### Video Transcript

The following graph shows three
lines. Which of the lines corresponds to
the current in the coil of a direct current motor? (A) Line I, (B) line II, (C) line
III, or (D) none of the answers are correct.

In this question, we are given a
graph with three lines corresponding to a current over a period of time. We need to work out which of these
lines corresponds to the current in the coil of a direct current motor.

First, let’s remind ourselves of
what a direct current motor is. Like its name suggests, a direct
current motor uses a direct current to generate mechanical energy. A direct current motor consists of
a coil of wire in a magnetic field. The coil is connected to the direct
current power supply using a commutator and two brushes. When there is a current in the coil
of wire, the coil and the commutator will rotate in the magnetic field. The brushes allow the commutator to
rotate while still remaining in contact with the external circuit.

To answer this question, we need to
work out how the current in the coil of the motor varies with time and how this
would be represented on a graph. We’ve already said that the motor
is supplied by a direct current power source. A direct current does not change in
magnitude or in direction. It simply has a constant value,
which does not change with time. If we were to represent a direct
current on a graph of current against time, it would look like this: a straight,
horizontal line, corresponding to the magnitude of the current, which we’ve labeled
𝐼.

However, we need to be careful
here. This question is not asking us
about the current supplied by the power source. This question is asking us about
the current in the actual coil of the motor. To understand why these currents
aren’t the same, we need to think about what happens at the commutator when the coil
rotates.

To make this easier to picture,
let’s zoom in on the commutator, coil, and brushes of a direct current motor. We’ll also color-code the different
parts, like this. We can see that the pink half of
the commutator is connected to the pink brush, and the blue half of the commutator
is connected to the blue brush. We’ll also color this side of the
coil blue and this side of the coil pink. Let’s also label the current. We’ll say that a direct current of
magnitude 𝐼 is coming in this direction, through the blue brush. If we continue the path of the
current around the coil, we can see that the current passes into the screen through
the blue edge, around, and then out of the screen through the pink edge. The current then passes out through
the pink brush.

Now let’s think about what happens
when the coil has rotated through one half-turn. The brushes don’t move, but as the
coil rotates, the commutator will also rotate. So, the blue brush is connected to
the pink half of the commutator, and the pink brush is connected to the blue half of
the commutator. Again, let’s draw in the path of
the current. The power supply hasn’t changed, so
the current will still come in through the blue brush, around the coil, and out
through the pink brush. However, there’s something
important we need to notice about the current in the actual coil. Let’s compare the direction of the
current in the blue edge of the coil in both diagrams.

In the first diagram, we’ve drawn
our current into the screen. In the second diagram, we’ve drawn
our current out of the screen. So, the current in the blue edge
has actually reversed direction. The same is true of the current in
the pink edge of the coil. In the first diagram, the current
in the pink edge is out of the screen, and in the second diagram, it’s into the
screen. So, the current in the coil has
reversed. This happens because, as the coil
rotates, the connections between the brushes and the two parts of the commutator
switch every half-turn. This causes the current in the coil
to change direction, even though the current from the power supply doesn’t
change. Note that the magnitude of the
current in the coil doesn’t change, only the direction it travels in.

So how would we draw a graph that
shows how the current in the coil varies with time? Well, let’s say that the current in
the coil is initially traveling in the positive direction. We would represent this with a
straight, horizontal line, corresponding to the value of positive 𝐼. However, after some time, this
current reverses, so it begins to travel in the negative direction. The current then becomes equal to
negative 𝐼. We would draw this as a straight,
horizontal line, corresponding to the value of negative 𝐼. The current then reverses again and
returns to positive 𝐼. So, this is what our graph of the
current in the coil should look like: sections of straight, horizontal lines that
alternate between being above the axis and below the axis.

If we look at the graph given to us
by the question, we see that the graph we drew doesn’t match any of the options. Line II is a straight horizontal
line, but it’s always above the axis, meaning it corresponds to a current that only
ever travels in a single direction. So, line II can’t be right. Line I also shows a current that
only travels in the positive direction. This also represents a current with
a changing magnitude. We know this can’t be right
either. Line III shows a current that
periodically reverses direction, but again the magnitude of this current is
changing. So, we can eliminate this option as
well.

So, the correct answer to this
question must be option (D). None of the answers are
correct.