Video: Finding the Number of Electrons That Correspond to a Given Charge

To start a car engine, a car’s battery moves 3.75 × 10²¹ electrons through the starter motor. How many coulombs of charge are moved?

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Video Transcript

To start a car engine, a car’s battery moves 3.75 times 10 to the 21st electrons through the starter motor. How many coulombs of charge are moved?

We can call the number of electrons the battery moves 3.75 times 10 to the 21st 𝑁 sub 𝑒. We want to figure out how many coulombs of charge are moved. We can call that value 𝑁 sub 𝑐. To get started on our solution, let’s recall the charge of one coulomb. A coulomb is approximately 6.24 times 10 to the 18th times the charge of a single unit of charge, an electron.

Specifically, one coulomb is the amount of charge that a current of one ampere would move past a point over one second. So to find the number of coulombs of charge that the car’s battery moves, we want to divide the number of electrons it moves by the number of electrons, charges, in one coulomb.

Plugging in for 𝑁 sub 𝑒 and calculating this fraction, we find that, to three significant figures, 601 coulombs of charge pass through the battery. That’s how many coulombs of charge the battery moves.

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