In this lesson, we’re learning about electromagnetic induction in generators. We’ll see just how it is that generators use this process of electromagnetic induction to convert mechanical energy to electrical energy.
To start out, let’s recall a bit about just what electromagnetic induction is. We know that if we have a loop of conducting wire and a permanent magnet and we move the permanent magnet through the loop, then a current will be induced to flow in that wire. We saw that the reason this happens, the reason current started to flow in the loop, is that the magnetic field experienced by the cross section of the loop changed. And while that field is changing, current is induced.
We can write out then a statement of what electromagnetic induction is. We can say that electromagnetic induction occurs when the total magnetic field that’s passing through a conducting loop changes. And this leads to an induced voltage in the loop and therefore current flow in the loop.
Based on this definition of the total magnetic field passing through a conducting loop, we see that there are actually two parameters that we could change in any given scenario to induce voltage and therefore current. We could change the magnetic field experienced by a loop, like we did over here by moving our magnet. Or, as an alternative, we could keep our magnet stationary and change the size of the loop.
If we either increase that size or decrease it, so long as the total area of the loop is changing, in even a constant magnetic field, then that means the total magnetic field passing through the loop is changing. And therefore, current is induced.
One more thing to see about this idea of changing the area of the loop is we can keep the loop the same but change its area relative to the magnetic field by rotating the loop around some axis. In fact, this idea of turning a loop so as to change the area exposed to a magnetic field is behind many of the power-generation systems we see.
To understand that better, let’s talk now about generators. We mentioned earlier that a generator is a device for converting energy from mechanical to electrical. As a side note, this is opposite the way a motor works. A motor takes electrical energy and converts it to mechanical energy. But anyway, many generators, such as this one here, operate by the principle of electromagnetic induction.
If we were to take the cover off this generator to see the inner workings, on looking inside, we would see that this hand crank is attached to a coil of wire that can rotate around an axis through its center. This coil is positioned between the poles of a permanent magnet, north and south, which means that as the coil rotates, it’s rotating through a magnetic field. The wire that makes up the coil is in constant electrical contact with two metal rings. Through this contact, current generated in the loop is transmitted to the load circuit and the bulb lights up.
So overall, in this process, we have energy input as mechanical energy, the energy that we put in the turning the hand crank. And then through the process of electromagnetic induction, this is converted to electrical energy to light the light. Let’s look more closely now at this process to see just how it is that this energy conversion takes place. As we do, it will be helpful to get a bit of a different vantage point on this generator.
Let’s say that, rather than looking at it from this direction, we place our eye out along this line here along the axis of rotation of the coil. Looking at it from this perspective, we see the north pole of the magnet over here, the south pole over here, and in between the two we see the coil arranged like this, horizontally. And since we’re looking at the coil end on, that’s why it looks like just a flat line. But actually, it’s this rectangular coil we see here.
Now we’re actually going to look at our coil in several different orientations, not just when it’s flat. Just to visualize it more clearly, let’s slide the south pole of our magnet farther to the right. Okay, now we’ve drawn our coil by taking a snapshot of its position at one instant. But we know that the coil overall isn’t stationary. While the hand crank is being turned, the coil is constantly rotating with it, counterclockwise from this perspective.
As it continues rotating, after it’s been through a 90-degree rotation, our coil will look like this. And then in 90 more degrees, it will look like this, the same as original but now flipped or upside down. Then 90 degrees of rotation later, it will look like this. And finally, it will look flat again but this time will have gone through one complete 360-degree rotation.
To show that this coil is rotating, we could draw in area vectors. Those vectors could indicate to us that the coil indeed is rotating as we move from left to right in the sketch. As our conducting coil rotates in a magnetic field, we know that voltage and then current are being generated in it, because this light bulb is being lit as we turn the hand crank. In fact, we can overlay a plot of the voltage generated in the coil — we’ll call it 𝑉 — versus the angle — we’ll call it 𝜃 — of the coil.
What we’re saying is that, for different orientations of the coil, like we’ve drawn here, different potential differences are generated in it. And this all happens because of electromagnetic induction. To see what these voltages are, let’s start by considering our initial coil orientation, flat, horizontally arranged.
We see that if we sketch in our magnetic field lines pointing from the north pole of the magnet to the south pole, then when our coil is flat, when it’s horizontal, none of those field lines pass through the coil. They can’t because the area exposed to them is zero.
At this point, it’s helpful to remember our definition of electromagnetic induction. That definition told us that voltage is induced in a conducting loop when there is a change in the magnetic field it experiences. That word “change” is critical here. It means that what’s important is not the instantaneous position of our coil, but rather how it’s changing in time and how that affects the magnetic field it’s exposed to.
When our coil is oriented this way and rotating, as we know, counterclockwise, then we could say that, over a very small time interval, the orientation of the coil is changing from this to this. Just so the effect is visible, we’re really exaggerating the rotation of the coil that would actually occur over a very small time interval. But the point is that, in the top case, the magnetic field lines move through the coil in one direction, whereas in the bottom case they move through the coil the opposite way. That is, we could say that the magnetic field line up top is moving through the coil front to back, whereas in the bottom sketch, it’s moving through the coil back to front.
To give a bit of a clearer sense for that, if we color-code the two different sides of the coil, notice that, up top, the magnetic field line moves through the green side, whereas on the bottom sketch it moves through the gold side. All this to say, over the time interval indicated by the coil shown here, the magnetic field moving through the area of the coil is changing drastically, as rapidly as it ever will. Since the magnetic field through the coil is rapidly changing, that means a large amount of voltage is induced in the coil. For this orientation then, the magnitude of voltage induced in the loop will be the greatest it ever gets.
But there’s one more thing to notice. Based on the direction of what we’re calling the area vector of this loop, we can actually call the voltage induced in the coil negative. The reasoning behind that isn’t important for now. At this point, all we need to know is that the voltage induced in our coil is very large and it’s a negative value. So let’s plot this point out on our graph. We won’t assign values on the vertical axis. But we’ll just put this data point there to represent the voltage induced here.
Having figured that out, let’s let this coil continue to rotate through 90 degrees until it’s oriented like this, vertically. In this case, if we look at the change in the magnetic field through this loop as it moves through a very small time interval, if we once more exaggerate the angle that the loop would rotate through, it would look something like what we see here. In this case, because the magnetic field lines are moving through the same side of the loop, the gold side as we’ve colored it, and that that loop area barely changes as we go through this rotation, that means the total change in magnetic field experienced by the loop is really quite small.
In fact, when the coil is arranged this way, that value is approximately zero. So we can go up to our graph and plot that point. We then move on and let our coil rotate through 90 more degrees. At this moment, the instantaneous change in the orientation of the coil with respect to the field looks a bit like this.
Notice that, in our top sketch, the field line goes through what we’ve colored the gold side of the coil. But in the bottom sketch, it goes through the opposite side, the green side. This indicates a drastic change in the magnetic field experienced by the coil and this orientation. And this time, the voltage induced at that point will be positive. The magnitude of that induced voltage though will be the same as the magnitude as our original data point.
To plot this data point then, we’ll go up vertically the same distance we’ve gone down vertically to plot that original point. And we’ll locate this data point right there. Moving on, our coil keeps rotating through another 90 degrees. And now it’s vertical once more. Over the very small time interval, around this instant in the coil’s position, we can see that, at both ends of this time interval, the magnetic field lines from the magnet move through the same side of the coil. Once more, the change in exposed area of the coil to the field lines is very, very small. And therefore, the change in magnetic field through the loop is also quite small.
Just like before, when we had a vertically oriented coil, the induced potential difference in this coil is effectively zero. We plot that point on our graph and then we move on to the last position of the coil. Take a look at the direction of what we’re calling the area vector on this orientation. See that it matches the initial area vector. That means our coil has now been through a full 360-degree rotation. And, actually, finding out the voltage induced in this particular orientation of the coil will go quickly because it will be the same as the voltage induced when the coil had that same orientation earlier. So we find that same vertical point on our graph and plot our data point here.
Now that we have all these data points for the voltage induced in our loop, given certain orientations of that loop, let’s connect them with a line of best fit. It’s very important to know that the line of best fit will be a sinusoidal curve. That’s a fancy sounding word which means it will look like a sine curve. It will have a sine shape. The curve then looks like this.
And now that we have this curve, it means that we can figure out the voltage induced in our rotating loop for any angular orientation of that loop between zero and 360 degrees. One thing to realize, this graph we’ve created is for a single rotation of the coil. But of course, it keeps going and going and going as the hand crank is turned. So really, this line of best fit could extend out in the same sine shape to the right and to the left.
Now given this curve, let’s think for a moment. We know that this is a plot of the voltage induced in our rotating coil. But of course, it’s not the voltage that lights up this light bulb but the current is necessary to pass through the bulb in order for that to happen. So what then would a graph of the current generated by this generator look like?
It turns out that because voltage drives current and because our circuit here just has a single resistor, the light bulb, that the graph of the current versus angle will look very much like the graph of voltage versus angle. That graph may well look like this. Notice we haven’t marked out the values on the vertical axis of either of these two graphs. The point here is that these two graphs line up. They’re in phase, meaning that the troughs of the one line up with the troughs of the other and the peaks of the one graph line up with the peaks of the other. This means that when voltage in the circuit is at a maximum, so is the current. And when voltage is at a minimum, so is the current.
As we look at this graph of current, notice that some of the current is positive above the horizontal axis and some is negative. This means that the current induced in our circuit is constantly changing direction. One minute it’s flowing clockwise, and the other minute it’s flipped around and going the opposite way. The name for current that does this is alternating current or AC.
In some electrical circuit applications, alternating current is exactly what we want. But in other cases, we want the current always to be moving the same direction around the loop. We don’t want it reversing direction back and forth. It’s possible to make a modification to our generator here in order to ensure that the current generated always does flow in the same way. That modification involves taking our two metal rings here — what are called slip rings — and combining them into one split ring. This ring literally looks like two halves of a ring brought near to one another. The name for this split ring is a commutator. The function of the commutator is to make sure that even though the current generated in the rotating coil is AC, by the time it gets to the load circuit, it’s been converted to DC. That is, it always moves in the same direction.
So if we said that our plots of current and voltage versus angle were plots of those values in what we’re calling the load circuit, the circuit with the bulb in it, then putting our commentator into the generator would change these curves like this. All of the portions of these graphs which used to be negative, which used to be below the horizontal axis, have been flipped or rectified above that axis.
Looking at our graph of current then, see that the current is now always nonnegative. It does get to zero sometimes, but it never crosses into a negative value. That means the current is always moving in the same direction through our load circuit. And that’s been accomplished by using a commutator in our generator.
By the way, that term “generator” is usually associated with AC, alternating current, output. When we do put a commutator in and convert the output to DC, direct current, then instead of a generator, the device is often called a dynamo. One way to remember that is dynamo corresponds with DC, and so generator corresponds with the other current type, AC.
And one last bit about vocabulary. When an AC signal, such as the one we originally had for our current, is turned into a DC signal by the insertion of a commutator, we say that that signal has been rectified. That’s the way of saying that all the negative values have been flipped around the horizontal axis so they’re now positive.
Let’s take a moment now to summarize what we’ve learned about electromagnetic induction in generators. In this lesson, we were reminded that electromagnetic induction is when a changing magnetic field in a conducting loop induces voltage and therefore current in the loop. Then we saw that generators use electromagnetic induction to convert mechanical energy into electrical energy. We learned that generators produce AC output, alternating current, that would look like this on a graph. While a device called a dynamo, which uses a commutator, produces rectified DC output that looks like this, where in this case all the current values are nonnegative. They’re either zero or positive.