Here we are in chapter seven. In this chapter, we're going to be looking at inductors, capacitors, and transformers. In this particular section, we're going to be looking at our old friend inductors.

### Inductors

Inductors are another basic building block of electronic circuits. Like resistors, they tend to impeded current flow. Notice they tend to impeded current flow. However, the opposition offered by inductors is different for AC and DC circuits. What we will find is that they offer a great deal more impedance to AC than they do to DC. In fact, with DC we'll find that they offer almost no impedance and that the impedance they offer to AC has a lot to do with what is the frequency that we're sending through that inductor. Inductors may also be called chokes or coils. The term choke refers to how inductors can be used to suppress undesired frequencies. Electromagnetic induction is at the heart of inductor theory of operation.

### Electromagnetic Induction

We're going to look at this thing. What is electromagnetic induction? To illustrate the principle of electromagnetic induction, think of two coils of wire wound on a common core. Here we have a common core and we have two inductors. There's one inductor here, one here. One of them is connected to an alternating current source, so we're sending current through this one. This one is not connected to any voltage source. It is connected to a meter so we can see what is indicated by this coil. We're going to have an induced current in this as a result of what's happening with this one.

The core has high permeability. Permeability is a measure of how easily a magnetic field can be set up in a material. As the current changes continuously in the coil, the magnetic field in the core also changes. Current introduced in one coil will induce a current in the other coil. This is possible because of the moving magnetic field. The thing that causes the movement there, there's no moving parts there, the only thing that's moving is here we have an alternating signal. Once it's going positive we have electrons in one direction, and when it goes negative the electrons are moving in another direction. That is the only thing is moving here, but it is moving and there is a change. The magnetic field is changing and that change is induced into this coil.

### Factors Affecting Induction

Factors affecting this thing we call induction. Several factors determine the amount and polarity of and induced voltage. Probably obvious, the magnetic field strength. Here we have a magnet. Here we have a coil, and the strength of this magnet is going to have a lot to do with how much current is induced in this coil. The rate of relative motion between the flux and the conductor, so how much motion is there between this magnet and this conductor because that will affect how much current there's going to be. The angle of relative motion between flux and conductor, so what is it? Is it coming in from this way? Is it coming in from this way? The angle is going to have something to do with it. The number of turns of wire in the coil so the more turns in this coil the more induction. The direction of relative motion between the flux and the conductor, so what is the direction of the motion between this magnetic flux and this conductor. Also, the polarity of the magnetic field. We've drawn it north and south, but it would be different if it was south and north.

Let's see, let's jump over here too so I can click on this link. We have a little link here. This is an experiment that Faraday did actually in 1831. He was on of the guys that were experimenting with magnetic induction. We have something like what we just saw on the previous screen. Here, we have a battery. The difference is that this just a DC battery; whereas, the other source we were looking at was AC. Notice he has a coil, and here is another coil, and they have a center core here. When this is closed, a current will be induced in this coil and a magnetic field will be induced over here. He connected a compass to this because he wanted to see what would be the effect because remember this coil is going to induce a magnetic field. Let's close the switch and observe this compass. Let's see if I can make that switch close. Let's see, you'll notice that when it closes the magnet goes this way, and when it opens the magnet jumps this way. Now notice it doesn't permanently stay in any position because remember the DC it's current is only going in one direction. When the switch is closed, there is a sudden change in the magnetic field the compass reacts to it, but then it just goes back to its normal position. Then, when it is released, again, there is a change. Notice it went the opposite direction, by the way, because of the coil again it changed. Now was releasing of the magnetic field, but as the magnetic field develops and closes the compass reacted to that.

### Effects of Induced Current

Effects of induced voltage. When a current is induced in a coil by a changing magnetic field, the current creates a second magnetic field. The magnetic field produced by the induced current has a polarity that opposes the change in the original magnetic field. This is called Lenz's Law. What you'll see here is here we have a magnet, and here we have a coil, and there we have a meter, and we're looking at what current is being induced into this coil by the movement of this magnetic field we're looking at right here. Now as this magnet moves close to that coil, we see that some polarity or magnetic polarities develop across this magnet. You'll notice that the north-south is the moving magnet and the coil that is moving toward noticing the fields that develop here. The side closest to the magnet is north. Remember, that two like poles will tend to repel each other. Now, this is going this way, so there is opposition.

There are two things that are going to be inducing current. First of all, there is the movement. That's the most important part, but the opposition is part of it as well. The movement is the biggest part. As this is moving towards this magnet, it establishes this field and that motion induces the current. In fact, the motion is the thing that makes the current happen, is the movement, because when the magnet stops so the current stops as well.

Notice down here, here we have our magnet and when our magnet is moving away notice the polarity switches on this magnet. Remember, this is relative motion. Now the motion is moving away, and now that polarity changed over here, and now it is north and notice the south and the north will tend to attract each other. Again, it is being pulled away. Again, there is opposition here. It would prefer to go this way, but it's going this way. There's an attraction but it's pulling away, and so the poles change direction.

When the poles change the direction, the current changes direction as well. In this top here, the magnet is moving toward the coil, the coil develops a field and we saw the polarity. When it's going away, does just the opposite and it's going one way. It's going toward the coil, current goes one direction when it's pushing away, the coil goes another direction.

Here we have another simulation. This is a simulation of Lenz's Law. This is a magnet. This is a coil. What this is designed to simulate is as this magnet moves there will be magnetic fields that will be developed around this coil. Also, there will be current in this coil. As I press this up you can observe it. You notice the blue circles there that is the magnetic field. You see the little yellow dots here that is the current flowing through this coil. The important thing to observe is that as I'm going up you notice the current is going in this direction, and it goes the other direction it changes. The magnetic fields are moving the other direction and the electrons are going the opposite directions. As you go up, you see it going one way. As you're going down, you see it going the other way. That's exactly what we were depicting right here.

Then, this is just a review of what we just looked at. I've just written it out here. As the magnet motion moves toward the coil, the magnetic field induced in the coil opposes the magnet (North to North), the motion induces a current in the coil. If there was no motion there would be, notice, no current. As the magnet moves away in the lower picture, notice the north-south magnetic field switches. We looked at that on the previous slide.

### Inductance and its Factors

Inductors are merely coils of wire. I'm going to turn this back on. They are merely coils of wire, an inductor. Current flowing through the turns of an inductor will produce a magnetic field around each turn. Any change in the current flow will produce a corresponding change in the magnetic field.

Any change in the magnetic field of a coil will produce a voltage change in each of the turns of the coil and that voltage will be opposing the original change in current. That's the theory that we just looked at.

An inductor opposes any change in current. That is the nature of an inductor, especially AC. The property of an inductor that opposes current flow is referred to as inductance and is represented by a capital letter L. The unit of measurement for inductance is the henry. This is the formal definition of a henry. If current changes in an inductor at the rate of one amp per second and causes one volt of self-induced voltage, the inductor has a value of one henry. We think of one amp of change per second and causing one volt of induced voltage in the inductors we say that an inductor has the value of one henry.

Couple concepts here, and we've already briefly alluded to these. When current changes in an inductor a voltage is induced in the turn of the inductor that opposes the initial change in current. An inductor opposes the change in current. This is the nature of the inductor. It opposes changes in current. Later in this particular chapter, this is poorly drawn, this is supposed to be a capacitor, but when we look at capacitors what we'll find out is that a capacitor opposes a change in voltage and an inductor opposes changes in current.

Physical factors that affect inductance. First of all, the length of the coil. What we'll find is the length of the coil is inversely proportional to the inductance. If you have a very long coil, you'll have less inductance. If you shorten that coil, you'll increase inductance. The cross-sectional area of the coil, how thick is the wires in the coil. It is a direct relationship between the area of the coil like I said the more area, the more inductance. The number of turns. The number of turns is the function of N squared where N is the number of turns, and then you square that and that will be a direct relationship to inductance. The more turns, the more inductance. Here we say times three and since it's squared inductance would be up by a factor of nine. Then, the permeability of the core. The more permeability you have the higher the inductance because the permeability is going to impact the transfer of the magnetic field.

### Inductive Reactance

An inductor in a circuit that has a sinusoidal current will self-induce a voltage that is sinusoidal but opposing the inducing current. The opposition to a sinusoidal alternating current flow is called, and here we have a nice term, inductive reactance. An inductive reactance is measured in ohms, kind of like resistance. The symbol for reactance is nice big X. Inductive reactance is designated X of L. Inductance here, reactants. Inductive reactance is calculated by, and there's a formula for this, it is two pi times the frequency times the inductance where F if the frequency of the sine wave. From the formula, we see that reactance is a function of frequency and inductance. As frequency and inductance are modified, we will see changes in the reactants.

Here is the formula again, and remember reactance is measured in ohms. I have a couple of problems here. This would be a calculation for what is the reactants. We're taking two times pi and I've shortened pi to 3.14 just for simplicity, actually, there's a whole bunch of infinitely number digits here, but we'll just say 3.14 times. Here we have a frequency of 50 KHz. That's 50,000 Hz times, and then our inductance would be 50 mH. If we multiply that out we'd get 15.7 k ohms. That's 15,700 ohms of resistance. Now down here what we've done, we've changed the frequency to 10 Hz. If we multiply this, everything else remains the same. We've just changed the frequency. We've taken it down to a very low value. Notice the results. That now the inductive reactance has taken a dramatic drop. We're down at a very low frequency, down near zero hertz z and notice that our reactants have also dropped down to a near zero value, going from 15.7 K down to 3.14 Hz. Frequency, reactants in a large way is dependent upon what is the frequency going through them. This is why in that introductory section we mentioned that sometimes inductors are used as chokes to filter out certain frequencies, so this would be the case that if you had a frequency you wanted to eliminate an inductor might be used if it was high frequency. Notice what happens, the resistance goes way up and it tends to choke out that particular frequency.

### Phase Relationships

Then, phase relationships. The sinusoidal voltage across and inductor will always lead, notice will lead the sinusoidal current, in this case, 90 degrees. Note that when current is zero when the voltage is at 90 degrees and 270. The greatest change in current will be during the greatest changes in voltage. What are we saying?

Here we have a circuit. We have an alternating voltage across an inductor. What we're saying here is that if we were to set up an oscilloscope to measure this value we would find see the alternating voltage. If we were to measure the current at the same time, we would find that the current is impeded. Remember that an inductor opposes the change in current, and so what we'll find is that the current lags behind the voltage by 90 degrees. What's that mean?

Here we have a sine wave. If we were to measure, in fact, in here if we measured from here to here, that would be 360 degrees. This is actually the current here, and this is the voltage. Let's just say, the voltages from here to here that would be 360 degrees. What we want to look at is notice we said that voltage will lead current by 90 degrees. Here we have a voltage, here we're at the positive peak, and you'll notice that the current is at zero at that point.

In an inductor, remember we looked at that magnetic field and when we had the magnet moving that's when we saw current induced. It's going to be much like that in this situation. When we go from this point, this is from 90 degrees down to 270 is where we have the greatest change in voltage. From here to here we see a lot of change. From this point to this point, you notice that the current, notice we see this change. Remember we started at 90 degrees, and something to observe is at that point there is a point where there is very little change, right in here, the voltage changing almost ceases. It's interesting that when the voltage changes notice what's happening with current, it is almost at zero. Then, when we have this massive change, that's when we see the massive change in current. When we get to this point, again, there is that point where at least momentarily there's no voltage change, look what's happening with the current. Current again has ceased to move. When we move, again, from 270 up to 90, again, we have this massive change going from the negative peak to the positive peak and notice what happens in current. Here we have a massive change in current as well and again we get to the point where there are almost no change and almost no change in current, it's at zero. We're looking at something called phase relationships. This is just the same thing I just talked about.

This is a schematic from Multisim that allows for viewing of the phase shift between voltage and current. I built this with the student version of Multisim. Actually, you have the textbook version. The student version has a little bit more in it. What this is, we have a circuit and notice we have the voltage source and we have it across an inductor. Channel A right directly across the inductor. Channel B I've actually wired it into the circuits so that we'll be looking at current, so you'll notice the path for electrons. It comes up through the ground, through this resistor, and then it goes through the O-scope and then through the inductor. Channel B will be looking at current and channel A will be looking at voltage.

I have recorded a simulation of this circuit and I'm going to be editing it and adding it to this particular presentation when. The switchover occurs it should be seamless. If the audio level switches a little bit you may need to either turn your volume up or turn your volume down.

This is a simulation in Electronics Workbench showing the relationship between voltage and current across an inductor. We had just looked at how the current lags the voltage by 90 degrees in an inductor. This is a simple circuit. We have a signal source here producing a one KHz signal and it is across an inductor. The way this has been set up channel A is across the inductor and channel B has been placed in the circuit. You notice current flow goes through the resistor, goes up into channel B, and then through the inductor and back to ground.

Let's take a look at this signal. I think I'm going to put the Multisim into pause so we can analyze this signal a little bit better. We can drag this over a little ways, and then let's look at the signals. Remember, the voltage is leading the current. Let's see, let's grab another point to look at. Let's look at right there. Notice the voltage at this point right here when it's set at the positive peak it gets close to no change. When there is no change notice what's happening. This is the current right here that we're looking at. Notice the current is at zero when there is no voltage change. When the voltage change is the most profound going from the positive peak to the negative peak, observe what happens in the current. Notice we have this change right here. Then, again, when we get to the negative peak and voltage, again, there's that momentary time when there is virtually no current flow or no voltage change. Notice what happens to current. It just ceases. When we're dealing with an inductor the current is changing in proportion to the changes in the voltage. If the voltage is not changing, the current change in the inductor ceases and there ceases to be current induced in that inductor.

This is the student version of Multisim. You will not have the connections like this with the negative and positive. You'll simply have ground over here in your textbook version of Multisim. If you try to simulate this you may have a little difficulty on your version of Multisim.

This concludes chapter 7.1A.