CMF points along our Kirchoff loop, then the voltage it picks up is actually going to be positive. So what happens here is if our loop is in this direction. So this is our loop, and my induced EMF points in this direction like this. Then it's going to be positive. If it points in this direction, then that induced e m f is going to be negative for our Kirk Absolute And the same thing goes for the opposite direction. If our loop points in this direction and we have an E m f that points in that direction, then it's going to be positive. And if it points in this direction, then it's going to be negative. All right. So when we use our Kirchoff sloops, these the rules that we have to follow. All right, so Let's go ahead and take a look at an example here. We've got kerchiefs loop rule for the following circuit, and we're gonna assume that the voltages of the battery is increasing. So let's see, we've got a battery like this, so I have a voltage from the battery and then we have a voltage from the induct er that's gonna BVL and then we have a resistor right here. So it's also gonna have a voltage. So what I'm gonna do as I'm just gonna go ahead and pick a direction for my Curtis loop. So I'm just gonna go ahead and choose this direction and let's see the battery actually has the positive terminal that goes to the left. So that means that I know the current is gonna be in this direction. So that's I. So that means the current is this And the current is this and I also know now that current is increasing. So now what I want to do is figure out what my kerchiefs loop rule is. So that's gonna be Delta V is equal to zero. The sum of all the voltage is equal to zero. That's kerchiefs loop. So let's see, we've got three terms. We've got the battery's voltage. We've got the voltage across the induct er v l. And then we have the voltage across the resistor that is VR, and that's all equal to zero. The only thing I have to do is figure out what the direction is. What's the sign of each of these terms here, and that's basically determined by in which direction my loop is going. So let's see for the first guy as I'm going along the loop, I'm going in this direction and the polarity of the battery is this way. So that means that this voltage is positive. That's a positive voltage right here because we're going along the positive terminal. Then what happens is this current is increasing. So now what we have to do is figure out what the direction is of the induced UH, E M F from the induct er is if it's in this direction and it's getting stronger than that means that the induced E. M F from the induct er wants to point in this direction. So that's Epsilon induced. And because the loop goes in this direction, actually, I should probably write that in black, actually, So the induced e m f. Is actually gonna be pointing this way. So that's epsilon induced. And because it points in the opposite direction. My loop goes this way. But my epsilon goes this way. Then it picks up that negative sign. So basically, what that means is that my V l is going to be negative. And then finally, what happens is that I'm going in this direction of the current, and my loop also goes in this direction across the resistor. So that means that that's also going to be negative as well. So basically what my Kirchoff Slew parole looks like is VB minus L times Delta I over Delta T and then minus I times are is equal to zero. Okay, that's basically what our kerchiefs loop rule looks like for this kind of circuit. And we're gonna go ahead and take a look at a couple more example problems. Let me know if you have any questions