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Anderson Video - Charge in a AA Battery

Professor Anderson
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Okay, so here's a double-a battery, right? It has some available amount of charge in there. Namely if I hook this up to a wire it can power a circuit. And it will run for some amount of time, right? You've got these things in all sorts of electronic devices, of course. There must be some amount of charge that it can move. Let's figure out what that is. And if you look at the double-a battery it says the voltage is 1.5 volts. If you look up the specs on a double-a battery it'll tell you how long it lasts. And it says that a current of 100 milliamps will last for a delta T of about 10 hours. Okay, 100 milliamps out of this thing it'll last for about 10 hours. Okay. Let's figure out how much charge that means is coming out of this double-a battery. So what do we know? We know I current is Delta Q over delta T . We also know that we have I, we have delta T we're looking for Delta Q and that's going to be in coulombs. So let's just solve this or Delta Q. Delta Q equals I delta T. And we have all those numbers so let's plug it in. Delta Q equals I delta T which is 100 milliamps 100 milliamps is 100 times 10 to the minus 3 amps and it's going to last for 10 hours. Delta T is 10 hours but hours is not SI units we need to get that into seconds. And so we have 3,600 seconds is 1 hour. So the hours will cancel out and we will end up with amps times seconds And let's run those numbers and see what we get. So 100 times 10 to the minus 3 is the same as 10 to the minus 1. And then we have a 10 from the 10 hours and then we have 3,600 which is 3 point 6 times 10 to the 3 and if we plug in all those numbers into your head it's not so bad right? We've got a 3.6 and then we've got a 10 to the 3, a 10 to the 4 and then we're subtracting 1, so it's a 10 to the 3 again and so we just end up with 3.6 times 10 to the 3. And the units are amp seconds, okay? And that is coulombs, right? We said one amp second is a coulomb. So 3,600 coulombs of charge in a double-a battery that is available for your use. How many electrons is that? Well 3,600 coulombs. I want to convert that to electrons so all I have to do is multiply by 1. So coulombs has to go on the bottom, electrons has to go in the top and now I need to put a number here somewhere. What do I know? I know that one electron has a charge of 1.6 times 10 to the minus 19 coulombs. And so we get 3.6 times 10 to the 3 divided by 1.6 times 10 to the minus 19 3.6 over 1.6 is pretty close to 2 it's a little bit more than 2, but that's approximately 2, right? 2 times 10. I have to add 19 to the top. So I get 2 times 10 to the 22. That is a lot of electrons, right. We're thinking about how many electrons are going to come out of this thing when you run it. 2 times 10 to the 22 electrons. That's a phenomenal number. It shouldn't scare you though right because we've talked about big numbers before. Avogadro's number is 6.02 times 10 to the 23, right? So this is on the order of that, which sounds reasonable.