The graph shows four diagrams of potential difference against time. What type of current is produced by these four varying potential differences?
Taking a look at the four diagrams, we see that each one shows potential difference plotted on the vertical axis and time plotted on the horizontal. Beyond that, each of the four diagrams shows a sinusoidally varying potential difference versus time. That means that, as we can see, some of the potential difference has a positive value. And some has a negative value. And it flips back and forth between them.
In this first question, we want to know what type of current is produced by these varying potential differences. Even though we don’t have a plot of the current in front of us, we know that it will follow the trend established by the potential difference in each of the four cases. That is, where the potential difference in a plot has a peak, so the current will have a peak there too. And where the potential difference has a trough, the current will have a trough or minimum there as well.
In other words, just as the potential difference in each of these four diagrams is sometimes positive and sometimes negative, so will the current be. The name for the type of current that does that, that’s constantly switching direction and therefore having positive and negative values, is alternating current. This is the current type indicated by these four varying potential differences. Let’s look now at the next question in this exercise.
What graph shows a varying potential difference with the greatest frequency?
Taking a look at each of the four graphs, we see that each of them shows time values from zero to 650 units of time, whatever that unit is. The way to figure out which of these four graphs — a, b, c, and d — has the greatest frequency is to see which one has the most wavelengths of potential difference that fit between zero and this time value of 650. The one that has the most wavelengths in that time interval will also have the greatest frequency.
So then, let’s go through these graphs in order and count the number of wavelengths each one has in the interval from zero to 650 units of time. Looking first at graph a, we see the first wavelength is here, then two wavelengths, three wavelengths. And it looks it’s be three and a quarter wavelengths in their total time interval. Moving on to graph b, we start at zero and then find one wavelength, two wavelengths, three wavelengths, and then three and a quarter at 650, just like graph a.
Moving on to graph c, we’ll notate these wavelengths a bit differently. Starting here at zero, we have one wavelength, two wavelengths, three, four, five, six, seven, eight, nine, 10, 11, 12, 13. And it looks like 13 lands exactly on 650 units of time. Then, looking at graph d, we start at zero. And we go out to the first wavelength, that’s here. And then out to here is one and a half wavelengths. And at 650, it’s a little bit more than one and a half.
So graphs a and b both had three and one quarter wavelengths in this time interval span. Graph c had 13 whole wavelengths, while graph d had a little bit over one and a half. Since graph c has the most wavelengths in this time interval, that means it also has the greatest frequency. We’ll choose this as our answer.
Our next question asks, what is the peak voltage of graph c?
The peak voltage is simply the maximum voltage that the potential difference signal achieves. If we look at graph c with all its oscillations, we can see that the peaks of these wavelengths all run along a horizontal line, which we can sketch out with a dotted line. In order to answer this question of the peak voltage of this graph, we’ll want to find where this dotted line intersects the vertical axis. We can see that happens somewhere between 200 and 250 volts.
If we look very closely at this section of the axis, we see that this interval, from 200 to 250 volts, is divided into five even spaces. And, looking closer still, it seems that our dotted line crosses the axis three of these spaces above 200. So, since five of these spaces divide up 50 volts, that means one space corresponds to a difference of 10 volts. And that tells us that since our dotted line crosses the axis three spaces above 200, then that must be at a value of 230 volts. And we’ll write that down as our answer for the peak voltage of graph c. Let’s move on now to the next question.
What graph shows a varying potential difference with the lowest frequency?
Thinking back to our count of wavelengths in each graph, we saw that a and b had three and a quarter wavelengths in our time interval. Graph c had 13 while graph d had a little bit more than one and a half. Since graph d has the fewest wavelengths over the same time interval of all four graphs, that means it also shows the lowest frequency. That, then, is our answer. It’s graph d which shows a varying potential difference with the lowest frequency.
And, lastly, we want to know what is the peak voltage of graph d. Just like we did with graph c, we’ll find the maximum voltage value on the red curve in graph d and then draw a dotted horizontal line from that point to the vertical axis. Where this dotted line crosses that axis is the peak voltage of this graph. We can see it’s somewhere between 100 and 150 volts.
Once again, that difference of 50 volts is divided into five even spaces. Each space then corresponds to a difference of 10 volts. Looking closely at this part of the graph, we see that our dotted horizontal line intersects the access two spaces above 100 volts. That, then, corresponds to a value of 120 volts. And that’s the answer we’ll give for the peak voltage of graph d. Based on our analysis, it’s 120 volts.