# Lesson Explainer: Current Rectification Physics

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

A generator is a device that transfers mechanical energy to electrical energy. It does so by applying mechanical force to rotate a coil of wire in a constant magnetic field. The coil rotates through a plane that is perpendicular to the magnetic field, as shown below.

Even though the field is constant, the total magnetic field passing through the coil changes as the coil turns.

Due to this change, potential difference is induced in the coil.

Potential difference in the coil creates a current, which is how the generator transfers electrical energy to an external circuit.

The current induced in the rotating coil will be an alternating current (ac). The current in the coil changes direction every time the coil completes a half-rotation. Thus, the current generated over time appears as follows.

Though the current created by a generator is naturally alternating, many practical uses of electrical energy require a current that always points in the same direction. Such a current is called a direct current (dc).

For a generator to deliver dc, the current it produces is changed through a process called rectification.

Given the alternating current shown above, the rectified output of that current would appear as follows.

Note that rectifying an alternating current does not change the current’s magnitude. Rectification only changes the direction of the current so that it is always the same.

Recall that when a generator produces a current, that current is delivered to an external circuit. The external circuit may connect to the rotating coil of the generator by means of parts called slip rings, as follows.

Slip rings are conducting rings that make constant electrical contact with the ends of the rotating coil. They enable current transfer even as the coil turns, as depicted in the diagram below.

Each slip ring is fixed to one terminal of the external circuit. Since each ring maintains contact with the same terminal at all times, slip rings themselves do not affect current direction. Any change in the direction of the current in the coil is passed on to the external circuit.

Slip rings are an effective means of transferring ac to an external circuit. However, to transfer dc, the current must be rectified as it is being transferred.

This is accomplished using a device called a commutator. A commutator is a split ring of conducting material, as shown below.

Unlike slip rings, a commutator rotates with the coil. Each half of the commutator maintains constant electrical contact with one end of the coil.

Consider the following closer look.

Each end of the rotating coil is fixed to one half of the split ring commutator. As the coil and commutator rotate together, electrical contact with the external circuit is maintained by what are called brushes.

The commutator is a ring split into equal halves. For one-half of a rotation, it will contact one brush, and for the other half, it will contact the second brush.

The current in the commutator alternates direction, just as it does in the coil. However, the rate of this alternation matches the rate at which the commutator switches electrical contact with either end of the external circuit.

The net effect is that even though the current in the coil continues to alternate, the current in the external circuit always points in the same direction. By this means, the commutator rectifies current.

We now consider the rectified current produced by one complete revolution of the rotating coil.

The magnitude of the current generated depends on the angle of the coil with respect to the magnetic field. We can say that initially, the coil has the following position.

In this orientation, the coil produces no current. This is always true when the coil lies in a plane perpendicular to the magnetic field.

The coil turning through other angles, however, generates current that is then rectified by the commutator.

The rectified current delivered to the external circuit over one full rotation of the coil is shown in the following figure.

Note the orientations of the coil relative to the field that produce minimum and maximum currents.

### Example 1: Identifying Current Output from a Rectified Generator

The motion of an alternating current generator at the successive instants , , and 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 and ? Green arrows represent induced current.

### Answer

From the three images of coil motion, we see that, at instant , the plane of the coil is parallel to the magnetic field, which points from right to left.

Oriented this way, the current induced in the coil reaches its maximum magnitude.

We also see that, at and , the plane of the coil is not parallel to the magnetic field, indicating that the current induced at these instants will be less than the maximum amount.

We can say, then, that the curve correctly showing induced current across the time interval specified will be higher toward the middle and lower toward either end of the curve.

Of our four answer options, the only curve following this description is the blue curve. This is the line correctly showing the generator output between and .

### Example 2: Identifying Future Coil Position and Current Direction in a Generator

The motion of an alternating current generator at the successive instants and is shown in two images. The output of the current is rectified using a commutator. Which of the following images correctly represents the position of and output from the generator at an instant , where ? Green arrows represent induced current.

### Answer

Observing the position of the coil at instants and and noting that these instants are successive (one right after the other), we see that, between these times, the coil has rotated approximately clockwise from our perspective. Furthermore, looking down on the plane of the coil, we see the current pointing clockwise in both instants.

We now imagine advancing time to an instant . Time is as far ahead of as is ahead of —that is, the difference between these pairs of times is the same.

We can therefore picture the coil at as having rotated beyond its position at . Because this rotation is less than , we expect that when the plane of the coil is viewed from above, the current will point in the same clockwise direction as at and .

Reviewing the answer options provided, both B and C appear to meet these criteria. Looking more closely, however, the red- and blue-colored connectors in option B match the order of those given in the problem statement, while those in choice C are reversed.

This reversal indicates the progressive rotation of the coil inaccurately. Therefore, we eliminate option C from consideration and choose option B as our answer.

Even when current is rectified so it points in the same direction, the magnitude of output current may vary significantly, as shown below.

To “smooth out” the rectified current produced by a generator, the following approach may be adopted.

Recall that induced-current magnitude is greatest when the plane of the rotating coil is parallel to the magnetic field and smallest when perpendicular to that field.

Consider a set of four identical coils arranged at to one another.

Each of these four coils will experience induced current as the apparatus turns, and each will contribute to an overall current generated.

Because none of the coils lie in the same plane, each will generate current with a different phase than the others.

In the following graph, the red, green, blue, and purple curves represent the rectified current generated in each individual coil.

At any given time, we find the total current generated by adding together the red, green, blue, and purple curve values.

In the following figure, these values are combined at two time values.

At each instant, the black dot is the sum of the red dot values. The black dots lie along the black curve, indicating that this curve represents the total current generated at all times shown.

This summation can be shown more explicitly in the following figure.

Note that current magnitude varies less over the black curve than over any of the others. If even more coils were added at intermediate angles, the total current curve would be flatter still.

Let us study a related example.

### Example 3: Identifying the Alternating Current Output of a Generator’s Coils

A rectified alternating current generator contains four coils that are aligned to each other at equal-interval angles, as shown in the diagram. The graph shows the output of the generator, where the red, green, blue, and purple lines correspond to the output of the individual coils. The origin of the graph corresponds to the loops occupying the positions shown in the diagram.

1. Which loop’s output corresponds to the blue line?
2. Which color line corresponds to the total output of all the loops?

### Answer

The blue line reaches a maximum value at . The four coils in the diagram are shown at this instant. We know that a coil with its plane parallel to an external magnetic field will generate a maximum current magnitude at that instant.

The coil with this orientation at is labeled IV. This is the loop whose output corresponds to the blue line.

The total current output of all the loops equals the sum of the individual currents generated. The curve of this combined output is given by adding the red, blue, green, and purple curves together at each instant in time. Therefore, the orange line shows the total output of all the loops.

### Key Points

• Alternating current generators can output direct current through the process of current rectification.
• Rectifying such a generator’s current requires the use of a split ring commutator, or commutator for short.
• Induced current is greatest in magnitude when the plane of a coil is parallel to an external magnetic field and least in magnitude when it is perpendicular to that field.
• Output current can be “smoothed out” by using multiple coils oriented at fixed angle differences from one another.

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