Video Transcript
Rectified current generator I uses multiple current loops at different angles from their common axis of rotation. Rectified current generator II uses the same number of loops but all at the same angle. Both generators rotate at the same rate in the same magnetic field. The following graph shows the outputs of both generators. Which output is that of generator I? (A) Output A. (B) Output B. (C) There is no way to tell.
On this current-versus-time graph, we see two outputs, one labeled output A and the other labeled output B. We want to find which of these outputs, if we can find it out, corresponds to that of generator I. Based on the descriptions given to us, let’s draw our sketches, both our rectified current generator I and rectified current generator II.
A generator, we recall, is a device that converts mechanical energy into electrical energy. This typically happens by a mechanical arm rotating a coil of wire between the poles of a permanent magnet. In this sketch, we imagine seeing these individual loops of wire end on. As the loops rotate through a constant magnetic field, current is induced in them. By the nature of this setup, the induced current is alternating current. It periodically reverses direction. But if we connect the output current leads to a commutator, a split ring that rotates with the coil, then the current output over time by this generator would be direct current. That is, it would be rectified.
In the case of generator I, we have a number of loops. Here, we have one, two, three, four loops of wire that are offset from their immediate neighbors by a constant angle. This is in contrast to generator II, which uses the same number of loops as generator I, but they’re all in a line, at the same angle. Generator II is also a rectified current generator. And recall that we want to see if we can figure out which of these two outputs, output A or output B, in our graph corresponds to the output from generator I.
We’ve drawn each of our generators as having four distinct loops in their coils. Current will be induced in each one of these four loops. That induced current is naturally alternating as the coil rotates through the magnetic field. But then, it is rectified by the commutator before being read by the ammeter in each circuit. The fact that current is rectified in both cases means that our current-versus-time graph will show no negative current values. What will be different between the currents that are generated in each individual loop in our two generators is the phase relationship between them.
Note that in generator I, each one of the four loops is separated from its nearest neighbor by an angle of 45 degrees. This means that the alternating currents generated in these loops will be offset from one another by that same phase difference of 45 degrees. If we could somehow separate out the current generated by each individual loop in our first generator, after it’s been rectified, the current induced in each of the four loops would look something like this. Between each one of these colored curves, there’s a 45-degree phase difference.
On the other hand, if we could look at a similar curve for the output of generator II, there would be no such phase difference for the currents generated in each of the four loops. As we’ve seen, this is because in generator II all four of the loops have a zero-degree angular difference between them. The outputs we see in our graph, output A and output B, correspond to the sum of all of these currents in the case of generator I and the sum of all of these currents in the case of generator II.
For generator II, the overall summed output will have a shape that is similar to the shape of each of the individual inputs. For generator I though, the overall shape of these currents summed together will be similar to a curve that follows along the top of each one of these four individually generated currents. We can see then that for generator II, the total summed current will retain the full rise and fall of the amplitude of this wave, while for generator I, the changes over time in the overall current generated will be smaller.
At this point, we can now match up the outputs from generator I and generator II to output A and B in our graph. Following the overall shape of the current generated by generator II, we see that this is a match for the red line. Correspondingly, the overall shape of the current generated by generator I is a match for the black line. The black line on our graph is labeled as output A. And we therefore know how to answer this question. The output current corresponding to the output of generator I is labeled as output A.
