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0:04
>> Hi, class. How is everybody doing? Have a good, a good weekend? >> Yes. >> Yeah? Anybody watch that World Cup game? >> Yes. >> It was a good game, very, very exciting game, very neat and tidy. I wished that it was a little more messy. Yeah, I know it's early. It's Monday. All right, let's talk about electric circuits and current.
0:35
Some of you guys have already started playing around with electric circuits in your laboratory courses, so you'll hopefully be familiar with a lot of this stuff. But the idea with an electric circuits is this, you're going to put some sort of battery, V, and typically anytime you write a battery you always make the long side the positive side, the short side the negative side, okay? So this is what a battery looks like in a circuit diagram, long bar and short bar. You have a metal wire.
1:10
There's a resistor, which looks like that. And that makes a very simple circuit. Okay, this is the most basic circuit that you could have. This portion of the circuit is a metal wire, okay? Everywhere you have this straight line that's a metal wire. When we get to capacitors we'll have a different circuit element, when we get to inductors we'll have a different circuit element, but for now we have two. We have a battery and we have a resistor, and they are connected by metal wires.
1:43
Now one thing that you've been working on in your labs is what are the voltages at different points around the circuit. And when you do that remember about metal wires. What is a metal wire? A metal wire is a piece of metal, literally, it's a long thin strand of metal. But as we learned in class metals are equipotentials, they have the same potential everywhere. So the potential anywhere from this side of the battery, all the way around to this side of the resistor is exactly the same.
2:17
That potential is the same along that wire. Likewise, on the bottom side here, from the negative side of the battery, all the way to the bottom side of the resistor that potential is also equipotential, it's constant around there, okay? So when you were doing your lab experiments it doesn't really matter if I take the voltage there, or I take the voltage thFere, or I take the voltage there, or there, anywhere along that wire I'm going to measure the same voltage, likewise along the top wire.
2:50
Okay, what happens in this circuit? Well, in this circuit the battery is just like a capacitor, okay? You have a bunch of positive charge on one side, you have a bunch of negative charge on the other. And if I put a bunch of positive charge on this side and I put negative charge on this side it's going to do something to the charges that are in the wire. It's going to push on them, okay? And so it's going to generate a current, current flows in this circuit.
3:27
Now you might think that all these positive charges on the top of the battery would push positive charges around, but that's not what actually moves. What actually moves in a metal is electrons, and so we'll talk about the sign [assumed spelling] of current in a second, okay? But what is this current? Current I, we write it with a capital I, is just how much charge you move in how much time. It's delta Q over delta T, how much charge moves in a given amount of time.
4:24
Okay, so before we were always talking about statics, right, nothing was moving. Now we have movement of charge, charge is moving around in the circuit. What are the units on current?
4:38
The units on current are amperes, and we write it with a capital A, okay? You can also say amps, all right?
4:50
We just watched Apollo 13 yesterday with my daughters and my oldest daughter said, you know, this is pretty good for an old movie.
5:02
Like old? That's an old movie? They talk a lot about amps in there because they were trying to figure out how to power up the spacecraft with a very limited amount of batteries available, a very limited amount of battery energy available. So they always talked about, well, how many amps is that going to draw, and how many amps is this going to draw? And so they had to get really creative in how they discuss that. What is an amp? Well, it is apparently delta Q over delta T,
5:30
but we know what that is. Delta Q is coulomb, delta T is seconds. Can you guys still see that over there on the screen?
5:41
>> Yes. >> Okay, good. Coulomb per second is an amp, one amp equals one coulomb per second. All right, so when we think about a wire now, let's think about what is actually happening in this wire. Okay, let's think about a wire, what does a wire look like? A wire looks like this, it's a big chunk of metal, cylindrical in shape. We've got these charges that are going to move down the wire.
6:16
If I think about the cross sectional area, A,
6:22
of this wire then what can we say about this current, I, that's flowing in the wire? The current, I, is equal to the charge,
6:35
crossing that cross sectional area, A, in some unit of time. Okay, all that charge is going to have to go through that cross sectional area, A, in a certain amount of time. If you increase the amount of charge, doing that you increase the current. If you decrease the amount of time it takes to do that, you increase the current.
6:59
Now when you look at this wire, you look at these things that I just drew, there's some sort of charge carrier, but what we really know is a wire has atoms in it
7:13
that have protons and electrons.
7:18
And so there is some positive charge here and there is some negative charge right next to it, and when I apply a field to this thing to generate this current it's actually the electrons that move, okay? The positives stay where they are, the electrons are the things that move.
7:47
And here's the deal, if the current, I, is to the right then the current, I, here is still
7:57
to the right, even though the electrons are moving to the left, okay? So the electrons move opposite the current direction, and that's because they are negatively charged, all right? Q for an E minus is negative, and so a positive current to the right is really the same as negative electrons moving to the left. So whenever we draw current you're always talking about which way do the positive charges go, even though in reality we know the positive charges more
8:38
or less stay where they are, the electrons move this way. Now if electrons are moving to the left there ends up a net positive charge over here on the right, and so it's effectively like those positive charges moved to the right, okay?
8:56
Okay, so here's a AA 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 AA battery it says, the voltage is 1.5 volts.
9:32
If you look up the specs on a AA 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 AA 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.
10:27
So let's just solve this for 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 million amps, 100 million amps is 100 times 10 to the minus 3 amps, and it's going to last for 10 hours.
10:55
Delta T is 10 hours, but hours is not SI units, we need to get that into seconds, and so we have 3600 seconds is 1 hour,
11:10
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 3600, which is 3.6 times 10 to the 3.
11:37
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 1 amp second is a coulomb.
12:17
So 3600 coulombs of charge in a AA battery that is available for your use. How many electrons is that?
12:36
Well, 3600 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 on the top, and now I need to put a number here somewhere. What do I know? I know that 1 electron has a charge of 1.6 times 10 to the minus 19 coulombs, okay?
13:05
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,
13:27
2 times 10 I have to add 19 to the top,
13:33
so I get 2 times 10 to the 22. That is a lot of electrons, right? We were 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.
13:53
It shouldn't scare you though, right? Because we've talked about big numbers before. Abogado's [assumed spelling] number is 6.02 times 10 to the 23, right? So this is on the order of that, which sounds reasonable.
14:07
Okay, let's ask one more follow-up question, let's ask how much energy is available in the AA battery? How do I calculate energy? Well, we talked a little bit about work and what you should remember is, oh, energy is in units of electron volts.
14:28
Electron is charge. V is, of course, volts. So EV is energy. So work or energy is just equal to Q times V. And, look, we have our Q right here, it's 3600 coulombs.
14:47
And so energy is 3600 coulombs times the voltage that they come out of that battery at, which is 1.5 volts.
15:02
And these are all SI units, coulombs and volts are all SI units, and so the SI unit of energy is, of course, joules and you get 5400 joules,
15:16
this is how much energy is in a AA battery. So that is a number, we've got to decide if that's a big number or a small number. How do we figure that out? Well, let's say we took a car and we jacked it up some amount, okay? If you jack up a car and you lift it a height, H, above the ground it takes energy to do that, right?
15:58
It takes an energy of MGH to do that.
16:06
Now a typical car has a mass, M, of 1,000, 2,000 kilograms, okay? So let's say it's 2,000 kilograms,
16:22
we'll write 2,000 here for M, G we know is of course 9.8,
16:32
and then we have H, and now let's set it equal to the work from the AA battery, 5,400 joules.
16:41
All right, how high can we raise that car? Well, we've got 5,400 divided by 2,000, times 9.8. Somebody punch that into your calculator and tell me what you get and we'll approximate it here, 2,000 times 9.8 is pretty close to 3,000, and then I have 5,400 over 3,000, which is 5.4 over 3, and 5.4 over 3 is not quite 2, it's maybe 1.7 or something like that.
17:20
Anybody get a real number there? I got 0.27 >> You got 0.27, did we do something wrong? Oh, yeah, we forgot this thing right here, right?
17:35
No, you're right, I was wrong. Right, because we've got 5,400, which is 5.4 times 10 to the 3, and then we've got 2,000 times 9.8. I don't know what I was talking about there. This is 2 times 10 to the 4 approximately.
17:53
Good. Anybody watching at home? Nobody is watching, okay, fine. So 5.4 over 2, times 10 to the 4, now we're going to get what you said, right? Because this is 5.4 over 2 is 2 and a little bit more, 2.7, but then we have a 10 to the minus 1, so exactly what you said, right? 0.27. Okay, 0.27 meters, right? which is 27 centimeters, that's like that high.
18:28
So, wait a minute, are we saying that you could take a AA battery and jack up your car by 27 centimeters?
18:37
Yes, that's exactly what we're saying, okay? You would have to gear down this and it would take you 10 hours to do it, but eventually your car would lift off the ground. Now this is if all the energy was used, right? You're going to lose some energy in the transfer to the electrical motor to crank the gears and so forth, but even if it's off by a factor of 10 you could still raise your car 3 centimeters, that's enough to change the tire, right? So they should just start selling you know carjacks
19:12
powered by AA batteries. I think that'd be cool.
19:16
Plug it in and wait for 10 hours and then you can change your tire.
19:20
Okay, let's talk about current for a second, this idea that different devices are going to use different amounts of current and let's see if we can come up with some typical numbers here for different items. How much current they're going to use. So let's say I have an LED, right? If I turn on just a little red LED, green LED, how much current does it draw, any ideas? And we're talking about in the scale of amps, right, that's our SI unit. Well, it turns out an LED draws somewhere
20:03
around 10 milliamps, okay? There's kind of a wide scale, but this is a typical number there for an LED, 10 milliamps.
20:13
What about your smartphone?
20:21
Okay, when you're walking around with your smartphone how much power does it draw? Let's say you're not even talking on the phone right now, it's just doing it's normal thing, talking to the cellular towers, doing some internal processing. A smartphone is about 100 milliamps.
20:41
Now that should make sense to you because we just talked about a AA battery, right? A AA battery running 100 milliamps will last about 10 hours. Your smartphone doing its normal thing will last the full day, right? 10 hours or two batteries in the 20 hours, okay?
21:02
What about a lightbulb, let's say you go to Home Depot in the past because you can't buy a 100-watt lightbulb anymore, but let's say you go to Home Depot, right, and you buy a 100-watt lightbulb, the incandescent lightbulb, not the new compact fluorescents, not the new LED. You buy a normal 100-watt lightbulb, how much current does that draw? It's about 1 amp, okay? So we've gone up by an order of 10 each time, I've got 10 milliamps, 100 milliamps, 1,000 milliamps which is 1 amp.
21:42
What about your hairdryer?
21:48
Okay, when you fire up your hairdryer how much current does it draw?
21:55
Well, we talked about the power of the hairdryer, right? And when you turn on your hairdryer you can actually see the lights dim in your house a little bit, so it seems like it's got to be considerably more than a lightbulb and, in fact it is, it's on the order of 10 amps, okay? So, look, we've already gone four orders of magnitude here, up to a hairdryer.
22:18
What about the total current that's available coming into your house, right? There's a big powerline on the telephone pole, there's a big metal wire that comes down to your house, and there is some amount of current that is available to your house and that's it. If you draw more than that the electricity company is going to have a problem with you. So how much is that total house current available? Well, it's basically another factor of 10, 100 amps, okay?
22:55
When you go out in the morning and you start your car there's a 12-volt battery in there and there's cables that are connected to the starter motor in your car. And when you turn the ignition what happens is it powers up the starter motor, that starter motor pushes against a gear that attaches to your engine, and that electric motor actually spins your whole engine for a little bit until the engine starts firing and the gas takes over, okay, and then the thing retracts
23:30
and then the electric motor just sits their idle until you need to start the car again.
23:36
But during that start the battery has to provide a lot of current, okay?
23:46
And you notice, right? Because if you're sitting there holding the key and your car is not starting you can only do that for a few minutes before your battery just drains, it doesn't work anymore, right? So you're hoping, you're crossing your fingers, come on, start on this one, I know this is going to do it, and then you're trying to decide should I push real hard on the accelerator, should I not, you know, the whole science of flooding the engine or not.
24:11
How much current is available during the start of your car? Is it really more than your whole house current? It is, it's like 300 amps, okay? They call this the cold cranking power of your battery, and it can be hundreds of amps.
24:34
How do you know this? Well, when you look at your car battery those cables that are attaching from the terminals of the battery down to the starter motor those are big heavy, thick cables. They need to be carrying a lot of current, a lot of electrons per second to get that car to start. Okay, so that can be like 300 amps. All right, let's get to something really big.
24:57
Lightning strike.
25:02
A lightning strike is when there's a big voltage difference between the cloud and the ground, so much so that the electric field strips the electrons off of the molecules that are floating around in the air, all the nitrogen, the oxygen, the carbon dioxide, the carbon monoxide, and it creates this huge amount of current and that's what we see as a lightning strike and that can be 100,000 amps up to a million amps, okay, 10 to the 5, to 10 to the 6 amps.
25:35
All right, so this is a sort of scale of things that you're talking about. We've got, you know 8 orders of magnitude here. It's interesting thinking about stuff like LEDs, right, how little current they draw compared to things like your hairdryer.
25:54
And this is why there's this big push for LED lighting, okay? Because LED lights just draw a lot less current and still produce the same amount of light. A 100-watt lightbulb, an incandescent lightbulb is not very good at converting electric power into optical power, whereas something like an LED is much more efficient at converting electrical power into optical power. And so now you should all be buying LED bulbs. When you go to Home Depot, right, buy the LED bulb
26:26
and it'll say, oh, it's a 75-watt equivalent and it only uses 7 watts, something like that, okay, it's like 10 times as efficient as an incandescent lightbulb. All right, when you think about types of current you also need to think about is it DC or is it AC, and let's talk about that. Okay, let's talk about DC current. DC means direct current, versus AC current, which is alternating current.
27:08
Okay, and this goes back to the early days of electricity, people like Thomas Edison and Ben Franklin and Tesla, and there was this big debate about should we just power the United States by DC current or AC current? What won out, of course, was AC and when you plug into the wall it is AC current, but batteries are all direct current. So direct current just means the following, the current, I,
27:44
doesn't change as a function of time, it's that, it's all heading in one direction.
27:54
AC current, of course, means that it alternates. So as a function of time AC current looks like this, it's sort of sinusoidal, it's going positive for part of the time and then it's going negative for part of the time, positive and then negative, okay? So when you fire up your AA battery you get 1.5 volts and that's it, but when you plug something into the wall you get 120 volts AC and that AC means that it's going positive for part of the time and then it's going negative for part of the time,
28:32
positive and negative. And so the current is actually going this way and then that way, this way and that way, it's pushing and pulling all the time. All right, how do we think about current in terms of other things that we like to understand, like gravity?
28:52
Well, for DC currents at least there is a nice waterfall analogy, and it's this. If I take a battery and remember the long side is positive, the short side is negative, and I hook it up to a resistor, then there is current that's going to run around that circuit, current I, like that. We know that it's electrons going the other way, but forget about that, whenever you draw I it's always referring to positive current, which way is the positive sign.
29:29
This is just like a waterfall, okay? And the analogy is the following,
29:37
here is our waterfall, and here comes the river and it goes over the waterfall, and then it goes down across the rocks.
29:53
V is the height of the waterfall, okay? That's the battery.
30:00
R is the rocks, and what rocks do is they try to slow down the current, they try to prevent the current. The water is, of course, the current, all right? Height of the waterfall is the battery, the amount of water flowing is the current, the rocks in the river those are the resistance. Put a bunch more rocks in there it's going to agitate the water and slow it down a whole bunch, no rocks the water is going to flow much more smoothly, okay?
30:42
So when you think about a battery, one thing that you might consider is, well, how do I recharge the battery, right? The battery in your smartphone drains, okay, I need to refill it, and that is the pumping station that's going to pump the water back up to the top of the waterfall.
31:05
All right, any questions up to this point? You guys doing all right?
31:11
Okay, so one of your homework problems is number 18.01 in your chapter and also on mastering, anytime it has a number on mastering that refers to problems out of the textbook. So let's look at 18.01. 18.01 says a current of 1 amp flows in a wire, how many electrons are flowing past any point in the wire per second?
31:40
All right, here's our wire, we've got current, I,
31:48
and it tells us that I, and we can use my numbers here just for fun, is 1.10 amps. And it wants to know how many electrons are flowing past any point in the wire per second? All right, pick a point in the wire and say, all right, how many electrons are flowing past it? Well, we probably know that, right? Because I is delta Q over delta T, which is number of electrons per delta T,
32:38
which we can just call a second, right?
32:43
So all we have to do is convert 1.1 amps to electrons,
32:52
1.1 amps is 1.1 coulombs per second. And we just want to convert coulombs to electrons. So, like we said before, 1.6 times 10 to the minus 19 coulombs is the charge of 1 electron. And so we get 1.1 over 1.6, times 10 to the minus 19,
33:28
somebody punch that into your calculator and tell me what you get?
33:32
1.1 over 1.6, that's got to be really close to 0.
33:41
-- I don't know, 6 something, maybe closer to 0.7, and then we have times 10 to the 19, that thing ends up at the top. Did anybody get a real answer there? Zero what? 6, 9, okay, so that is equal to 6.9 times 10 to the 18 electrons. Okay, I don't know if it'll let me punch it in here or not, let's try it. Samuel, does this thing work yet?
34:19
No.
34:25
That's all right.
34:28
Let's see if the number pad works. 6, enter -- no, okay, it doesn't work on there, but I'm pretty sure that's going to be the right number. So when you get your current just multiply by this factor right here and you should be okay.
34:45
All right, let's talk about one of the big ones for dealing with circuits, which is of course Ohm's Law. George Simon Ohm was a German who lived from 1789 to 1854 and he came up with the law that we now of course all Ohm's Law, which is simply this. V equals IR, okay? V is, of course, volts.
35:18
I is current, which is amperes.
35:24
R is ohms.
35:28
And the way we write this stuff is capital V for volts,
35:35
capital A for amps, and the Greek letter for ohms, right there, just capital Omega.
35:47
All right, let's try a very simple Ohm's Law problem, and it's the lightbulb problem. And we're going to say that we have a lightbulb that's connected in a circuit, okay, a lightbulb, an incandescent lightbulb is like a very thin resistor, okay? It's a wire essentially that's in a glass housing that is in a vacuum and so the thing won't oxidize, and when it gets hot it emits light. Okay, so it looks just like a resistor, even though there is this glass housing around it.
36:36
This is our lightbulb.
36:41
And when you get that little filament hot enough it starts to emit light, okay?
36:51
If you puncture a hole in the lightbulb, it breaks the vacuum, the filament burns out very quickly, but if you can keep a good vacuum in there then it'll last a reasonably long time. All right, let's say that this is a, not a house lightbulb but a flashlight bulb, okay? So in your flashlight you've got a couple of D batteries, a D battery also has a voltage of 1.5 volts, but let's say we have two of them in a row. So we'll say V is 3 volts, and the current that runs
37:31
through it is maybe 400 milliamps, which is 0.4 amps. And let's figure out what the resistance of the bulb is. Current, I, resistance, R. All right, Ohm told us how to do that, a piece of cake, right? R is just V over I, and we know V, V is 3 volts, I is 0.4 amps,
38:06
and that means we're going to get a resistance of 7.5 ohms,
38:15
okay, which is pretty small. When you guys were playing with circuits in the lab you were dealing with hundreds of ohms, thousands of ohms, okay? A lightbulb has a very low resistance because it's essentially a piece of wire, it's a little piece of wire that you run current through and that thing gets hot.
38:35
You're not trying to necessarily impede the current, you're trying to get that thing to get really hot and so it will emit light. Let's try your clothes dryer, you have an electric close dryer at home, and let's ask the question, how much current is going to go through the clothes dryer? Now electric clothes dryers are typically run off of the 240-volt supply and the resistance is on the order of 11 ohms, and let's ask the question what is the current
39:16
that's going to your clothes dryer? All right, no problem. I is V over R, and we have those numbers. So this is 240 volts divided by the resistance, 11 ohms, and if you punch in those numbers you should get 21.8 amps.
39:45
Now that is a lot of current, right, 21.8 amps.
39:51
So when you think about the current that's going into your house, right, we had 100 amps that was going into our house, but now on one device you're using a fifth of that, 21.8 amps. And when the power comes into your house it goes into this big metal box, right? Here's your house, and the power comes in from the line, and then there's a big box, which is the first thing that it attaches to, this is the powerline, okay? And then inside your house somewhere you have the clothes dryer.
40:32
Yes question? Does it work the same way when the powerline is underground? >> Yeah, same idea, it doesn't really matter if it's aboveground or underground. Typically in older neighborhoods it was all aboveground, in newer neighborhoods it's underground. It just depends on where they put the powerlines, and it turns out to be a little cheaper to put them above ground than to dig all these big trenches underground, but it's a little bit nicer for the community
40:56
and ultimately safer if they're under the ground, right? Because if they're under the ground you don't have these big telephone poles that can get blown over in hurricanes and you know injure people or animals or things. So when the powerline comes into your house, right, the first thing that it hits right here,
41:14
that is called the circuit breaker or the breakout box.
41:21
And usually it's outside next to your garage, and in there there's a whole bunch of switches. What do those switches do? Every now and then you have to go flip one of those switches. You say, oh, we tripped the circuit breaker, and you go out there and you flip the switch and stuff turns back on again.
41:45
What is that there for, anybody know?
41:51
Your clothes dryer is trying to draw 21.8 amps,
41:55
but let's say the clothes dryer malfunctions and it starts to draw four times that amount, 40 amps. If it does that bad things can happen, namely the wires that are going to the clothes dryer can get hot and burn up, and if they do that then your house can burn down. And so to prevent that they put circuit breakers right here, which is essentially a little safety switch. And what the circuit breaker does is I'm going to let through up to 25 amps or 30 amps, but I'm not going to let
42:36
through 40 amps or 50 amps, and if it does that, if it tries to draw too much current the circuit breaker flips and it disconnects the supply and so it immediately cuts off the electricity. And so for this number right here, your circuit breaker value will be 25 to 30 amps, so it allows this much current, but if any more comes through, any more than 25 or 30 then it closes it off. And that's what you're doing when you go reset it, you're just resetting the switch and saying, okay,
43:18
I fixed the problem, I'm going to do it again. If that circuit breaker keeps flipping a lot then you probably need to like look at the problem a little more closely, maybe hire an electrician and say, this thing keeps flipping back and forth, okay? What you don't want to do is just tape it closed and hold it shut. All right, let's take a five-minute break and then we will be back here in just a few to continue this discussion.
43:47
Hello, everybody, welcome back. How is everybody feeling? Good, hanging in there? I know, it's Monday, like right around lunchtime and you're just crashing. I understand.
43:59
We should just, you know we could all take a nap here and then the people watching at home would be like what happened, it went dark? All right, let's continue our discussion, let's talk about resistance. If I can spell it, resistance, and resistivity.
44:25
Okay, we talked a little bit about resistance, right? Resistance is measured in ohms and at some reluctance of the current to flow, right? There's rocks in the river and it's preventing them from flowing very easily. But let's think about this in terms of this wire that we've been drawing. Okay, here's our wire, it's got cross sectional area, A, it's got some length to it, L. And as current is flowing to the right what that means is there are some sort
45:02
of charge carriers that are going to move, okay? And we know it's electrons moving to the left, but don't worry about that, just pretend they're positive charge carriers moving to the right. And when those things move they don't move in a straight line, they bounce around. Okay, why do they bounce around like that? Well, because there's other things in there, right? There's all sorts of atoms and molecules that are in this material and the electron jumping from one
45:32
to the next wants to move to the left a little bit and then to the right for a few, and then maybe straight, and then to the left, okay? And so there is this general drift of the charges in the direction of the current, but they bounce around all over the place. So this is our piece of wire, it is resistive.
45:55
How do we characterize the resistance of this wire? The way we do it is the following, resistance, R,
46:09
is row times L over A, where row is the resistivity, which is kind of like friction.
46:28
Okay, resistance is row times L over R. If you have a wire that is more resistive then it has a bigger overall resistance. If it is longer then there is a bigger overall resistance,
46:46
but if it is thicker, if it has a bigger cross sectional area, A, then it is less resistive. And this is why when the car battery is attached to the starter motor they use big thick cables because they want to lower the resistance of the cable and so they make the cross sectional area very big, and that should make sense, right? If this really was a river then A would determine sort of how wide the river is and the wider it is the easier it is for current to flow down that river.
47:21
All right, resistivity is characteristic of the materials, so every material has its own resistivity, row, and the units on resistivity are ohm meters. So, for instance, gold and silver have a resistivity of the following, 1.72 times 10 to the minus 8, or 1.59, times 10 to the minus 8, whereas something like silicon has a resistivity of 10 to the 3,
48:16
and Teflon has a resistivity of 10 to the 16, okay? 10 to the minus 8, up to 10 to the 16, that's a lot, that's 24 orders of magnitude difference between those two, and there must be some key here, right? Gold and silver, what types of material are those? Those are metals, right? Those are conductors.
48:55
Teflon with this huge resistivity is, of course, an insulator.
49:05
Silicon is one of these interesting materials that is sort of in between the two and, in fact, it can act like an insulator or a conductor and that's why we call it a semiconductor. So that's a word that you've heard a lot, a semiconductor. It somewhat conducts or it conducts some of the time, okay? Semiconductors are, of course, what powers all of your computer chips. All right, so let's try an example of calculating some resistances of different things.
49:43
The important thing to remember here is that resistivity depends on the atomic structure, resistance depends on the dimensions, okay? What it's made out of, but also how long it is and how thick the cable is. All right, let's try an example. And let's do an aluminum wire and a copper wire.
50:20
And let's say that these things have the same dimensions, okay? The aluminum wire and the copper wire are the same thickness and also the same length.
50:40
And let's tell you that the resistance
50:44
of the aluminum wire is 0.2 ohms, and let's ask the question, what is the resistance of the copper wire?
50:56
Okay, let's go back to our definition of resistance, right? Resistance was resistivity, row, times L over A. L over A is the same for both, okay? Same L over A, if all those dimensions are the same,
51:21
and so we can rewrite this equation slightly as the following, L over A equals R over row, and now we can write this for aluminum, L over A equals R for aluminum, over row for aluminum, and for copper,
51:47
L over A is equal to R for copper, over row for copper. And now we can put these things together, right? L over A is the same, so we can equate the right sides, and what we're looking for is R of copper. So let's write it like this, R of copper, divided by the resistivity of copper, is equal to R of aluminum, divided by the resistivity of aluminum. So what is R of copper? It is row of copper, divided by row of aluminum, times R of aluminum. What we told you was resistance for aluminum.
52:30
What we need is the resistivity for aluminum and copper, right there. And that you have to look up in the textbook, okay? So if you flip open the textbook and you find the correct table in this chapter you should get the following, resistivity of copper is 1.72 times 10 to the minus 8 ohm meters, those are SI units. Aluminum is 2.82 times 10 to the minus 8, also ohm meters, and we have a resistance now of 0.2 ohms, which was given to us. So if you plug in all those numbers,
53:18
I did it earlier, you get 0.12 ohms.
53:28
All right, R of copper we just found was 0.12 ohms.
53:42
So which of these makes a better extension cord? Does aluminum or copper make a better extension cord?
53:52
>> Copper.
53:55
>> Okay, copper, right? Everything else was the same, same length, same width, and yet the copper has a resistance that is much smaller than the aluminum, right? it's on the order of half the resistance of aluminum, and so when you go to Home Depot and you buy a big long extension cord those cables that are inside the thing those are going to be made of something like copper, a good conductor. Aluminum turns out to be not a very good conductor.
54:28
All right, if you spend more money on your extension cable it will also be thicker,
54:36
so what you'll notice is in the extension cord aisle there will be a 25-foot extension cord for charge10 and then next to it they're all be a 25-foot extension cord for charge20.
54:49
Look at the cross sectional area, A, and what you'll notice is the more expensive one is thicker, it has a bigger A, which is ultimately going to get you a lower overall resistance.
55:03
Okay, so let me just say a couple things about Austin's question. There are a few circuit elements that are going to be key. One, of course, is the battery, the battery we write with a V, and the way you write it in a circuit is a long line and a short line. There is, of course, the resistor, R, that you write with a sort of squiggly line like that.
55:41
There is a capacitor, C, a capacitor is two parallel lines, okay? Not a long line and a short line, that's a battery, a capacitor is two long parallel lines. And then the last thing is an inductor,
56:05
we're going to write an inductor with an L, and it actually looks like a corkscrew. These are the four basic elements that you would have in a circuit, and so if I was going to draw the circuit it might look like this. Resistor R capacitor, C inductor L all powered by some voltage, V. Now we know what resistors do, right? Resistors resist the current, okay?
56:47
They resist current.
56:53
Capacitors, C, we know what those do, they store charge, all right? You can power up a capacitor, you put a bunch of charge on it. What do inductors do? Inductors it turns out they do something very special, they resist changes in current.
57:26
Okay, resistors just resist current in general, but inductors resist changes in current. It's hard to rapidly change the current through an inductor.
57:39
There's another really cool way to think about this, and we haven't got to magnetism yet, but we will soon.
57:47
When capacitors charge up they store electric field, E, right?
57:57
A capacitor that has a positive plate and a negative plate there's an electric field in there,
58:03
but inductors store B fields, which are magnetic fields. And it turns out that that means they are resistive to changes in current, okay, as opposed to just being resistant to current. These are the three elements, we're going to learn all about how they play into the circuit and what they respond to.
58:35
For now we've only introduced the resistor, but in the next couple of chapters we're going to introduce the capacitor and the inductor. Maybe you guys are already looking at that in lab. Okay, is that enough, Austin? >> Yes. >> All right. Okay, let's talk a little bit about resistance and volume. All right, what we said earlier was resistance is resistivity times L over A, make your cable longer, it gets more resistance, make it thicker it gets less resistance.
59:19
Let's think about this section of cable here. A is, of course, a cross sectional area, L is the length. So this cable occupies some volume. The volume is just the cross sectional area, A, times length, right, that's the volume of this cylinder. All right, can I factor that into the resistance?
59:52
Resistance we said was row, L over A, and I can say this is row, L over -- what if I just solve this for A? I get A equals volume, over L. So let's put that right here, volume over L, and now I know what I do, I flip the L's up to the top and I get row L squared, divided by volume.
1:00:25
So resistance, R, is in fact proportional to 1 over the volume. And this is, in fact, one way that you can measure stuff like blood flow, okay?
1:00:55
You guys are biology majors, a lot of you, you can in fact measure the blood flow this way because it's easy to measure the resistance of someone. You put an electrode here, you put an electrode there, you can measure the resistance of that circuit and if that resistance is in fact proportional to one over the volume, namely the volume of blood flow, then you can in fact calculate how much blood flow there is.
1:01:26
Is that person suffering from high blood pressure, low blood pressure, good circulation, bad circulation? You can do it by measuring something in physics called resistance, and that's a lot of the times when you see those electrodes hooked up to people, right, one, they're measuring electrical signals from the heart firing, but two, they can also measure how much blood is in them and how much blood is flowing in them. Just kind of cool. All right, resistance also varies with temperature.
1:02:08
So resistivity at some temperature, row, this is resistivity row, at some particular temperature, T,
1:02:22
is in fact equal to row naught, some calibrated resistivity.
1:02:34
And then there is a scaling factor, which is the following. One plus alpha T, minus T naught.
1:02:47
What are all these things? One is, of course, the number one. What's alpha? This is called the temperature coefficient of resistivity. This is still the temp, T, and the temp, T naught, okay? This thing is rather critical to how the resistor behaves, and if it's a metal then alpha is a positive number, but if it is a semiconductor then alpha is a negative number. All right, let's multiply both sides by L over A and then we can change this into resistance.
1:03:43
So if we multiply both sides by L over A, what do we get? We get row, L over A, equals row naught, L over A, times 1, plus alpha, T minus T naught. And now this thing is just a resistance, R equals R naught, 1 plus alpha, T minus T naught, okay? And this is a relationship between resistance and temperature. So if I have a normal metal filament and we plot out R as a function of temperature, T, what it looks like is this. Okay, the resistance increases with temperature.
1:04:43
And you might be doing experiments of this kind in the labs, where you turn on a lightbulb, and when the lightbulb is cool it has a very low resistance, but as it gets hotter and hotter it increases its resistance. Okay, let's try another example. Let's take a long thin wire and let's run some current down it, and let's say that this thing is pretty long. L is 175 meters. There is some voltage which is driving current down this thing, and so there is some voltage difference between the two ends.
1:05:42
And let's tell you that that voltage, V, is 0.3 volts. And let's tell you that the amount of current flowing in this thing is 125 amps, and let's say that this thing is made up of aluminum.
1:06:06
Mass density is of aluminum,
1:06:12
so this is an aluminum wire, is the following. Mass density, row, is 2700 kilograms per cubic meter,
1:06:27
and let's do the following, let's find the total mass, M, of this wire.
1:06:40
Okay, it might seem like we don't really have enough information right? Because we just talked about how much current is flowing and somehow we want to get the mass of the wire, it seems a little strange, but the key is that it's aluminum and we know a little bit about aluminum. So how do we do this? Well, mass, M, is just going to be the mass density, row, times the volume. Okay, mass is density times volume. But we also know a little bit about resistance.
1:07:19
We know that resistance is going to be R of aluminum times L squared over the volume. We derived that a second ago,
1:07:34
and so now we can we rewrite this for the volume. Volume is equal to what, I'm going to multiply across by volume or divide by R, so I get row, aluminum, L squared, all over the resistance, R,
1:07:51
but I know the voltage and I know the current.
1:07:56
And so in fact I do know the resistance, R. This becomes row of aluminum, L squared, divided by R, and we know that V equals IR, and so R equals V over I,
1:08:17
so we can put that right here, V over I.
1:08:20
And now I think we almost have all the numbers that we need for there, but we still want to get mass. So mass, M, is equal to row, mass. This is unfortunate that we're using row for mass, density, and also for conductivity or resistivity, but that's just how it goes. And we've got to multiply it by volume, which we said was this, so we get row, aluminum, L squared, that I flips up on top, and we get a capital V for voltage in the bottom, and now we have all those numbers.
1:08:56
We have the mass density right there, 2700. We know what row aluminum is, we just did that earlier, we can look it up in the book. We've got I, we've got L squared, and we have V,
1:09:08
and if you plug in all those numbers what do you get? Well, let's just do it again right here. We've got 2700, the row mass density. Aluminum we said was 2.82 times 10 to the minus 8.
1:09:26
L was 175. I was -- what'd we say for I? 125 right?
1:09:38
125 amps, and then let's divide the whole thing by V, which was 0.3 volts, okay?
1:09:52
And if you punch in all those numbers in your calculator you can double check me, but I got a mass, M, for that wire of 971 kilograms. Okay, which is a pretty big wire, right? It's almost a metric ton, but it's long and it's carrying a lot of current, which means it's going to have to be quite thick. Okay, has anybody ever heard of superconductors? Any of you guys ever heard of superconductors?
1:10:40
You've probably heard that term in the news, right? Sometimes they talk about levitating trains using superconductors in them. What is a superconductor? Anybody know?
1:10:55
What's the property of a superconductor?
1:11:02
A superconductor is something that is super at conducting, okay? It's right there in the name. In fact, it's so super that R doesn't just go to something small, it in fact goes to zero, okay? And this is very interesting to people, right? Because if you have a resistance that goes to zero you can run current through these wires and they don't heat up. All right, there is no resistance there. That water flowing down the river doesn't experience any rocks in the river and it just flows smoothly
1:11:42
without any trouble at all.
1:11:44
So if we think about our good old metals,
1:11:50
what we said was a metal looks like this, okay? There's some resistance as a function of temperature, T. But a superconductor does the following, it goes down and then quickly drops to a resistance of zero, and then from there on out it has a resistance of zero, all the way down.
1:12:24
This temperature where it does that is called the critical temperature, okay?
1:12:34
Superconductor drops to zero at some temperature that is not at absolute zero.
1:12:42
So the goal of superconductors is to find the temperature that is reasonable.
1:12:57
You want that to be a high temperature. And this is where all the research in superconducting materials has gone into, how do we push that temperature higher and higher? Okay, you want your metal wire to be able to operate at room temperature or at least something remotely close to that. So where are they now? The current record, at least of a couple years ago, you can double check me on this, maybe they're a little bit higher now, but the current record is about 125 degrees Kelvin,
1:13:41
and this is something called mercury copper oxide,
1:13:53
that's the material that it's made out of. Which 125 Kelvin, that sounds a little cold still, right, because room temperature it's like 300 Kelvin. But the point is it is well above the temperature for liquid nitrogen, liquid nitrogen is about 77 degrees Kelvin.
1:14:19
So if you take some of the stuff, mercury copper oxide, and you make a wire out of it and dip it in liquid nitrogen all of a sudden it becomes a superconductor. It can conduct electricity with zero resistance. And this has interesting implications, not just for carrying electricity, but for carrying magnets on top of them, okay? If you take a magnet and you put air on top of a superconductor it levitates above the superconductor, and so this is the goal behind these levitating trains,
1:14:55
make superconductors, put magnets on the train, let it levitate above it, and then you can move things really easily. So superconductors are a very interesting region, an interesting area of research, and basically the whole idea is let's get this temperature even higher.
1:15:15
All right, let's check the time here, it is 1:30.
1:15:22
I think maybe that's going to be it for today. Tomorrow we're going to start talking about electric power and how we understand power considerations in these electric circuits.
1:15:36
Any questions before we take off? No? Okay, cool come on we're out of here. I will see you guys tomorrow morning. Cheers.
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