A current of 0.2 amps passes
through a wire for a period of 60 seconds. Calculate the total charge
delivered by the wire.
A current in a wire is due to the
flow of electrons. Currents have units of amperes, or
amps for short. One amp is defined as one coulomb
per second. A coulomb is a unit of charge. One coulomb is equivalent to the
charge of 6.24 times 10 to the 18 protons. This means a current of one amp
flowing through a wire is equivalent to 6.24 times 10 to the 18 positive charges per
second. It’s unfortunate that the current
is defined in terms of positive charges. It was defined this way before the
electron was discovered. We know now that current is due to
the flow of these negatively charged electrons moving in the opposite way that we
define the current.
Fortunately, this isn’t too big of
a problem as the charge of the electron is the opposite of the charge of the
proton. This means the flow of negatively
charged electrons moving in one direction can be treated as positive charges moving
in the opposite direction, which is in line with the definition of current. This means that a current of one
amp through a wire is due to the flow of 6.24 times 10 to the 18 electrons every
second. It’s unlikely that electrons will
flow for just one second through a wire. In this problem, the electrons flow
for 60 seconds. And we need to calculate the total
charge that flows through the wire in that period of 60 seconds.
A current that lasts for a time 𝑡
will involve a total charge 𝑄 that is equal to the current multiplied by the
time. In this problem, the current was
0.2 amps, which flowed through the wire for 60 seconds. As units of amps are equal to
coulombs per second, we can see the units of seconds in our calculation cancel,
which leaves us with units of coulombs. Performing the calculation gives us
a total charge delivered by the wire of 12 coulombs.