Video Transcript
Which of the following correctly
shows an alternating current on a graph of current against time? Is it option (A), (B), (C), or
(D)?
In this question, we must determine
which of the current–time graphs properly shows an alternating current. Recall that an alternating current
has a periodically changing direction. On each graph, the horizontal axis
shows values of time, while the vertical axis shows values of current.
It is important to notice that the
vertical axis of the graph extends above and below the horizontal axis. Values of current above the
horizontal axis are positive, and values below the horizontal axis are negative. The sign of a value of current
indicates the direction of the current. A positive-valued current and a
negative-valued current are in opposite directions.
Now let’s use this information to
analyze the current–time graphs that we have been given.
We can immediately eliminate graph
(A) as the line never crosses the horizontal axis. This means that the current never
changes direction to become negative, so we know that the graph cannot represent an
alternating current.
Similarly, we can eliminate graph
(D) as the line on this graph also never crosses the horizontal axis. The current never changes direction
to become positive, so it is not an alternating current.
For graph (B), we can see that
there are alternating positive and negative values of current. Is graph B showing alternating
current then? Well, if we look at the graph
carefully, we can see that in the time interval between one second and two seconds,
the value of the current is zero. Such intervals of zero current
recur periodically. And in those intervals, the current
takes on a constant value for an entire second. An alternating current should have
a value that’s always changing and so is never constant. Thus, we know that graph (B) does
not show an alternating current, so we can eliminate this option.
For graph (C), notice that the
value shown by the line is always changing. Here, the line shows alternating
values of both positive and negative current. In order to do this, the line must
cross the horizontal axis. So notice that the value of the
current is zero at zero seconds, one second, two seconds, and so on. But the value of current is zero
only for the instant in which the direction of a current changes.
Therefore, graph (C) correctly
shows alternating current, so this is the correct answer.
