Intro to Current - Online Tutor, Practice Problems & Exam Prep

Intro to Current

Hey, guys. So up until now, we've been dealing with electrons, calculating forces, potentials, and energies. All of this stuff is electrostatics because the charges aren't moving. Now we're gonna get into electrodynamics, which is what happens when charges start moving. And basically, that's the definition of currents. So current is simply just a flow of charges from one place to another. So imagine I have these two plates right here. One's positively charged, one's negatively charged. 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 are gonna want to go in this direction. That's a flow of charges. In other words, that's a current. 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 of hundred years ago when we were studying this stuff, we had a 50-50 shot of guessing whether it was the positive charges that are moving or the negative charges. We guessed wrong. We thought it was positive charges that are 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 they 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 of hundred years ago called the electromotive force. It's basically just it's not really a force, it's just the thing that moves electrons from one place to another. Now, you might also see this as EMF or this fancy little curved E as the symbol right here. So all of these things mean the same thing. Potential difference, voltage, electromotive force, all of these things may mean the exact same thing. So now that we've dealt with the direction, what does this current actually represent? Well, imagine I had this tube right here and I have all these charges. I'm just gonna represent them as Q, not actually electrons. And I have all these charges that are moving past the sort of cross-sectional area. In other words, this little blue dotted, you know, circle that I've made. And the way we define current is a flow of charges. How many charges flow through a specific place in a certain amount of time? So ΔqΔt. 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 ampere is just 1 coulomb per one second. You can see that it's just charged per time. And that's basically it. So let's go ahead and take a look at a couple of examples. So we've got this capacitor that's initially charged to 5 nano coulombs, 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 discharge? Well, if we're looking for the currents, we're just gonna use our current equation. So in other words, ΔqΔt. We just have to figure out how much charge is moving, so we have 5 nanocoulombs, and all of that stuff is gonna completely discharge in 10 milliseconds. So in other words, we have 5 nanoCoulombs, which is 5 times 10 to the minus 9, divided by 1 times or actually rather, this is gonna be 10 milliseconds, so 10 times 10 to the minus 3. And so if you go ahead and plug this in, you should get a current of 5 times 10 to the minus 7, and that's gonna be amperes. Okay? So pretty simple. So this I equals ΔqΔt. So let's take a look at another sort of example of this. Now we have one milliamp of current is passing through a wire, and we want how many electrons are gonna pass through in 5 seconds. Well, this is a little bit different because now instead of relating this back to current, we need to figure out how many electrons pass 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, what we can do is we can relate this back to the charge by using this formula that we that we used a long time ago, which is that q=ne⋅e, where e is the elementary charge. Now we're just talking about electrons here, not protons or positive charges, so we can kind of just assume that this, you know, term is 0 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 ΔqΔt. We have what this delta T is equal to, and this is the amount of current, so we 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 1 milliamp, milliamp, which is 1 times 10 to the minus 3. And now I've got 5 seconds. So if you work this out, this is just gonna be 5 times 10 to the minus 3. Now we can just plug it into this equation, or what we can do is we can just divide over the elementary charge over to the other side, and then we should just get the number of electrons. So in other words, if I take this Q here, which is 5 times 10 to the minus 3 coulombs, divided by the elementary charge, which is 1.6 times 10 to the minus 19, 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 thing is 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 I 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 at a couple more practice problems, and I'll see you in the next one.

A lightning bolt hits the ground carrying a current of 3 × 10⁴ 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 × 10⁵
• D. 1500 C