Question Video: Identifying the Output of an Alternating Current Generator | Nagwa Question Video: Identifying the Output of an Alternating Current Generator | Nagwa

Question Video: Identifying the Output of an Alternating Current Generator Physics • Third Year of Secondary School

The motion of an alternating-current generator at successive instants 𝑑₁, 𝑑₂, and 𝑑₃ 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 𝑑₁ and 𝑑₃? Green arrows represent induced current.

02:19

Video Transcript

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

In order to answer this question, let’s recall how induced current works in a coil like this. The current induced in the coil by a magnetic field is maximum when the plane of the coil is parallel to the magnetic field lines. From looking at this diagram, we can see that the figure at time 𝑑 two corresponds to this position, because the magnetic field lines go from north to south. This means that the maximum possible induced current occurs at time 𝑑 two, and since 𝑑 two occurs between 𝑑 one and 𝑑 three, the order in which these three times occur on the horizontal axis of our graph will look like this.

Since the induced current must also be at its maximum at time 𝑑 two, that specific instant must correspond to the very center of the graph. The time 𝑑 two cannot appear at either of the ends of the time axis because it is not the smallest time β€” 𝑑 one is smaller β€” and it’s also not the largest; 𝑑 three is larger. If we look now at the coil positions at the two instants 𝑑 one and 𝑑 three, we see that the coil is angled off of a horizontal line by the same amount in both cases. That is, the coil is the same angular distance away from being horizontal. Therefore, the same magnitude of current will be induced in the coil at these two instants. We should expect then that the graph will show the same current value at these two times.

With this in mind, we can identify likely positions of 𝑑 one and 𝑑 three on the graph. The current at these times must have the same magnitude and must also be indicated by just one of the curves on the graph. Since 𝑑 one is less than 𝑑 two and 𝑑 three is greater, 𝑑 one must be somewhere to the left of 𝑑 two, while 𝑑 three is somewhere to its right. We can now see that the only way for current at 𝑑 two to be a maximum, while the induced current at 𝑑 one and 𝑑 three is equal and also less than that maximum value, is for these times to indicate the curve colored in blue.

The correct option then must be this line. The color of the line on the graph that correctly shows the output of the generator between times 𝑑 one and 𝑑 three is blue.

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