A cell does 20 joules of work to
separate four coulombs of charge. What potential difference does this
create across the terminals of the cell?
This question asks us to calculate
a potential difference. The information we are given is how
much work it took to separate an amount of charge. Given what we are looking for and
what we have to work with, we can recall a formula that relates all three of these
quantities. The formula we need tells us that
the potential difference across the terminals of a cell is equal to the work done to
separate the charge divided by the total amount of charge that was separated.
When we substitute 20 joules for
the work and four coulombs for the charge, we have that the potential difference is
20 joules divided by four coulombs. Now, to figure out what value this
is as a potential difference, we first divide 20 by four, which is five. And then we notice that the units
in the numerator are joules and the units in the denominator are coulombs. Whenever we have a numerator with
units of joules divided by a denominator with units of coulombs, the units of the
final quantity are volts. So the potential difference that we
are looking for is five volts.