Question Video: Matching Current Output with a Rectified Current Generator | Nagwa Question Video: Matching Current Output with a Rectified Current Generator | Nagwa

Question Video: Matching Current Output with a Rectified Current Generator Physics • Third Year of Secondary School

Rectified current generator I uses multiple current loops offset 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 II? [A] Output A [B] Output B [C] There is no way to tell.

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Video Transcript

Rectified current generator I uses multiple current loops offset 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 II? (A) Output A. (B) Output B. (C) There is no way to tell.

In our graph, we see two current-versus-time curves: one labeled output A and the other labeled output B. We want to figure out which one of these outputs, if we can figure it out, corresponds to what’s called rectified current generator II. Using the descriptions given to us here, let’s make sketches of both generator I and generator II.

Clearing some space on screen, let’s first consider this sketch of generator I. A generator, we recall, is a device that converts mechanical energy into electrical energy. In this sketch, we’re looking end on at four loops in a coil of wire. These loops are rotated by mechanical means. And because the loops are made of conducting material and they rotate within a uniform magnetic field, current is induced in each loop. That current is naturally alternating. That is, it periodically changes direction. However, this component here, a split metal ring called a commutator, makes it so that the current that is finally output from our generator is rectified. That is, it all points in the same direction.

In our problem statement, we were told that each one of these loops is separated from its nearest neighbor by a constant angle. Since there are four of these loops drawn in, we know that that angle is 45 degrees. Generator II is similar to this in the sense that there are also four loops in this generator, but the loops are all in line with one another. The angle of separation between them is zero.

Just like for generator I, the current generated in generator II is rectified. But because the loops in these generators are arranged differently with respect to one another, the overall output current from each generator will be different. We could see this a bit more clearly by imagining a graph that shows us the current generated in each individual loop of our generator.

Say for generator I that this was a plot of the rectified current versus time for one of the four loops. If we were then to plot the current generated by the next adjacent loop in the coil, just as that loop is offset from the previous loop by 45 degrees, so would the current generated be offset from the previous current generated by that same phase difference. The same thing is true for the current induced in the next loop and the fourth and final loop in the coil.

Practically speaking, with the circuit we have set up here, we wouldn’t be able to see a graph like this. Rather, this ammeter would measure the total current generated by all four loops. We find that by adding together all four of these individually generated currents. The overall shape of that resultant curve, not its magnitude but its shape, would follow along with the tops of the peaks of each of these individually generated current graphs. We can say then that this scalloped shape, we could call it, would be the shape of our overall current generated by generator I.

In our question though, we’re asked about generator II and which of these graphs, if we can tell which one, corresponds to the output from that generator. We’ve noted that in generator II, all four of the loops are in phase, we could say, with one another, separated by zero degrees. Therefore, if the rectified current generated by any one of these four loops looked like this, then the current generated in any of the remaining loops would look the same way. Therefore, when our ammeter essentially adds all four of these individual currents together, it will display over time an amplified version, we could call it, of this graph. That is, it would look something like this.

We see then that we can match up the output of generator II with one of the outputs on our graph. It corresponds with the red line that’s labeled as output B. What’s important with this red line is not where it starts at a time value of 𝑡 equals zero but rather that it climbs all the way up from a current of zero to a maximum current value, thereby demonstrating that the generator used to generate this current had loops of coil that were in phase, we could say, separated by an angle of zero degrees from one another. For our answer, we choose output B. This is the current output corresponding to rectified current generator II.

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