Question Video: Comparing Input Power and Output Power for a Non-Ideal Transformer Physics • 9th Grade

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_𝑤)_𝑝 and the output power (𝑃_𝑤)_𝑠? Assume that the two axes are drawn with the same scale. [A] Graph (A) [B] Graph (B) [C] Graph (C) [D] Graph (D)

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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.

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