### Video Transcript

The red line represents the change in the instantaneous value of the alternating current carried by a conductor. Which of the lines correctly represents the root-mean-square value of the current?

Well, we can start by recalling the formula for determining the root-mean-square value of current, which is one over the square root of two times the peak or maximum value of the current. We can see that the peak current lies about here on the vertical axis. And because the axis is unmarked, let’s just say that the peak current equals one. And yes, the unit of current is the ampere. But here, because we’re not really doing any calculations and we’re only dealing with values of current, let’s just focus on their magnitudes and understand that units of amperes are implied.

Now, to make the vertical axis more readable, let’s mark a midpoint between zero and the peak current. So here is 0.5. And we’ll also mark two more midpoints to be 0.25 and 0.75. Now that we have a scale to compare the values of these lines, let’s calculate the root-mean-square current by substituting one for the peak current in the formula. So the correct root-mean-square value is one over the square root of two, or about 0.71.

Looking back at the graph, we can tell that the yellow line is way too low, at about 0.3 or so. And the black and green lines are closer, but they’re still too low, at about 0.5. Now, the purple line actually looks a bit too high, around 0.8 or so. The correct line has a value of about 0.71, which should lie just beneath the 0.75 mark.

So, by determining the value of the correct root mean square and marking out a scale on the vertical axis, we can tell that it’s the blue line that correctly represents the root-mean-square value of the alternating current.