27. Resistors & DC Circuits

Intro to Current

1

concept

## Intro to Current

5m

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Hey, guys. So up until now we've been dealing with electrons, calculating forces, potentials and energies. All of this stuff is Elektra statics because the charges aren't moving. Now we're gonna get into electric dynamics, which is what happens when charges start moving. And basically, that's the definition of current. So current is simply just a flow of charges from one place to another. So imagine I have these two plates right here once positively charged one's negatively charge. So I've got all these positive charges, all these negative charges, and we know that the electrons are gonna want to move. So if I connect this wire, this connecting wire, the electrons, they're gonna want to go in this direction, that's a flow of charges. In other words, that's occurrence. But what happens is the way we draw our conventional currents is actually in the flow of positive charges. The reason for that is a couple 100 years ago, when we were studying this stuff, we had a 50 50 shot of guessing. Whether was the positive charges that are moving or the negative charges we guessed wrong. We thought it was the positive charges. They're moving, and now we know a little bit better, but everybody still uses it this way. So instead of the current being drawn as the direction of electrons flowing, it's actually gonna be drawn in the direction of where positive charges would like to flow. And the letter for that current is this little I right here. Now the reason that these charges are moving is because there are motivated by the potential difference between the plates. In other words, the voltage we know that letter is V, but there's not actually another letter or another word that you might see for this. It's a fancy $5 word that we kept from a couple 100 years ago called the Electro Motive Force. It's basically just it's not really a force. It's just the thing that moves electrons from one place to another. You might also see this as E. M. F or this fancy little curved E as the symbol right here. So all of these things mean the same thing. Potential difference, voltage, electro motive, force. All of these things may mean the exact same thing. So now that we've dealt with the direction, what is this current actually represent? Well, imagine I had this too bright here and I have all these charges. I'm just going to represent them askew, not actually electrons and have all these charges that are moving past this sort of cross sectional area. In other words, this little blue dotted, you know, circle that I have made and the way we defined current is a flow of charges. How Maney charges flow through a specific place in a certain amount of time. So Delta Q over Delta T now the unit for that is actually amperes, or amps for short. And that's designated by the letter A and all that represents that lamp here is just one cool. Um, for one second, you can see that it's just charged for time, and that's basically it. So let's go ahead and take a look at a couple of examples. So you've got this capacitor that's initially charged to five Nano columns, and it's got a wire connected between the positive and negative plates. So now what's the current in the wire if it takes 10 milliseconds to completely discharged? Well, if we're looking for the currents, we're just gonna use our current equation. So in other words, Delta Q Divided by Delta T We just have to figure out how much charges moving. So we have five nano columns, and all of that stuff is gonna completely discharge in 10 milliseconds. So in other words, we have five Nano columns, which is five times 10 to the minus nine divided by one times are actually rather this is gonna be 10 milliseconds. So 10 times 10 to the minus three. And so, if you hadn't plugged this in, you should get a current, ah, five times 10 to the minus seven. And that's gonna be amperes. Okay, so pretty simple. This I equals Delta Q over Delta T. So let's take a look at another sort of example of this. Now we have one mil. Amp of current is passing through a wire. We want how many electrons are gonna pass through in five seconds? This is a little bit different because now, instead of relating this back to current, we need to figure out how many electrons passed through in a certain amount of time. Now, what's that variable? The number of electrons. This is an equation that we've seen before that's actually represented by the number of electrons N E. Now we can. What we can do is we can relate this back to the charge by using this formula that we use a long time ago, which is that Q is equal to the number of protons minus the number of electrons times the elementary charge. Now, we're just talking about electrons here, not protons or positive charges. So we can kind of just, like assume that this, you know, term is zero or just cancel it out. And what we want is we want the amount of charge. Now, how do we relate that back to the current? Well, remember that the current equation right here this I is equal to Delta Q over Delta T we have with this Delta t is equal to, and this is the amount of current. So you can relate that back to the charge. So let's go ahead and do that. So if I go ahead and rearrange this, I've got I times Delta t is equal to the amount of charge. And once I figure that out, I could basically just plug it into this equation and then figure out what the number of electrons is. So this current right here is one mila AMP which is one times 10 to the minus three. And now I've got five seconds. So if you work this out, this is just gonna be five times 10 to the minus three. Now, it could just plug it into this equation or what we can dio is we could just divide over the elementary charge over to the other side and that we should just get the number of electrons. So in other words, if I take this queue here, which is five times 10 to the minus three cool OEMs divided by the elementary charge, which is 16 times 10 to the minus 19. That's the That's the elementary charge. Then we should just get the number of electrons, which is equal to 3.13 times 10 to the 16th. So that's the number of electrons. Now, just in case you're wondering what happened to this negative sign right here, the things we're looking for, a number of electrons. So we're just gonna assume that all of these numbers here are gonna be positive. You can't come up with a negative number of electrons or anything like that. Okay, So all I did there was a kind of just dropped off this negative sign, just in case. You're curious. Alright, guys. That's it for this one. We're gonna take a look. A couple more practice problems, and I'll see you the next one.

2

Problem

ProblemA lightning bolt hits the ground carrying a current of 3 × 10^{4} A. If the strike lasts 50 ms, how much charge enters the ground?

A

1.5 C

B

1.67 × 10

^{−6}C

6.0 × 10

^{5}D

1500 C