Question Video: Understanding the Output Graph of an Alternating-Current Generator Physics

Video Transcript

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

The three images referenced in the question are these three images at the right. They show the generator in chronological order at times 𝑡 one, 𝑡 two, and 𝑡 three. The question asks us to identify which line on this graph that shows current with respect to time corresponds to the output of the generator, as shown in these three images, between 𝑡 one and 𝑡 three. To start with, let’s figure out which points on the time axis of our graph correspond to the instants shown. We know that 𝑡 one is the first instant shown, and 𝑡 three is the last instant shown.

Looking at the images, we can see that the instant 𝑡 two occurs approximately halfway between 𝑡 one and 𝑡 three. To distinguish between our possible choices, recall that the magnetic field between two magnets has a direction from the north pole to the south pole. Now, recall that when the loop of an AC generator is perpendicular to the magnetic field, the flux through the loop is maximized. But the change in flux through the loop is zero. Since current is proportional to the change in flux with respect to time, if there’s no change in the flux through the loop, there is no current. So at 𝑡 three, the current is zero.

Looking back at our graph, we see that the black and green lines both show zero current at 𝑡 three, which means that the red and blue lines cannot show the correct output of the generator because they show a maximum current at 𝑡 three. Since we’ve already looked at when the loop is perpendicular to the magnetic field, let’s now look at when the loop is parallel to the magnetic field, which occurs at 𝑡 one. Recall that when the loop is parallel to the magnetic field, the orientation of the loop relative to the magnetic field is changing. So the change in flux is actually maximized. Where the flux changes maximum, so is the current. So we’re looking for the line that shows a maximum current at 𝑡 one.

Looking at the graph, our choices are either the green line or the red line. However, we’ve already rejected the red line since the red line isn’t zero at 𝑡 three. Therefore, the only line that shows a maximum current at 𝑡 one and a zero current at 𝑡 three, and therefore the only line that could correctly show the output of the generator based on our images, is the green line.