An electric motor is connected to a
nine-volt battery. Over a period of time, the motor
converts 450 joules of electrical energy into kinetic energy, heat, and sound. How much charge passes through the
motor over this period of time?
So what we have here is an
electrical motor being powered by a nine-volt battery. We want to know over the time it
takes the motor to convert 450 joules of electric energy into these other kinds of
energy — kinetic energy, heat, and sound — we want to know how much charge passes
through the motor over that time. To figure this out, we can recall
the relationship that connects voltage, energy, and charge.
Electrical energy 𝐸 is equal to
the amount of charge 𝑄 multiplied by the potential difference across which the
charge moves 𝑉. In our particular case though, we
don’t want to solve for 𝐸, but we do want to solve for the charge 𝑄. So we can rearrange this
equation. When we do, we see that charge 𝑄
is equal to energy divided by voltage. And in our problem statement, we’re
told the energy used by the motor as well as the voltage powering it.
When we substitute in these values,
we have 450 joules of energy divided by nine volts of potential difference. This fraction comes out to 50
coulombs of charge. This is the amount of charge that
passes through the motor over this period of time.