Video Transcript
A cell does work on the charges
within it to create a separation of charge across its two terminals. Complete the following sentence:
The potential difference provided by the cell is equal to the blank divided by the
blank. (A) Amount of charge that has been
separated, amount of work done. (B) Amount of charge that has been
separated, distance between the terminals. (C) Amount of work done, amount of
charge that has been separated. (D) Amount of work done, distance
between the terminals.
Knowing that we’re working here
with a cell, let’s clear some space at the top of our screen and consider what’s
happening in this cell. This cell contains electric
charges. It has positive charges, we’ve
shown them here in red, arranged in an orderly grid. And it also has negative charges
here in blue. These charges are able to move
throughout the cell. We’re told that the cell does work
on these charges to separate them. This means it exerts forces on the
charges and causes them to move. We mentioned that the red charges,
the positive ones, are fixed in place, but the blue negative charges can move. So this force will make the blue
negative charges concentrate at one end of the cell.
For that reason, this end of the
cell is called its negative terminal. And that means the other end, where
there are more positive than negative charges, is the positive terminal. So the cell has done work on the
charges within it to create a charge separation. This separation of charges means
there’s now a potential difference across the cell.
We want to know which of our four
answer options best describes this potential difference by filling in the gaps in
our sentence. The first thing we can say about
this potential difference is that it depends on the amount of work that was done to
separate the charges in the cell. The greater the amount of work, the
more negative charges would tend toward the negative terminal, and therefore the
larger the potential difference would be. Now, notice that our sentence is
describing a fraction. Whatever goes in the first blank is
being divided by whatever goes in the second blank. We can think of this sentence in
fact as being similar to a mathematical equation for potential difference.
Clearing just a bit more space
still, we can write that that equation would go like this. The potential difference provided
by the cell, we’ll call it PD, is equal to whatever goes in the first blank of our
sentence divided by whatever goes in the second blank. A moment ago, we noted that the
more work was done on the charges in the cell, the greater the potential difference
across the cell would be. And that tells us what must go in
the first blank in our sentence. The amount of work done by the cell
must be in the numerator of this fraction. Looking over our answer options, we
see that only options (C) and (D) have the amount of work done going in that first
blank.
Right away then, we can eliminate
options (A) and (B) from consideration. Options (C) and (D) are different
in what they suggest for completing the second blank. Choice (C) gives the amount of
charge that has been separated. Option (D), on the other hand,
describes the distance between the terminals, that is, the physical distance between
the positive and negative terminals of our cell.
Now, let’s think for a moment about
work as it applies in physical situations. The work done on an object, say,
one of these charges in the cell, is equal to the force exerted on that charge
multiplied by the distance the charge travels. In other words, the distance these
charges move is already included in this idea of work. We don’t need to take that distance
into account again, as option (D) suggests. If, instead of distance, we put
charge in the denominator of this fraction, then we see that for some fixed amount
of work done on the charges, more charge having to be separated means that fixed
amount of work doesn’t separate the charge very much. And that means that the potential
difference is not so great.
On the other hand, for a smaller
amount of charge, a fixed amount of work can push those charges relatively farther
apart from one another. Fewer charges to separate then
means a greater potential difference again for a given amount of work done. It does make sense then that work
would go in the numerator of this fraction and charge in the denominator. For our answer then, we choose
option (C). The potential difference provided
by the cell is equal to the amount of work done divided by the amount of charge that
has been separated.
