Video Transcript
If a motor was connected to a direct current source without using a commutator, which of the following would occur? (A) The motor would not turn at all. (B) The direction of the rotation of the motor would periodically reverse. (C) The motor would turn at different average angular speeds in the two halves of one of its rotations.
To answer this question, we′ll start by drawing a diagram. This diagram shows us a normal motor. This rectangle in the middle is the coil. These two blocks either side of it form the north and south poles of the magnet. Then we have two brushes, one connected to the positive terminal of the motor circuit and one connected to the negative terminal. And our final component is the commutator. The commutator rotates with the coil and makes sure that the left-hand side of the coil is always connected to the positive terminal, and the right-hand side of the coil is always connected to the negative terminal. The combination of the current through the coil and the magnetic field across it creates a force on each side of the coil, and this causes the motor to rotate.
What we notice here is that the direction of the force depends on the direction of the current. So here on the left-hand side of the coil where the direction of current is into the diagram, the force is downwards, whereas on the right-hand side of the coil where the direction of current is out of the diagram, the force is upwards. If we let the coil rotate, we see that the forces on each side of the coil are the same, and this continues right up until the point where the commutator splits in two.
When the coil rotates past this point, the half of the commentator that is in contact with the positive and negative terminals switches. This means that the direction of current inside the coil itself has reversed, so the direction of current on this side of the coil is into the diagram and on this side of the coil is out of the diagram.
This also causes the direction of force to reverse, meaning the force on this side of the coil is now downwards and on this side of the coil is now upwards. And this allows the coil to keep rotating in the same direction it was before, which in this case is anticlockwise. And this is the key function of the commutator. And it means that whichever side of the coil is on the left-hand half of the motor experiences a force in one direction, in this case down. And whichever side of the coil is on the right-hand half of the motor experiences a force in the opposite direction, which in this case is upwards.
So what would happen if we didn′t have a commutator? Let′s imagine an identical motor. But instead of having brushes and a commutator, one side of the coil is connected permanently to the positive terminal of the motor, and the other side of the coil is permanently connected to the negative terminal. At the start of its motion, this is identical to a normal motor. The direction of current through the coil is into the diagram on the left and out of the diagram on the right. As we saw before, this will result in a force on each side of the coil, so the motor will begin to turn.
At this point, we can look at option (A), which states that the motor would not turn at all. We′ve shown that this is incorrect, so we can rule this out. In actual fact, our modified motor with no commutator would behave identically to a normal motor up until the point where the coil passes through the vertical. At this point, the direction of current in the coil wouldn′t reverse as these wires would cross over. So the direction of current on this side of the coil is still out of the diagram and on this side of the coil is still into the diagram. This means the direction of force on each side of the coil does not change. However, the coil that was rotating anticlockwise now has forces resisting this. And eventually, the direction of rotation of the coil will actually reverse.
Once again, the coil will continue to rotate until it passes through vertical. At this point, the forces would once again resist the motion. And eventually, the direction of motion would reverse again. This behavior is known as oscillation, where the motion of the coil reverses periodically. This lines up nicely with option (B), which states that the direction of rotation of the motor would periodically reverse. We have shown this to be true, so this is a good candidate for being the correct option. Option (C) states that the motor would turn at different average angular speeds into two halves of one of its rotations.
To work out if this is true, we can use the following equation to work out the force on each side of the coil. It states that the force on one of the sides of the coil is equal to the magnetic field strength multiplied by the current in that side of the coil multiplied by the length of that side of the coil. Now, in our modified motor, the magnetic field strength is constant. Without a commutator, the current in the coil is constant and the side length of the coil is constant. Therefore, the force on each side of the coil is constant throughout its motion.
If we assume there is no friction in the motor, then the two halves of one of the motor′s rotation will be symmetric. That means that if we start the motor from this position, it will rotate to the mirror image of this position before rotating back. And even though it is rotating in opposite directions, the average magnitude of its angular velocity will be identical. Option (C) states that the motor will turn at different average angular speeds in the two halves of one of its rotations. We now know that this can′t be correct. The average angular speed of the coil in the two halves of one of its rotations will be identical. Therefore, we can rule out option (C).
We′ve ruled out options (A) and (C), and we′ve shown that option (B) is correct. Therefore, if a motor was connected to a direct current source without using a commutator, the direction of the rotation of the motor would periodically reverse. Option (B) is the correct answer.
