Lesson Video: Current Rectification Physics

In this video, we will learn how to describe the use of a commutator in converting the output of an alternating-current generator into a direct current.

15:42

Video Transcript

An alternating current generator produces current that switches periodically between two different directions. In this lesson, we’re going to learn about a mechanical device called a commutator. When an AC generator is connected to a circuit through a commutator, the commutator rectifies the current so that it always has the same direction in the circuit, even as the current changes direction in the generator. To understand how commutators rectify alternating current, let’s start by reviewing the operation of a simple alternating current generator.

A simple alternating current generator consists of a wire loop rotating in a uniform magnetic field between two magnets. As the loop rotates, the total magnetic field passing through the loop, also known as the magnetic flux, changes with time, which induces a current in the loop. Now, recall that in a particular circuit, current can have one of two possible directions. So we can represent a current with a positive or negative number where the size of the number corresponds to the strength of the current and the sign of the number, positive or negative, corresponds to its direction. If we use this to draw a graph of the current induced in our generator with respect to time, we get a graph that shows the current periodically switching between a most-positive and a most-negative value and then back again to most positive.

Note that whenever the current is positive, it has one direction. And whenever the current is negative, it has the other direction. The switch between these directions happens anytime the current passes through zero since the current has a different sign just before and just after these times. To better understand how to rectify this current, we’ll need to know the orientation of the loop relative to the magnetic field every time the direction of the current changes. It turns out the orientation we’re looking for is when the loop is perpendicular to the magnetic field. To see why this is true, consider a side-on view of the magnetic field.

When viewed from this angle, the loop appears to be a single line because the depth of the loop is a longer direction of vision. Here we’ve drawn the loop at some particular instant in time, where it’s cutting across three magnetic field lines. Now let’s watch what happens as the loop rotates. At this time, the loop is now perpendicular to the magnetic field. As we can see in the diagram, with the loop perpendicular to the magnetic field, it now cuts across five field lines instead of only three like before. In other words, in completing this portion of the rotation, the flux through the loop has increased. However, as the loop continues to rotate, it will now rotate away from its position perpendicular to the magnetic field.

The result is that the loop, now represented by this dotted line, will only cut across three field lines again. So the flux through the loop has decreased. To connect these changes in flux to the alternating current, let’s use this top edge in our 3D diagram as a reference. In our 2D diagram, this reference edge would appear as a green dot at one end of the loop. By choosing this reference, we can now unambiguously say that the increase in flux on the left side of our diagram represents a positive change, while the decrease represents a negative change. The reference allows us to do this because we can now unambiguously say that when the reference edges in the top half of the diagram, the flux through the loop is positive.

However, as the loop passes through the horizontal position, its orientation relative to the magnetic field changes, so the sign of the flux changes. But with our reference, we can now unambiguously say that this means that whenever the reference is in the bottom half of the diagram, the flux is negative. Before finishing up this discussion, it’s worth mentioning how the orientation of the loop changes relative to the magnetic field as it passes through the horizontal position. Here we have two pictures of the loop, one just before and one just after the loop is horizontal. In both pictures, the magenta arrow represents the direction of the magnetic field.

As we can see, before the loop is horizontal, the magnetic field lines pass over the unmarked edge of the loop through the loop and then under the reference edge. However, after the loop has rotated past horizontal, the magnetic field lines now pass under the unmarked edge through the loop and over the reference edge. What this means is that the magnetic field lines now pass through the loop in the opposite orientation. To see this more clearly, we can imagine coloring one face of the plane of the loop blue. Then, before the loop is horizontal, the magnetic field passes through the blue face first. And after the loop is horizontal, the magnetic field passes through the orange face first.

So the orientation of the loop relative to the magnetic field has swapped and the flux changes sign. Anyway, now all we need to do is recall that the induced current in an AC generator is proportional to the rate of change of magnetic flux through the loop. Since we can see that the rate of flux change goes from positive to negative as a loop rotates through vertical, this must also correspond to when the induced current changes signs. Furthermore, the current either changes from positive to negative or from negative to positive. One of these corresponds to the reference edge being up in the diagram, and one corresponds to the reference edge being down. The particulars of which is which will depend on the particulars of our generator.

The important takeaway, regardless of which is which, is that the current induced in an AC generator will change direction any time the loop is perpendicular to the magnetic field. Let’s now use this fact to construct a commutator. Remember, the commutator needs to be a device that will reverse the connections between the generator and the circuit once every half cycle. Every commutator has two basic parts, a ring that’s split into two halves and a pair of brushes, one for each half of the ring. Both the brushes and the two halves of the rings are made of conducting material so they form electrical contact. For the commutators we’ll be considering, the ring will be connected to an external circuit and the brushes will be connected to the wire loop of an AC generator.

Other commutators reverse these connections, where the brushes connect to an external circuit and the ring connects to the loop of an AC generator. But both commutators behave the same way. Here is a diagram showing how a commutator connects between the wire loop of an AC generator and an external circuit with a resistor. Remember, as the loop rotates, current is induced in the loop at the same time as the brushes slide along the inside of the ring. Because the brushes and the ring form electrical contacts, the loop, the commutator, and the resistor form a complete circuit. The current in the rest of the circuit then outside of the wire loop will be towards the commutator on the right, out of the commutator and into the external circuit, through the resistor from right to left, out of the external circuit and back into the commutator, and from the commutator towards the loop on the left.

All right, let’s now see how the current in this setup changes with time. To help us do this, we’ve drawn two graphs to accompany our diagram. One shows the current in the loop with respect to time and the second shows the current in the resistor with respect to time. The horizontal axis in both graphs has the same scale. So corresponding points with the same horizontal position also represent the same time. At the instant of time currently pictured, the loop is horizontal and the green reference edge is towards the left. So the current has its maximum positive value, where we’ve used the green reference edge to help us to find positive and negative current.

If the current in the loop has its maximum value, so does the current in the resistor. And we have chosen the direction of current from right to left through the resistor as the positive direction. We know that as the loop continues to rotate, the current is going to decrease from its maximum value. But let’s see what happens to the brushes and the current in the resistor as this happens. At the instant in time we’re looking at now, the brushes have slid about a quarter of a way around the ring and the loop has gone from being horizontal to being almost vertical.

During this quarter turn, the current in the loop has been decreasing since the current has a maximum value when the loop is horizontal and is zero when the loop is vertical. Although the size of the current has been decreasing, the direction has been constant since the direction of the current changes only when the loop passes through vertical, where, as always, by vertical we mean perpendicular to the magnetic field. As for the resistor, the size of the current in the resistor has been decreasing since the size of the current in the resistor is the same as the size of the current in the loop. The direction of this current is also constant since the direction of the current in the loop is constant, and each of the brushes in the commutator is still in contact with the same half of the split ring.

Okay, now let’s see what happens when the loop rotates just a little bit farther so it’s totally vertical and perpendicular to the magnetic field. At the moment the loop is vertical, the brushes of the commutator are exactly aligned to the nonconducting gap between the two halves of the split ring. Because the brushes are not making electrical contact to the ring in anyways because the current in the loop is zero when the loop is vertical, there is no current through the resistor. Let’s now see what happens as the loop continues to rotate and the current now takes on the negative instead of the positive direction in the loop.

Once the loop rotates past vertical, the current changes direction. Before, the direction of the current was from the brush of the commutator toward the green reference edge. Now the direction of the current is from the green reference edge towards the brush of the commutator. Correspondingly, the current on the other side of the loop is now away from the brush and towards the loop instead of away from the loop and towards the brush. Note, however, that each of the commutator brushes is now making contact to the opposite half of the split ring than it was before. So the direction of the current is still from the brush into the magenta half of the ring and from the blue half of the ring into the brush.

The direction of the current in the external circuit must match the directions we’ve already described for the current in the loop and the commutator. So to have a current with direction from the blue half of the ring towards the loop, we need a current in the external circuit with direction from the circuit towards the blue half of the ring. On the other side, to have current from the loop towards the magenta half of the ring, we also need current from the magenta half of the ring toward the external circuit. Looking at our drawing then, we see that the current through the resistor must have a direction from right to left. So the current through the resistor is once again positive. In other words, it has the same direction as it had before.

The current in the resistor maintains a constant direction because at the same time as the current in the loop is changing directions, the brushes in the commutator are changing electrical contacts between the two halves of the split ring. The result is that the commutator effectively reverses the direction of the current in the loop to keep a constant direction in the circuit. This will continue for the next half-turn with negative current in the loop and positive current in the resistor. Then, as the current again reaches zero because the loop is vertical, the brushes in the commutator will again align with the gap between the two halves of the ring. After this point, the current in the loop will again be positive.

At the same time, though, the brushes will again swap electrical connections between the two halves of the split ring. So the current in the resistor will remain positive. As time goes on, the current in the loop will continue to cycle between positive and negative values. But the current in the resistor will always be positive or zero when the current in the loop is also zero. We call this current through the resistor a rectified current because we’ve taken the alternating current from the loop and converted it into a current that doesn’t change directions. Mathematically, we can see that the graph representing the rectified current is just the absolute value of the graph representing the alternating current. Now that we’ve seen how a commutator rectifies alternating current into a direct current, let’s work through an example.

The motion of an alternating current generator at the successive instants 𝑡 one, 𝑡 two, and 𝑡 three is shown in three images. The output of the current is rectified using a commutator. Which color line on the graph correctly shows the output of the generator between 𝑡 one and 𝑡 three? Green arrows represent induced current.

The three images referenced in the question are these three images at the right. They show the generator in chronological order at times 𝑡 one, 𝑡 two, and 𝑡 three. The question asks us to identify which line on this graph that shows current with respect to time corresponds to the output of the generator, as shown in these three images, between 𝑡 one and 𝑡 three. To start with, let’s figure out which points on the time axis of our graph correspond to the instants shown. We know that 𝑡 one is the first instant shown, and 𝑡 three is the last instant shown.

Looking at the images, we can see that the instant 𝑡 two occurs approximately halfway between 𝑡 one and 𝑡 three. To distinguish between our possible choices, recall that the magnetic field between two magnets has a direction from the north pole to the south pole. Now, recall that when the loop of an AC generator is perpendicular to the magnetic field, the flux through the loop is maximized. But the change in flux through the loop is zero. Since current is proportional to the change in flux with respect to time, if there’s no change in the flux through the loop, there is no current. So at 𝑡 three, the current is zero.

Looking back at our graph, we see that the black and green lines both show zero current at 𝑡 three, which means that the red and blue lines cannot show the correct output of the generator because they show a maximum current at 𝑡 three. Since we’ve already looked at when the loop is perpendicular to the magnetic field, let’s now look at when the loop is parallel to the magnetic field, which occurs at 𝑡 one. Recall that when the loop is parallel to the magnetic field, the orientation of the loop relative to the magnetic field is changing. So the change in flux is actually maximized. Where the flux changes maximum, so is the current. So we’re looking for the line that shows a maximum current at 𝑡 one.

Looking at the graph, our choices are either the green line or the red line. However, we’ve already rejected the red line since the red line isn’t zero at 𝑡 three. Therefore, the only line that shows a maximum current at 𝑡 one and a zero current at 𝑡 three, and therefore the only line that could correctly show the output of the generator based on our images, is the green line.

All right, let’s now review some of the key points that we’ve learned in this lesson. In this lesson, we learned that commutators rectify alternating current. To understand what this means, we first considered a simple alternating current generator consisting of a wire loop rotating in a uniform magnetic field. As the loop rotates, the magnetic flux through the loop changes, which induces a current in the loop proportional to that change. If the loop starts off perpendicular to the magnetic field and we see that the current initially induced is positive, then the current as a function of time looks like this graph.

Note that the current changes periodically between the positive and negative directions. The current changes direction each time the loop is perpendicular to the magnetic field when there is no induced current. If we attached an external circuit to this generator, the current in the circuit would alternate as well. If we instead connect a circuit to a generator through a commutator, the direction of the current in the circuit will stay constant even as the direction of the current in the generator changes. The commutator itself consists of two conducting brushes rubbing along the inside of the ring that is also conducting, but is split into two parts with an insulating gap between each half.

The brushes are connected to the two ends of the generator loop. The two halves of the ring are connected to the two ends of an external circuit. With these connections, the electrical contacts between the brushes and the ring form a complete circuit between the generator and the external components. Since the loop is physically connected to the brushes, as the loop rotates, the brushes rotate as well. As a result of these electrical connections, for one-half of the rotation, the current through the loop is just transferred directly to the external circuit. However, after half a rotation, at the moment the loop passes through perpendicular to the magnetic field, the brushes will switch connections between the two halves of the ring.

The brush that was in contact with the magenta half of the ring will pass over the gap and make contact with the blue half of the ring. And the brush that was in contact with the blue half of the ring will pass over the gap and make contact with the magenta half of the ring. The result of this is that at the exact moment the current in the loop changes direction, the commutator reverses the connections to the external circuit. So while the current has the negative direction in the loop, the current in the external circuit has the reverse of that direction or positive. The next time the current changes direction, the commutator again reverses the connections, which returns the connections to how they were originally.

So the current is again transferred directly from the loop to the circuit and is still positive. This process continues as long as the generator is producing current, and the result is an output current that is always positive or zero, in other words, a current with only one direction. We call this single directional current produced from an alternating current, a rectified current. And finally, we call the commutator, which achieved this rectification, a current rectifier.

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