### Video Transcript

A rechargeable battery is left to
charge for a period of time. It is charged with a current of 10
milliamperes. After it has finished, the battery
has gained 180 coulombs of charge. For how many hours was the battery
left to charge?

In this question, we want to find
the number of hours the battery was left to charge for, if it gained 180 coulombs of
charge from a current of 10 milliamperes. Letโs begin by recalling the
definition of electric current. Current is the flow of electric
charge. The current through a point can be
expressed by the equation ๐ผ equals ๐ divided by ๐ก, where ๐ผ is the current, ๐ is
the total charge moving past a point, and ๐ก is the time taken for that amount of
charge to move.

To find the amount of time needed
to charge the battery, we need to rearrange this equation to make the time ๐ก the
subject. We can do this by multiplying both
sides of the equation by ๐ก and dividing both sides by ๐ผ. This leaves us with the equation ๐ก
equals ๐ divided by ๐ผ. We are told in the question that
the battery has gained 180 coulombs of charge, so we have ๐ is equal to 180
coulombs. We are also told that the battery
is charged with a current of 10 milliamperes, so ๐ผ is 10 milliamperes. Notice that thereโs this unit
prefix, lowercase m or milli-, in the value of the current, so we need to convert
this into SI units before we can substitute this value into our equation.

We can recall that for every one
ampere, there are 1000 milliamperes. That is, one ampere is equal to
1000 milliamperes. So, this means that 10 milliamperes
is equal to 10 amperes divided by 1000. This is equal to 0.01 amperes. We can now substitute these values
for the charge and the current into our equation to find that the time the battery
was left to charge. This time is equal to 180 coulombs
divided by 0.01 amperes. Completing this calculation, we
find that the time is equal to 18000 seconds.

Now, we note that the question is
asking us for the number of hours that the battery was left to charge. So we need to convert our answer of
18000 seconds into hours. There are 60 seconds in one minute,
so we can divide 18000 seconds by 60 to find that the time is equal to 300
minutes. There are 60 minutes in one hour,
so we can divide 300 minutes by 60 to find that the time is equal to five hours.

And so we have arrived at our final
answer. The battery was left to charge for
five hours.