Video Transcript
The motion of an alternating
current generator at the successive instants π‘ one, π‘ two, and π‘ 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 π‘ one and π‘ 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 π‘ one, π‘ two, and π‘ 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 π‘ one and π‘
three. To start with, letβs figure out
which points on the time axis of our graph correspond to the instants shown. We know that π‘ one is the first
instant shown, and π‘ three is the last instant shown.
Looking at the images, we can see
that the instant π‘ two occurs approximately halfway between π‘ one and π‘
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 thereβs no change in the flux through
the loop, there is no current. So at π‘ three, the current is
zero.
Looking back at our graph, we see
that the black and green lines both show zero current at π‘ three, which means that
the red and blue lines cannot show the correct output of the generator because they
show a maximum current at π‘ three. Since weβve already looked at when
the loop is perpendicular to the magnetic field, letβs now look at when the loop is
parallel to the magnetic field, which occurs at π‘ 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 weβre looking for the line that
shows a maximum current at π‘ one.
Looking at the graph, our choices
are either the green line or the red line. However, weβve already rejected the
red line since the red line isnβt zero at π‘ three. Therefore, the only line that shows
a maximum current at π‘ one and a zero current at π‘ three, and therefore the only
line that could correctly show the output of the generator based on our images, is
the green line.