Question Video: Explaining Why One Current on a Graph Is Not the Rectified Version of Another Current Physics

The red line shows an alternating current. Which of the following best explains why the black dashed line does not show this current rectified? [A] The black dashed line represents a current that reverses direction. [B] The black dashed line represents a different current amplitude from the solid red line. [C] The black dashed line shows zero current at some instance where the red solid line indicates maximum current.

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Video Transcript

The red line shows an alternating current. Which of the following best explains why the black dashed line does not show this current rectified? (A) The black dashed line represents a current that reverses direction. (B) The black dashed line represents a different current amplitude from the solid red line. (C) The black dashed line shows zero current at some instance where the red solid line indicates maximum current.

On our graph, the red solid line indicates an alternating current. We can see this because over some intervals of time, this current has a positive value, indicating it’s moving in one direction in a circuit. Over other time intervals though, the sign of the current changes to negative, meaning that it’s reversed direction in the circuit. Along with the red line, we have the dashed black line. And we want to pick which reason best explains why the black line does not show the rectified current version of the red line.

Current rectification, we recall, involves ensuring that a current always points in the same direction. In the case of the red solid line indicating alternating current, this current would be rectified if all of the negative values of current were inverted about the time axis. We can see that the rectified version of the red line does not match up with the black dashed line. Answer option (A) says that this is because the black dashed line represents a current that reverses direction. We see though that the black dashed line always has a nonnegative value, because this current is positive but never negative. That means it never actually does reverse direction.

Answer option (B) says that the black dashed line is not the rectified version of the red solid line because the black dashed line represents a different current amplitude from the solid red line. The amplitude of a wave, we can recall, is the maximum displacement of that wave from equilibrium. For both the red solid line and the black dashed line, that equilibrium is represented by the horizontal time axis. The maximum displacement of the red line from equilibrium is given by the length of this blue arrow. We see that this length matches up with the maximum displacement from equilibrium of the black dashed line. So, actually, the black dashed line and the red solid line both have the same amplitude. We won’t choose answer option (B).

This leaves us with option (C), which says that the black dashed line shows zero current at some instance where the red solid line indicates maximum current. Let’s consider the two points on our graph where the black dashed line indicates zero current. That’s right here and right here. At these two moments in time, the magnitude of the red solid line is at a maximum value. This is just one example we can see of a point in time where the black dashed line does not line up with the rectified red solid line. For our answer, we’ll choose option (C).

The reason that the black dashed line is not the rectified version of the red solid line is that the black dashed line shows zero current at some instance where the red solid line indicates maximum current.

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