Question Video: Finding the Charge Passing through an Electrical Component given the Energy Dissipated by It

An electric motor is connected to a 9 V battery. Over a period of time, the motor converts 450 J of electrical energy into kinetic energy, heat, and sound. How much charge passes through the motor over this period of time?

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Video Transcript

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.

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