The graph shows a current in a wire over time. What is the frequency of the current?
Okay, looking at our graph, we indeed see that it plots current in amperes versus time in seconds. And as we look at the plot of current, we can see that it oscillates up and down. It starts out at zero, then goes up to a maximum value, then comes back to zero, and then continues on to its maximum negative value, and then comes back up to zero to complete a full cycle of the wave before going on to continue this cycle.
We can see further that half of the time this current is moving in one direction in the circuit, considered the positive direction. But then the other half of the time, it reverses direction into what we could call the negative direction through the wire. Since the current regularly reverses direction in this wire, we can tell that it’s an alternating current. And our question says, what is the frequency of this current in the wire? To figure that out, let’s recall the definition of frequency.
The frequency of some system, be at the current in the wire, like we have here, or the hands on a clock or any regularly repeating process is equal to the number of cycles that system goes through in one second. In the case of this current then, to know its frequency, we’ll need to know how many cycles the current goes through in one second of time. And looking at our horizontal axis, we can see that one second of time occurs right here. So to figure out the frequency of the current in this wire, we want to count the number of cycles the current goes through from zero seconds all the way up to one second. We can see the current goes through a number of oscillations over this time interval. So let’s count them now.
Starting at zero seconds, we have one complete cycle of the wave here. Then, we move on to complete a second cycle of the wave there. And then a third cycle, we start and finish right here. So we’ve passed through one, two, three complete cycles of the current between zero and one seconds. That means we could write out the frequency of this current this way. We could express it as three cycles per second. But then, cycles per second is typically abbreviated using the unit hertz, Hz. Using this convention, we can say that the frequency of the current is three hertz.
Just as a side note, even if we hadn’t started at zero seconds and gone to one second, the frequency of the current we would calculate would be the same. For example, say we started instead at 0.4 seconds and then we went up to 1.4. That’s a total difference in time of one second. And if we would use that interval instead of zero to one seconds, we would have counted the same number of cycles the current went through. So regardless of the starting time we picked, we would still find that the frequency of this current is three hertz.