Video Transcript
A cell does work in order to
separate charge and create a potential difference across its terminals. Which of the following formulas
correctly shows how the potential difference created across the terminals relates to
the work done and to the amount of charge separated? (A) Potential difference equals
work done divided by charge separated. (B) Potential difference equals
work done multiplied by charge separated. Or (C) potential difference equals
work done plus charge separated.
This question asks us to identify
the relationship between three things: the work done to separate some opposite
charges from each other, the amount of charge that has been separated, and the
potential difference produced between the separated charges. Before we start, let’s look at the
units of each of these quantities. Potential difference has units of
volts, work has units of joules, and charge has units of coulombs.
We can see that option (C) suggests
adding together work done and charge separated. However, these have different
units, so we know we cannot add them. We can therefore rule out option
(C). And to clear some space, we’ll
remove it from the screen.
Let’s recall the definition of
electric potential difference. Potential difference is the work
done to move a unit charge between two points. Another way to say this is that
potential difference is equal to the work done to move some amount of charge between
two points per unit of charge. Now this “per unit of charge” is
very important. It means that if we are moving two
unit charges by doing the same amount of work on them as before, we’d divide the
potential difference by two. In general, we can write this as
potential difference is equal to work done divided by charge. This lines up perfectly with answer
option (A). So, we can rule out answer option
(B) and accept answer option (A) as our correct answer.
The formula that correctly shows
how the potential difference across the terminals of a cell relates to the work done
and the amount of charge separated is potential difference is equal to work done
divided by charge separated.
