Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about 20,000 C/s; this lasts for 100 ms or less. How much charge flows between the ground and the cloud in this time? How many electrons flow during this time?

Video transcript

Hey, everyone in this problem, we're told that electricity is a flow of charges, generally electrons from high potential to low potential. A circuit breaker is rated at 6300 amps. Okay. The breaker will trip if this maximum current is sustained for milliseconds when we're asked to determine the amount of charge that will flow within that time and the number of electrons that flow within that time. Alright. So let's start with part one. We're asked to find the amount of charge that will flow during that time. Well, recall that the charge Q is related to the current and the time through the following Q is equal to the current I times the time T. Okay. We're told the current, we're told the time. So this is just a simple plug in our values and look at the answer. Okay. So the current is 6300 amps and the time is 50 milliseconds. Okay. We want to write this in Coolum in the end and we know that a cool um is going to be an amp second. So we want to convert this from and I put meters per second. This is milliseconds we want to convert this from milliseconds into seconds. So in order to do that, we have the following, we have 50 milliseconds times one second per 1000 milliseconds. Okay. The unit of millisecond will divide out. And what we're doing is essentially dividing by 1000 to get from milliseconds to seconds. When we work this out, this is gonna give us a value of 315 we get amp times second, which is a unit of a cool. Um And so the charge is going to be 315 columns. That's part one. So we're doing a multiple choice test, we can already eliminate option D and E. Okay. Now let's move to part two. In part two, we're asked to find the number of electrons that flow within that time. Now, how can we relate the charge and the number of electrons what we call that Q, the charge is equal to end the number of electrons times E the charge of an electron. So we have 315 coolants is equal to end the number of electrons times the charge of an electron which is 1.6 times 10 to the -19 cool. Um Okay. And we're looking strictly at the magnitude of the charges here when we're talking about number. And so we will get that N is equal to okay with Coombs we're going to divide and we get a value of 1.98, 68, 7, 5 times 10 - 21. Okay. That is the number. And if we round this to three significant digits, we have 1.9, 7 times 10 to the 21. So that is the number of electrons that flow within that time. Okay. So we've done part one and we've done part two, we can go back up to our answer choices. Okay. And we see that we have answer choice. C the amount of charge that flows is 315 columns and the number of electrons is 1.97 times 10 to the 21. That's it for this one. Thanks everyone for watching. See you in the next video.