Inductors - Online Tutor, Practice Problems & Exam Prep

Inductors, represented by symbols like a bumpy line or loops, are crucial in circuits as they induce electromotive force (emf) when current changes. According to Lenz's law, the induced emf opposes the change in current, affecting its direction and sign in Kirchhoff's loop rule. For a circuit with an increasing current, the induced emf is negative, while for a decreasing current, it reinforces the magnetic field. The relationship is expressed as ε = −LΔIΔt, essential for analyzing circuit behavior.

Inductors in Circuits

Hey, guys. So we saw how in the last couple of videos, a coil of wire with a change in current can actually induce an EMF on itself. That was self inductance. But sometimes you need to know how these coils of wire behave in circuits. So we're going to go ahead and take a look at that in this video. Alright. So basically, if you place a coil of wire inside a circuit, it's known as an inductor. It's kind of like how we talked about capacitance and then we talked about capacitors and circuits. Then we talked about resistance and then resistors in circuits. Here we talked about inductance. Now, we're going to talk about inductors and how they behave in circuits. So, there are 2 common symbols that you're going to see in your classroom, in your textbooks. You're going to see this little bumpy guy right here, and 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 going to use these loops right here in the context of inductors. Alright? So just be aware that you can see both of those symbols there. It's the same thing. Alright. So because these inductors are circuit elements and we use them in circuits, we need to be able to use Kirchhoff's rules as we go around them in a circuit. Right? So we need to be able to use the loop rule and figure out what the voltages are. Now the first things first, we have to remember that inductors only do something if the current is changing. We saw that for a coil of wire, the self inductance, given by this little letter L is negative L times delta I over delta t. So they relate the current changing to the self-induced EMF. So what happens is if we have this diagram here and the current is constant, then that means that the change in the current over change in time is equal to 0, and there's going to be no EMF. So this inductor right here isn't doing anything because there is no change in the current. So it's only that when you have either an increasing or decreasing current in a circuit, you're going to get some kind of EMF. So we have EMF here, and we have EMF here. But what happens is that it's not just enough to know the magnitude of the EMF, we also need to know the direction and whether it's positive or negative in order to use Kirchhoff's rules. So we've got a battery right here and we've got a current that's going to go in this direction like this. So this is going to be our direction. And whenever we do Kirchhoff's 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 voltages. The problem is that I don't know whether the voltage across this inductor is going to 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 Lenz's law to figure out what the direction is of the induced EMF of the inductor. So let's take a look at this. Right? You have a coil of wire and it's going to generate a magnetic field in this direction. And what happens is 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 Lenz's 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 EMF is on the circuit, it's going to be the opposite of whatever it wants to do. So if it's going in this direction and it's increasing, the induced EMF is going to 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 what happens is that our EMF induced, if the current is decreasing, it actually wants to reinforce the weakening magnetic field. So the induced EMF is actually going to point along that direction. Okay. So it's not about where the direction of the current is. It's about where the current is pointing, and whether it's getting stronger or weaker. Now the thing is if the direction of your induced EMF, and this is the most important part here. If the direction of your induced EMF points along our Kirchhoff 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 EMF is going to be negative for our Kirchhoff's loop. And the same thing goes for the opposite direction. If our loop points in this direction and we have an EMF 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. Alright? So when we use our Kirchhoff's loops, these are the rules that we have to follow. Alright. So let's go ahead and take a look at an example here. We've got Kirchhoff's loop rule for the following circuit, and we're going to 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, then we have a voltage from the inductor, that's going to be v l, and then we have a resistor right here, so it's also going to have a voltage. So what I'm going to do is I'm just going to go ahead and pick a direction for my loop. So I'm just going to 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 going to be in this direction. So that's I. So it means the current is this, and the current is this. And I also know that that current is increasing. So now what I want to do is figure out