### Video Transcript

For a nonideal transformer with the
same number of turns for its primary coil and its secondary coil, which of the
following represents the relation between the input power 𝑃 sub 𝑤 𝑝 and the
output power 𝑃 sub 𝑤 𝑠? Assume that the two axes are drawn
with the same scale. Is it graph (A), (B), (C), or
(D)?

This question is asking about the
input and output power for the coils of a nonideal transformer. Even if we’ve only ever learned
about ideal transformers, we can still use that knowledge to make some reasonable
conclusions about a nonideal transformer.

To begin, let’s recall that with an
ideal transformer, no energy is lost when transferred from the primary, or input,
coil to the secondary, or output, coil. It’s worth noting that by saying
energy is lost, we mean it gets dissipated, or wasted to the surroundings, so that
it’s no longer useful to the transformer. Since an ideal transformer is
perfectly efficient, we can say that the input power is equal to the output
power.

The thing is, though, an ideal
transformer like this does not exist in real life. So more realistically, for a
nonideal transformer, there is some amount of energy that’s dissipated, typically in
the form of heat. Because of this, the power for the
primary and secondary coils are not equal. Rather, the input power is greater
than the output power. This is strictly true. Even if we were to increase the
power supplied to the primary coil, the power in the secondary coil would also
increase, but it would still always be less than the input power due to the fact
that some energy is lost during the transfer.

Keeping this in mind, let’s look at
the answer options. We need to choose a graph that
always obeys this relationship: 𝑃 in is greater than 𝑃 out. Now, this question uses a different
notation to represent the input and output, or primary and secondary, coils’
power. So to avoid confusion, we can just
make a note that each graph’s horizontal axis represents the input power, and the
vertical axis represents the output power.

Now let’s start by looking at
option (B). We were told that the vertical and
horizontal axes have the same scale. So since this plotted line makes a
45-degree angle with the horizontal axis, it shows the input and output power as
having a one-to-one ratio. Therefore, this graph suggests that
the input and output power are equal, but we know this can’t be true of a nonideal
transformer. We should eliminate option (B).

Next, we can quickly rule out
option (D) because the graph shows the output power decreasing as the input power
increases, which would make for a pretty lousy transformer. Let’s eliminate this option.

Moving on, option (A) shows the
output power as greater than the input power. This isn’t even theoretically
possible, as it would violate the law of conservation of energy. For a nonideal transformer, we know
that the output power must be less than the input power. So we should eliminate this option
as well.

That leaves us with option (C). We know that this must be the
correct graph because it’s the only one that shows the output power as less than the
input power due to the energy dissipated during the transfer. Thus, option (C) is the correct
answer.