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Electric Current

  • Electric current (I) is a continuous flow of charge. It is defined as how much charge (q) passes by in an amount of time:
    I = q

    It uses the unit of amperes (usually shortened to amps) (A). One amp is one coulomb per second.
  • The amount of current that will flow between two points is connected to the electric potential difference between those two points. A large voltage means more current flow.
  • Some materials resist current flow more than others. We account for this with resistance (R).
    R = V

    Resistance is measured in ohms (Ω).
  • If we know a material's resistivity (ρ), we can find its resistance depending on its length (L) and cross-sectional area (A):
    R = ρL

  • Since energy is involved in moving charge around, and we have a continuous flow of charge, electric current is connected to power (energy per unit of time). There are many ways to express this relationship:
    P = IV ,        P = I2R ,       P = V2

  • If we want a sustained current, we need a sustained voltage source. The two main ways to create a long-term voltage source are through generators and batteries.
  • While electricity flows very quickly, each individual charge actually flows quite slowly. This is because all the charges start flowing at once as soon as the switch is flipped, like turning on a hose full of water.

Electric Current

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Electric Current 0:31
    • Electric Current
    • Amperes
  • Moving Charge 1:52
    • Conceptual Example: Electric Field and a Conductor
    • Voltage
  • Resistance 5:05
    • Given Some Voltage, How Much Current Will Flow?
    • Resistance: Definition and Formula
  • Resistivity 7:31
    • Resistivity
    • Resistance for a Uniform Object
  • Energy and Power 9:55
    • How Much Energy Does It take to Move These Charges Around?
    • What Do We Call Energy Per Unit Time?
    • Formulas to Express Electrical Power
  • Voltage Source 13:38
    • Introduction to Voltage Source
    • Obtaining a Voltage Source: Generator
    • Obtaining a Voltage Source: Battery
  • Speed of Electricity 17:17
    • Speed of Electricity
  • Example 1: Electric Current & Moving Charge 19:40
  • Example 2: Electric Current & Resistance 20:31
  • Example 3: Resistivity & Resistance 21:56
  • Example 4: Light Bulb 25:16

Transcription: Electric Current

Hi welcome back to Today we’re going to be talking about electric current.0000

So far we’ve talked about stationary charges and it’s been a great way to build a foundation for understanding electricity.0006

We understand how the force the between one charge and another charge, how it interacts and what’s going on there.0011

The technology that we’re all using, it isn’t built around static stationary charge, it’s based on moving charge. It’s not that something’s just still, it’s flowing through the wires.0017

We call this continuous flow of charge electric current. Current, electric current we use the symbol i. It concerns itself with the idea of charge moving around.0027

Remember we’ve got all these electrons in the line and they’re all loosely connected. The outermost free electrons are loosely connected to copper, to all metals.0038

They’re able to slide around. If we’ve got a wire that’s connected to something, it’s going to have the possibility for those electrons to all slide simultaneously like water in a hose, all the water sliding simultaneously through the hose.0049

How do we tell how much charge is moving? How would we tell how much water is moving through the hose?0066

Well we have to set some point and then see how much charge passes by. If we were to see how many water molecules passed by we can see how much charge flows by.0071

I, the current is defined as the charge passed a point divided by the time it takes for that charge to pass.0081

Current is measured in amperes. Amperes? It’s French actually so I think I’m just ham fisting that word. Normally it’s shortened to amps, simple sound, amps.0090

It uses the symbol capital A. One amp is the same as one coulomb of charge per second. Which makes exact sense because it’s set as charge divided by time, so one amp is equal to 1c/1s.0100

We define the idea of current but what causes the charges to move around? One way we could look at it is electric fields. How we were looking at electric force previously.0114

If we had a conductor and an electric field, the free outermost electrons of each atom would want to move under the influence of that field.0122

Each of those electrons would see the field and it would be pushed. Remember once again, electric field goes in the motion of positive, so if we had an electron here, it would go this way.0129

In general we’re going to talk about positive charge moving, we’re going to pretend that there is this positive charge action moving along.0140

In reality what we’re seeing is the opposite to the electrons movement in the opposite direction. It’s okay, we’re able to deal with the idea of positive charge, just as the electrons in way leave a void, they have this wake behind them.0147

We imagine that the positive charge is that wake. When they’re originally working with the stuff there is no way to tell the difference until we had a better idea of the atomic model so that explains why we’ve got this sort of a little backwards.0162

We’ve got it all set by convention, is what humanity is used to doing. We keep it up just because…make things really confusing to switch over to electrons.0174

We imagine that this sort of imaginary positive charge is what’s sliding around even though the positive charge is actually in the nucleus and the nucleus is fixed in place.0184

Still it’ll work out fine. If we were to put a conductor in an electric field, those charges would get slid around because they have this force pushing on them from that electric field.0195

That might be one way to talk about current. That has a downside; the field varies as we move around. We saw this before that the field couldn’t be totally different from one place to another.0207

To know what current will be supplied by the field, we’d have to know a lot of information about the field. We’d have to know the field at every location along our conductor along with knowing stuff about the conductor.0219

If the conductor was really big and was really conductive in a certain area but later on it really small and tight and so it lowered it conductivity versus we had long length, it’s going to be not easy to do this way.0228

Electric fields isn’t the best way to do this. We don’t really want to have to do that because it’s going to take all this calculation and it’s actually going to require using calculation tools that we don’t have accessible to yet.0241

We’re going to need calculus before we can work that. We need something else. Voltage, what’s way easier to know is voltage.0250

If we know the electric potential at two points we can tell if there will be a current between them. Positive charge flows in the direction of high voltage to low voltage.0257

If we had some voltage source that creates a difference, if we’ve got some voltage source we’re going to have a current between those places.0267

If we’ve got some super positive thing over here and some negative thing here, we’re going to get current flowing between those two.0275

It’s going to depend on how conductive the material is but we’re going to have current flowing between the two.0286

The larger the electric potential the larger the difference there, we’re going to have more current flow. Electric potential difference also called voltage.0292

The more voltage we have between those two points the more voltage, the more current.0300

Given some voltage, how much current flows? That depends on how conductive the material involved is. If it’s a really good conductor it’s really easy for charge to flow, it’s not going to get in the way.0307

So given voltage will put out a lot of current, but if we have a bad conductor we’re going to get some resisting.0316

If it’s a good conductor charge flows very easily but if it’s not a good conductor it will resist some of that charge flow.0325

The less good a conductor that it is the more insulating is. The more of an insulator it is the more resistance it’s going to have. The more it will fight the current, the more it will resist the current.0331

With that idea in mind we’re going to create a new property called resistance which we denote with a capital R.0342

For a given voltage, the high resistance means less current. A low resistance means more current.0347

The more we resist it the less current will make it through. The less we resist it the more current comes through.0353

We define it as the resistance is equal to the voltage divided by the current. One way to look at it is that the current is also equal to the voltage divided by the resistance.0359

A large voltage with a small resistance is going to make a large current. But if we had a small voltage and a large resistance, if this was big and this was small, then we’re going to have the resistance being able to beat it out and we’re going to have very little current able to make it through the line.0372

We measure resistance ohms and it uses the symbol capital Omega from the Greek letters.0390

This relationship is sometimes called Ohms Law. This is actually a misnomer because it’s not always true. It doesn’t hold true for all materials at all voltages.0399

For our purposes it will be true, but an object’s resistance can vary based on the temperature, the amount of current flowing through it, and other variables.0409

It’s not a perfect law. Many materials will for some section of temperature, current and voltage will manage to have this nice linear relationship, but it’s not always true, especially at the far ends.0417

It is called Ohms Law but it’s not actually a law because it doesn’t hold all the time. Still you might hear it referred to as ohms law so I wanted to make sure heard that name for it all.0433

Just in general we’ve got resistances to find as voltage over current. If we know the resistance, we know the voltage, we’ve got the other.0442

If we know any of the two pieces of this puzzle, we know the third.0448

Resistivity, what about if we know….we talk about resistance, it allows to talk about how difficult it is to get current to flow.0453

What if we want to know an objects resistance without having to put a charge across? Without having to put that current down, without having to put that voltage down and see the current and see how much charge comes through then we’d be able to find out what the resistance is experimentally?0460

Instead if we can’t do it experimentally we can talk about its resistivity. Different materials have different conduction levels. Some conduct better, some conduct worse.0475

They’re each going to have a different resistivity, which we use rho once again another Greek letter.0488

If you’re remember…well you might remember that we talked about density using rho, we wind up using the same letter, but since these are not commonly showing up at the same time, we’ll be able to keep it straight. We don’t have to worry about accidentally have two different rhos showing up.0494

We’ve got a resistivity. We’ve going to have to use this resistivity to figure out how much resistance a type of material would have. If we’ve got a line of copper versus a line of gold versus a line of lead versus a line of graphite we’re going to wind up having different resistivities inside of that.0507

They’ll have different resistivities and thus different resistances. We also have to take the shape of the material into account. It’d be harder to push it over a long distance.0530

A 1,000 meters of copper wire, it’s hard to get a current to flow through than 1 millimeter of copper wire. It’s easier to get something to move through a small distance, it will take less force, a less voltage.0538

It’s also going to be easier if have more area to push along. A large pipe, it’s easier to have current flow without much pressure in a large water pipe.0549

If we’ve got a large area, a large cross-sectional area we’re going to be able to have more current flowing more easily. We’ll have less resistance the more area but we’ll have more resistance the longer the length.0558

All these ideas put together we get that the resistance for a uniformed object is going to be resistivity, rho, times its length divided by its cross-sectional area.0573

Rho times l over area if we know what the resistivity for a given material is. Then we can find out what its resistance is without having to just do it experimentally, without having to know the voltage and the current.0584

Energy and power. We know it takes energy to move charge around, to put a charge somewhere because we certainly have to deal with that on our electric bills and the fact that if we want our TV to turn we have to plug it in and we have to give it a source of energy.0597

How much energy does it take to get these charges to move around? We could figure that out if we had a fixed amount of charge. If we wanted to move one coulomb of charge from this place to this place, depending on some electric field in the area, it’s going to take some amount of work.0610

It’ll take some amount of energy. We aren’t dealing with that when we’re dealing with current. We’re dealing with not a fixed amount of charge; we’re talking about amount of charge per unit time.0629

If we’re dealing with current, we’ve got charge continuously flowing. It’s not like we’re picking up a sack of water and moving it to another location. We’ve got a pipe of water moving location…moving water’s location constantly.0643

We’re moving the water to a new location constantly and we’re bringing in a new sack every second or every couple of seconds effectively.0656

We can’t talk about it as one discreet chuck of energy; we have to look at it as a rate of energy.0663

What do we call a rate of energy? We have it as power. The power is the work, the energy, the change in energy divided by the time.0669

If we’re looking at current flowing we want to look at power. Since power equals work over time, and we talked about the fact that we define voltage was equal to the work divided by the charge involved.0679

That was how we defined the idea of voltage. If that’s the case, we can replace that work with qv. We can also slide that dividing by t over and now we’ll have q / t x v.0691

Well q / t was exactly how we defined current so in the end we’ve just got that the power is equal to the current times the voltage.0705

Now we know that power equals current times voltage. We also know that voltage is equal to the current times the resistance or alternately…we could rephrase this in many different ways but remember how we define resistance was resistance is equal to the voltage divided by the current.0715

Voltage is equal to the current times the resistance, all these sorts of things. We’ve got that relationship set up here.0731

If we know that we can also find some other ways to express power by trading things out.0737

First off we can drop in…since voltage equals current times resistance, we start off with our original power equation and then we replace the v with IR and so we simplify it and we get I²R.0743

The current squared times the resistance is another way to look at the power. What would be another way?0757

We could replace the other thing, instead this time we’ll replace current. Since current can be solved for up here by just dividing both sides by resistance, we get the voltage divided by the resistance.0762

We simplify that out some more and we get the voltage squared divided by the resistance is yet another way to express power.0773

At this point we’ve got three different ways to express power. If we want to know the electrical power involved, we have three different ways to find it.0780

Power is equal to the current times the voltage. Power is also equal to the current squared times the resistance. Finally power is equal to the voltage squared divided by the resistance.0787

With lots of different ways to look at energy and power. Well not really energy, power. If we want to find out what energy is, we have to see how long did we let this electric operate. How long did current flow through? How long was this power generating?0797

If we know something is some number of watts per second and multiply by 5 seconds, then we’ve got a solid amount of energy that was used in those 5 seconds.0810

Where does this voltage for a sustained current come from? If we charged up an object to a high voltage, put a lot of electric potential on it and we touched it another object, all that electric potential, the charges would go “Oh man, I want to go to a lower potential,” and they’d all slide over all at once.0820

They’d be this large current, it’d be this big zap as it popped over. It would be very brief. Once the charges rearrange themselves to equilibrium there’s no reason for them to keep going.0835

They’ve put the voltages to the same level by their sliding over. They’ve changed the involved electric fields; they’ve changed the involved potentials. Once they slide over to equilibrium they’re done.0845

Everything is back to how it started before we charged up the objects. This is exactly what happens when you get a static shock. You manage to charge something up to a very high potential, you touch it, it grounds to your body and becomes neutral once again and you experience the current flowing through, which causes your nerves to fire and you experience it as a shock.0854

That’s not a good way to make current. You don’t experience that shock continuously, it’s a brief instant and then it’s over.0875

That’s not a way to have a voltage source. We want something that’s going to be sustained; it’s going to give us a continual source of voltage, a continual source of current.0883

We want current to flow continuously, we need something that can sustain that potential difference over the long term.0891

Something that can keep up a steady pumping, not literally but if we thought about it in terms of water, once again we need something that’s able to keep pumping something up the pipe so we can have that water than go through some system where it does some sort of motion.0896

We need some steady pumping of current as opposed to one brief surge. How do we do that?0910

We get a voltage source. There are two main ways to obtain a voltage source, potential difference.0917

The first is with a generator and the second is by what we commonly call a battery. First a generator is way to convert mechanical rotational energy into electrical energy.0923

An electric motor is just a generator that operates in reverse; it takes in electrical energy and converts it into rotational energy which then through some manner of gears or something manages to normally turn it into linear momentum because rotational energy goes to the wheels if it’s an electric motor in a car.0933

Rotational energy goes to the wheels that rotational energy then through friction is applied to the ground and we get linear energy, linear kinetic energy.0949

In any case we manage to convert some sort of mechanical energy into electrical energy or vice versa for going in backwards, if we’re going backwards to get an electric motor.0957

We’ll explore why precisely this is working when we talk about magnetism but this is one just continual source. We could have a continual source of mechanical rotational energy and so we’re able to have a continual source of electric energy.0967

That’s great. Another great way to do is through a battery. A battery is not technically a battery unless it’s multiple cells. A battery is a collection of wet or dry cells where each cell has a voltage difference between its two ends.0978

If we line up a bunch of them we’re able to get that voltage difference to add up over all of them so we can get a larger voltage than just from a single cell.0994

We call multiple cells put together a battery but in common we also just tend to call them all batteries no matter what.1001

A clever application of chemistry allows us to do this, we won’t get into the why but it’s just a good use of chemistry, a great use of chemistry is chemical battery storage.1008

We can have a way to store electrical energy inside of a battery. Each cell is able to convert some of its chemical energy into electrical energy for us to use.1017

It does so at a steady voltage. It doesn’t just shove all of its energy out at once; it’s able to keep up the conversion over a slow steady thing, so we’ve got this great long term source of potential difference.1025

Speed of electricity. We’ve talked about current, about the amount of charge that flows by a point but we haven’t talked about how fast those electrons move.1037

We haven’t talked about how fast the current is flowing. It turns out that an electron is actually traveling through a conductor around a speed of, it depends on the conductor, it depends on a bunch of things.1048

Normally it’s going to be somewhere around this and in general it’s actually going to be way less than this. But it’s somewhere around 0.0001 meters per second. Keep that in mind, that’s 1 millimeter per second.1058

Or 1 centimeter per hundred seconds. That means it manages to make less than 1 ½ centimeters in 1 ½ minutes.1074

Manages to make less than a centimeter a minute, that’s a tiny, tiny amount of distance every minute. Wait what? That can’t be possible, you flip on a light switch and you know those electrons managed to move to that light like that.1080

You flip on a light switch you before you can say “Bob’s your uncle,” boom there’s light. What’s going on? How is it possible to for the electrons to moving so slowly and yet for us to be able to have effectively instantaneous for our point of view, motion of electricity through the lines?1097

The trick is that it’s not the electron in the light switch the moment you hit the switch, the trick is that it’s the entire column of electrons; it’s the entire wire of electrons moving as one.1114

They all start drifting towards the light as soon as you hit the switch on. It’s like if you had a hose full of water and turned on the water at one end, it’s not going to have to be that you wait for the water from end to get to the other end.1125

Since you’ve already got it full of water, you’ve already got the wire full of electrons just because that’s the nature of it being a metal. As soon as you flip the light switch on, the entire column starts to move at once and so it’s in the water example once again, it’d be that pressure wave.1139

How fast is that pressure wave propagating? The speed of sound in water is super-fast so as soon as you turn on the water at one end, boom; you’ve got water coming out of the other end. It’s the exact same thing with electrons.1152

We flip on the light and boom you’ve immediately got those electrons moving as one unified whole. They’re all handing their electron up to the next guy. It might be that they hand them up relatively slowly but since they’re all handing up simultaneously, the guy who’s already next to the light hands his to the light and we’ve got light the instant we flip on the switch.1163

Ready for some examples? If we’ve got a wire with a current of 0.5 amps flowing in it, how long would it take 30 coulombs of charge to move passed some point on that?1181

If we’ve got some point arbitrarily there, it doesn’t really matter. If we’ve got some wire that has a current of 0.5 amps in it, how long would it be for 30 coulombs of charge to pass that point?1191

We know we defined current to the amount of charge divided by the time. We know what the current is, the current was 0.5 amps.1201

We know how much charge we want to pass that point. We want 30 coulombs of charge. Divide by the time. So time is equal 30 / 0.5 and we’ve got 60 seconds.1211

With a 0.5 amp current it would take 60 seconds for any point to have 30 coulombs of charge pass it.1224

Second example. If we put a voltage, a potential difference of 120 volts across an object and 2 amps of current pass through it, what would be the objects resistance?1232

Here’s some object, we’ll model it as a resister and we’ll talk about circuit diagrams, but this the symbol for a resister.1241

Over here it’s at +120 volts and over it’s at 0, so negative we’d call it normally as its going plus to minus, going down.1247

What would be the objects resistance? We’ve got 2 amps flowing through. Well what was the relationship? It was voltage equals the current times resistance or many other ways to phrase it.1257

This is an easy one to remember. It takes the product of the current times the resistance. More resistance means less current for a given voltage, vice versa more current means less resistance for a given voltage.1268

We drop in 120 volts equals if we’ve got 2 amps flowing through and a resistance of R. We divide it out and we’ve got 60 ohms as our resister.1282

What if we had a slightly different case where we had that same 120 volts going through but we didn’t know the current but we did know the resistance was a 1,000 ohms.1294

We divide both sides by 1,000 and we get 0.12 and it must be in amps because it’s a current, 0.12 amps.1305

Third example. The resistivity for copper is rho of 1.69 x 10^-8 ohms times meters. Seems like a strange unit but it winds up working out to cancel precisely to being ohms at the end of that formula which is exactly what we want because it want it to be resistance.1317

The formula was resistance equals the resistivity times the length divided by the area. What resistance would 10 meters of copper wire with a diameter of 1.628 millimeters have?1333

That’d be about the size of medium duty extension cord. If you wanted to have a 10 meter extension cord and plug it in both end, it’s going to…the actual wire inside of those insulation is going to wind up being 1.628 millimeters.1348

If that’s the case we drop in the numbers we’ve got 1.69 x 10^-8 times the length, 10 meters, divided by the area, of well what’s the area?1366

Its diameter was 1.628 millimeters so diameter equals 1.628 millimeters. What’s its radius? Its radius is half of that. It’s going to be 0.814 millimeters. That’s great, but what are we working in? We’re not working in millimeters we’re working in meters.1379

We can convert that out and that’s going to be times 10^-3, since we’re already over 1 it becomes 8.14 x 10^-4 meters. We’ve got that, how do we find the area for a circle?1401

An area for a circle, πr². We toss that in down here, we’ve got π x 8.14 x 10^-4². Punch that all into a calculator and we get 0.081 ohms per 10 meters.1416

That’s actually a really small resistance. That’s a really small resistance and that’s 10 meters. That means we can cover an entire football field, we can cover an entire soccer field for only less than an ohm.1434

We haven’t really worked with the stuff much but a 1 ohm resistance is incredibly small. That’s going to allow for a massive amount of current to still flow through, that’s effectively negligible for what we’re getting here.1448

In over really, really long distance, if we were to lay a state wide, something that’s able to cross huge distance from city to city from power plant to the city it’s operating for, that’s going to start to be an issue.1459

Then that becomes more complicated and there have to be ways to step up the voltage so you have less resistance…the resistance of the line will have less of an effect in the power loss.1473

That’s more of complicated thing; we’re not going to get into that right now. It does mean for our purposes the extension cords, all the wires inside of a home are effectively no resistance.1483

If we can get that 120 volts, that 220, 240 volts, whatever voltage we manage to get into the home, we’re going to wind up having effectively no resistance inside of the home.1492

It’s going to be another issue that has to be worked out by the electric companies to be able to get the stuff there but there are clever ways to make sure that there’s not much resistance effectively in those lines, not much energy is lost to the resistance of those lines.1505

Final example. If we’ve got a voltage of 120 volts and we put it over a light bulb and that light bulb takes 100 watts of power, which is the standard incandescent light bulb, what resistance must the light bulb have?1517

Voltage equals current times resistance, but we don’t want voltage equals current times resistance. What we want know is power. What is power? Power was equal to current times voltage which is equal to current squared times resistance.1530

Which is equal to the voltage squared over the resistance. Which one of these would be the best choice to pick?1548

We know the voltage; we want to know the resistance. We know the power. This is the best one to choose. Power equals v² divided by resistance.1554

We plug in the numbers we know, 100 watts is equal to a 120² divided by a resistance of unknown, so the resistance winds up equaling 144 ohms.1564

144 ohms. So compare that 144 ohms is a fairly normal object, a light bulb. That’s resistance in a light bulb compared to what we’ve got when we’re dealing with that extension cord that we were just talking about.1580

That extension cord is practically no resistance for what it’s doing. Very, very little resistance compared to everything else that electric cord is going to wind up interacting with.1595

The current is going to not wind up noticing its resistance; it’s going to notice resistance of what it’s going to.1604

For our proposes we’ll be able to treat that electric current as if it’s one echo potential surface as if it all has no voltage drop over that wire.1610

The other half of this, if electricity costs .20 cents for kilowatt hour, a reasonable price for electricity, little high in some places, a little less than what it is in other places, how much would it cost to run that light bulb for 10 hours a day over the course of a month?1619

If its .20 cents per kilowatt hour and it’s a 100 watt bulb, then 100 watt for 1 hour, well how much energy does that wind up giving us?1634

Remember, watt is power so we have to multiply it some amount of time to turn that into an amount of energy. They sell us energy from the energy company, not power. They give us power through the lines but we’re going to buy energy.1644

100 watts for 1 hour, that’s going to wind up being 100 watt hours. If we’re going to have that run for 10 hours in a day, then that’s going to wind converting to 100 x 10, a 1,000 or 1 kilowatt hour.1659

We’ve got 1 kilowatt hour per day. If we run that for 30 days then we’ve got 30 kilowatt hours.1682

Then if we’ve got 30 kilowatt hours used over the course of our month of 30 days, reasonable length for a month. Then how much would it cost?1694

Well 30 kilowatt hours times .20 cents per kilowatt hour, we wind up getting, it costs $6.00. Running a 100 watt light bulb for the entire course of the night is a nice convenient thing, it might be useful to have a hall light on at all times.1701

That costs you $6.00 to have that convenience, something to think about. All of the lights you’ve got on, if you leave a light on all day, that’s costing real money and there’s actually some reasonable things.1725

It doesn’t turn up that much but over the course of a month or a year it totals up to something you can really care about, so it’s a good reason to keep your lights off when you aren’t using them.1735

Hope that was interesting, hope you learned a lot and we’re ready to hit electric circuits where we’ll really get the chance to start understanding something about how technology is working.1744

Alright see you at later.1751