Video: Finding the Period of an Alternating Current

The graph shows a current in a wire over time. What is the period of the current?

02:41

Video Transcript

The graph shows the current in a wire over time. What is the period of the current?

Okay, so in this graph, we can see that we’ve got the current through a wire on the vertical axis. And we’ve got time plotted on the horizontal axis. This means that as we move towards the right on the graph, we’re going along in time. And we can see the current increasing at first and then decreasing and then increasing again and so on and so forth. Now what we’ve been asked to do is to find the period of the current.

Let’s recall then that for any current oscillating up and down like this, or for that matter, for any wave which is oscillating back and forth at regular intervals, the period is defined as the amount of time taken for one complete cycle of the oscillation. Now, in the graph that we’ve been given, we see a sinusoidal alternating current, which means that it’s shaped like a sine curve. And so, the period of a sinusoidal wave, in this case, the current flowing through a wire, is the time taken for one whole cycle of that sine curve to be completed.

Which in this particular case means that if we start at a time of zero seconds, then the current firstly goes up, increases to its maximum value. Then, it decreases goes all the way back down to zero, but then continues to decrease because the current now flows in the opposite direction and reaches the maximum value in the negative direction, which means the maximum current flowing in the opposite direction. And then, the current continues to change until it reaches zero again.

And by that point, we’ve completed one entire cycle. In other words, it’s the time taken between any point on our wave and the next equivalent point, which will be this one in this case. And when we say equivalent point, we might think that this point here is equivalent to this point here. However, that’s not the case. Because at this point, the current is increasing to its maximum value, whereas at this point of the current is decreasing. And so, the period of oscillation is going to be the time taken for the wave to go from here to here. Which is the time at this point, which happens to be five seconds, exactly between four seconds and six seconds, minus the initial time stamp which is actually zero seconds. And therefore, this tells us that the period of the current is five seconds.

Now, note we could choose to start at any point along the wave. For example, let’s say we started at this peak here. Then, the time taken for an entire cycle to be completed is the time taken for the current to go from here all the way down to the negative value and then back up to the maximum point once again. Which is basically the same as saying that this point is the next equivalent point to this point here. And then, we could work out the time interval between these two points, which would also happen to be five seconds.

Hence, the answer to our question is that the period of the current is five seconds.

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