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Electric Circuits

  • Current always requires a return path. Every device that uses electricity must have a complete circuit back to the voltage source.
  • A resistor is a fundamental component of a circuit. It provides a resistance on an otherwise equipotential line of wire.
  • Make sure you familiarize yourself with all the different symbols used in writing circuit diagrams.
  • To help us analyze circuits we have Kirchoff's circuit laws: a pair of laws to help us understand what's going on in a circuit.
    • Current law: The current entering any point is equal to the current leaving that point.
    • Voltage law: The sum of the electric potential differences (voltages) of any loop is zero.
  • Resistors in series (end-to-end) have an equivalent resistance of just adding their resistances together.
    Req=R1 +R2 +R3.
  • Resistors in parallel (the circuit splits to get to each of them, then comes back together afterwards) have an equivalent resistance that can be found from the below equation:

    = 1

    + 1

    + 1

  • A voltmeter measures the voltage between two points. It is hooked up in parallel to the circuit.
  • An ammeter measures the current passing through a section. It is hooked up in series to the circuit.
  • Direct current (DC) is a steady, constant voltage. Alternating Current (AC) is a varying voltage, where it flips back and forth between positive and negative electric potentials.

Electric Circuits

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 Circuits 0:51
    • Current, Voltage, and Circuit
  • Resistor 5:05
    • Definition of Resistor
    • Conceptual Example: Lamps
    • Other Fundamental Components
  • Circuit Diagrams 7:23
    • Introduction to Circuit Diagrams
    • Wire
    • Resistor
    • Battery
    • Power Supply
    • Switch
    • Wires: Bypass and Connect
    • A Special Not in General
    • Example: Simple vs. Complex Circuit Diagram
  • Kirchoff's Circuit Laws 15:32
    • Kirchoff's Circuit Law 1: Current Law
    • Kirchoff's Circuit Law 1: Visual Example
    • Kirchoff's Circuit Law 2: Voltage Law
    • Kirchoff's Circuit Law 2: Visual Example
  • Resistors in Series 21:48
    • Resistors in Series
  • Resistors in Parallel 23:33
    • Resistors in Parallel
  • Voltmeter and Ammeter 28:35
    • Voltmeter
    • Ammeter
  • Direct Current vs. Alternating Current 31:24
    • Direct Current vs. Alternating Current
    • Visual Example: Voltage Graphs
  • Example 1: What Voltage is Read by the Voltmeter in This Diagram? 33:57
  • Example 2: What Current Flows Through the Ammeter When the Switch is Open? 37:42
  • Example 3: How Much Power is Dissipated by the Highlighted Resistor When the Switch is Open? When Closed? 41:22
  • Example 4: Design a Hallway Light Switch 45:14

Transcription: Electric Circuits

Hi. Welcome back to Today we’re going to talk about electric circuits.0000

Electric circuits are everywhere, they’re ubiquitous. They’re in the device you’re watching this on, they’re in cars, they’re in electric clocks, they’re in microwaves, they are in far, far, far more things than this short list.0005

Pretty much anything you interact with that involves electricity in the slightest way other than getting a static shock from a friend is going to have a circuit.0020

Even that is not quite a circuit, so static electricity is going to be the only thing that you’re going to wind up seeing that isn’t going to be a circuit.0029

Anything that’s got current flow has a circuit because we have to a return path for that and we’ll talk about that more as we go on.0036

Something runs on electricity it has an electric circuit. If we want to have any idea about how electricity works with technology and the modern world we’re going to have to discuss how electric circuits work.0042

For a device to run on electricity is must have current flow through it, but from the previous lesson we know current only flows when there is an electric potential difference.0053

This potential difference has to be supplied by a voltage source. From everything we know in real life, voltage sources come with a high potential and a low potential in pretty close proximity to each other.0063

The two ends of a battery, you’ve got your plus and your minus, they’re not very far apart from each other. The contacts in a wall outlet, they’re spaced by a very small distance.0075

Anything in general we’re separating a positive from a minus. We’ve got a high to low. If that’s the case we’re always going to have this pairing.0084

If a devise is to have a potential difference it has to touch both the high and the low potential. If it just touches the high potential then that means that the whole thing gets to have a high, it starts at that single plateau and it just stays there.0091

If it just touches the low then it just starts at that low plateau. It needs to have a connection from high to low so we have a reason for the electrons to travel, well not the electrons, the positive charges, but we need to have a reason for the current to flow downhill effectively.0103

We need something for it to have a reason to flow. If it doesn’t have that connection between the high to the low, there is no reason for it to flow because it’s just on flat ground effectively.0118

We need some way to touch; we have to touch both of our potentials if we’re going to get current to flow.0127

Since current always requires a…thus current always requires a return path. Every device has to touch both that high and the low potential.0135

It has to have a way for the electrons to flow through the whole thing, has to be able to go from that high potential to that low potential.0145

If it can’t go from high to low potential, it doesn’t have the current going. Since it is going from high to low potential, it’s completed a circuit with that voltage source we created.0152

The current has to be able to start at one place and then eventually make its way back to where it came from. Another way to think about it is if it didn’t have a way to make it back to where it came from, the electrons would start at a high potential and they’d get to the end of a wire.0160

They’d get to the end of something and they’d have to be pushed out into space. That doesn’t make sense unless it has such an incredibly high voltage like massive amount of voltage to hit the break down voltage for air where it’s going to be able to spark through the air.0175

Where it’s going to be able to get arching through the air, what we see when we see lightning. It’s not going to be able to have enough voltage to keep pushing those electrons through in a current.0189

The only way that we’re going to be able to have a current flow through is if we’ve got this massive voltage or we’re going to have to a way for those electrons to keep their circuit.0197

It’d be like if you had a pipe full of water and one end of was it closed off. If you tried to have water rush through this, it would hit that end of the pipe and it would just stop there until you put more and more pressure and so much pressure that it eventually you cause the end of the pipe to burst open.0208

You’re going to just have stuck water; it’s not going to have anywhere to flow. However if we were to have some system like this where the water flows through a line, it flows through a line until eventually it hits some pump.0224

It hits some pump that pumps it back up to its original place, so it gives it that potential energy; it puts energy into it again so it’s able to raise its potential so it can once again make the circuit.0246

That’s what’s happening with a voltage source effectively, is we’ve got this current flowing through and once it gets back down to the drop, it gets back down to zero, it hits the pump again and it manages to get back up.0256

We have to be able to complete a loop, if we don’t have the electrons…if we don’t have the charge flowing in the loop, whether we’re looking from the point of view of positive charge, which is how we look at when we’re circuit diagraming.0267

Or the electrons which is what’s actually moving. In either case we’ve got to have some way for it to complete its loop. If the charge can’t complete its loop then we’re going to have that same effect of bottling up the pipe and expecting water to still flow.0276

It doesn’t make sense unless we put so much pressure into that it burst and then it’s not going to be controllable because it’s going to burst every which way and we won’t be able make a useful circuit out of it.0289

We won’t be able to do any useful work, so we’ve got to always have a return path. Without a return path, current doesn’t flow, at least for our purposes.0297

Resistor. The fundamental components that makes up a circuit, there are many of them, but one of the most fundamental is the resistor. It’s an object with a known resistance; remember we talked about resistance in the last lesson that can be wired in.0306

We’ve got a resistor with some resistance. If we wire it into a circuit it provides resistance in that circuit. It makes it harder for current to flow through.0319

This can be useful for a variety of reasons and one of them major ones is that it will lower the current flow in a circuit. If we put in a resistor and we’ve got current flowing through, well it’s going to encounter that resistor, it’s going to resist the flow of the current.0327

For the given voltage we’re going to get less current flowing through. That might turn out to be useful. Another reason why is a resistor is going to…when we’ve got a voltage going across it, it’s to push that current through, it has to take energy, it takes power for that current to go through.0340

That power gets dissipated in the form of heat. If you’ve ever used an electric heater, if you’ve ever used a toaster, that’s exactly what’s happening.0355

We’ve got a resistor there that exists just to resist to electric flow. We plug it into the wall, we’ve got a big resistor and it basically just spits out heat.0362

It spits out a bunch of heat and it warms out food or it toasts our toes. Something that it makes things warm in a way that we want it to be warm.0372

Other times we can treat other objects as resistors, like lamps. We don’t just use it as a resistor or a light…a lamp will provide the light for us, but it does provide resistance.0380

As we talked about in that previous example in the last lesson, we were able to talk about putting a lamp in a circuit, putting a voltage across a lamp. We weren’t talking about it as a circuit but now we see that it would have to be a circuit.0391

If we put a voltage across a lamp, then it had to have some resistance for any power to be coming through it.0403

We can treat it as a resistor for the purposes of a circuit. Any object that we’re putting in that resists some of the current, we can also talk about it as a resistor, as a resistance.0411

There are a bunch of other things. This course will deal only with resistors but I do want to point out that there are many other fundamental components that make up electric circuits.0425

The capacitor, the diode, the inductor, and many others. The idea of a resistor will give us plenty to think about and it’s defiantly a great way for us to dip our toes in and get an idea of what’s going on in electric circuits.0433

We can diagram a circuit through the use of a circuit diagram. If we’re going to build something we want to have some way to be able to engineer our plans.0446

You need a blueprint to build a house; you need a circuit diagram to build a circuit, an electric circuit.0452

These diagrams have standards symbols so let’s talk about those standard symbols so we can talk about our circuit diagrams.0457

First one, the most basic one is a wire. It’s something that has an effectively zero resistance conductor…zero resistance conductor.0463

We’ll treat it as an echo potential path, something where it takes absolutely no voltage to get through it. The voltage, any point on a wire has the same voltage unless we have to pass through a resistor.0471

If we pass through a resistor, we’re going to get a drop in the voltage, these otherwise we didn’t have anything to push that current flow through.0483

We have no way to push charge through unless we have a loss in potential. As long as we’re on a wire with nothing else between it we can treat the whole thing as being the same potential.0490

A resistor, something the resists the flow of current. One of the forms that a resistor can come in in a drawing is this. Lately they’ve been changing to using just a simple square; it depends on what books you’re reading, what teacher is teaching you.0501

I prefer the first one because that’s what I grew up using but you also might see squares. The important part is its going to be one of those two and they don’t get reused for other things.0515

A battery. A battery is a chemical device to create a voltage source as we talked about before. Technically this is actually the symbol for a single cell; the large side is always the positive side.0526

Since we talk about current flowing from the positive way, this is the current going to flow like this and it would wind up going through some circuit and it would have to come back in on the negative side, the negative terminal.0536

Technically I want to point out that this is actually a cell, often when we’re working in diagrams we’ll only wind up seeing a cell on our diagram but technically a battery is multiple cells put together.0548

If we were to show a battery we might wind up having something like this, but normally for our proposes it’s going to be fine to just treat battery and cell as having the exact same picture, but if you wind up seeing this, know that it means something similar, you’ve got a voltage source.0562

Just it’s built out of multiple cells. A power supply, so we might also have a power supply just in general.0579

Like if we’re going to get it from a wall outlet, if that’s the case we just have a circle that has the high voltage with the plus and a circle that is the low voltage with the negative.0586

We go from plus to negative, we down the hill basically. We want to talk about just any general voltage source we use this symbol.0593

Finally the idea of a switch. A switch is a device that allows us to make or break contact in the wire giving us control over whether or not current can flow through that section of wire.0603

Possibly if that’s the…wire has to…if current has to flow through that wire to complete the circuit then we’d be able to break the entire circuit and stop current from moving at all by breaking this switch.0612

If you see a light switch in general or a switch on anything this is one of those examples. There are many different kinds of switches; there are push switches that stay broken expect for a brief period of time when you push them in and then open back up.0622

There are other ones that are cancelation depression where they stay contacted until you push on them which point the circuits broken.0635

There are ones that stay off and then stay on or flip between two different things, but for our purposes it’s enough to talk about this one switch but there are many different kinds of switches out there.0641

We’ll talk about one of the other kinds when we get to the final example for this section. One last idea, occasionally wires has to pass each other to connect.0648

If we want to show two wires that are passing each other but not connecting then we’re going to have a bypass and a bypass uses a little bridge.0659

You might occasionally see this but that’s really confusing because we don’t know if we’re talking about connecting or if we’re talking about bypassing.0668

The way that we show connection is we’ve got a little solder blob because in real life we have to take a wire and put it to another wire but then we need to use some way to make sure they stick.0675

So we use solder which is amalgam of varies metals of reasonably high conductivities that’s also melts easily. We heat a little bit of solder up over it, it drips down onto the two wires, it then re-solidifies and it becomes solid.0686

We’ve got the solid conductive thing connecting the two wires. We can connect them with this little blob because if we just see it going directly over we won’t be sure if we mean that it’s bypassing or its connecting.0699

If you do just see them touch if generally means connect but sometimes you can’t be sure. In general if you’re working on your own you want to make sure you use bypass if you don’t them touch and a little dot to show if you defiantly want them to touch.0709

Final important note, in circuit diagrams when we’re figuring out the direction of current flow when we’re talking about stuff moving, we always follow positive current flow.0726

Even though it’s really the electrons doing the following, the electrons doing the moving around. Talked about this before, we stick with the positive because of long, long held convention.0736

We’ll always pretend that it’s really positive charge is moving from the line, through the line from positive to negative. In reality the electrons are moving from negative to positive but we’re always going to diagram stuff as its going from positive to negative.0745

We’ll still have the same effect of being able to create technology doing it this way. It’s just that not technically what the natural world is doing.0758

Really simple circuit diagram might look like this. We’ve got some voltage source up here and we’ve got some switch here and we’ve got a resistor here.0766

If the switch is open no current can flow because if current were to flow it would get blocked here, so as long as the switch is open no current can flow.0775

If on the other hand we depress the switch and connect it, all of a sudden now current can flow. Current flows all the way around until it gets back to the other terminal and we’ve got a real circuit.0783

We’ve got a circuit that’s been completed. A more complex diagram might be this.0794

In this one we’ve got a voltage source, we’ve got a switch, and we’ve got a bunch of stuff to happen. In this one current would flow like this and now it’s got an option.0798

It can go through here or it can go through here. However if the switch is open it can’t get anywhere so it’d just stop here. So all the current, as long as the switch is open would have to go through here.0807

Then it would come up through here and now it’s got an option, it can take either one of these. It goes through the two resistors, splitting depending on resistance.0815

Then it comes back together and we’ll go back up and we’ll travel through this and it’ll come back to the negative end.0825

As long as that switch is up, as long as that switch is broken it’s not going to be able to dodge any of the resistors. It has to go through the all the resistors.0831

If on the other hand the switch were down, say the switch were down, then the current comes through like this and now it’s got an option.0839

Either it can flow up through here or it can continue on its merry way this way. Well if it flows up through here then it moves this way and it gets to here.0847

On the other hand if the current were to flow like this, then we’d have to go through these resistors and we’d have to go through this resistor.0855

Well it’s got an option. It can either go this nice easy wire that’s perfectly, no voltage change, completely echo potential. No difficulty to go through this wire that’s up here.0865

Or it could go through more difficulty. From the point of view of the current, even though it doesn’t really have a point of view, it’s just functioning under natural laws.0877

Why go through the harder thing? It’s just going to say “To heck with that, I’m just going to stick with the top loop,” and it’s going to wind up only going through this one.0885

It’s going to just wind up completely dodging those bottom resistors because it’s going to have no reason to go through it.0892

In reality we wind up having just a tiniest, tiniest amount of resistance in those wires but it would be really, really small so a little bit of current would make the option to flow through the other resistors but it’s going to be so small it’s effectively negligible.0897

We can treat it as if it’s just flowing through that top section once that switch gets closed. It’s a much more complex idea. We’ve got something where current is always flowing but depending on the way that the switch is down we get different things to happen in the circuit.0912

There’s a lot really cool ideas we could come up with here and that’s what engineers are able leverage so powerfully to make all the technology we use and see around us today.0925

If we want to analyze what’s going on in a circuit we need some tools. We have Kirchhoff's Circuit Laws, a pair of laws that allow us to better understand a circuit.0934

The first one is the current law. The current entering any point is equal to the current leaving that point. That makes sense. If we’ve got a pipe of water coming along and then it could split into two paths.0942

Then say it may be does a loop to loop, it’s going to wind up having that whatever flow goes in here, we don’t have more water spontaneously get generated and charge comes as fundamental discreet packets.0956

We can’t just spawn new charge because we have a break happening. So the charge gets split up. Some of it will go down one path and some of it will go down the other path.0973

Then if we wound up reconnecting, if we wound up reconnecting when they meet back up, they’re going to have the exact same amount that they had come in.0983

The amount that goes into any point has got to be the amount that comes out of any point. The amount going in is the amount coming out.0999

What comes out here gets split into these two paths and then what comes in here gets recombined. We know because the way this worked that the two currents here and here have to be equal.1006

We can start analyzing more complex things with this. Our complex diagram, if we had looked at the current going in here then we know that the current coming out here and here, we know that we’ve got i1 equals i2 + i3, the current going in has to be the equal to current coming out.1018

The second idea is the voltage law. The directed sum of the electric potential differences, voltages of any loop is zero.1038

What is the directed sum mean? That means that we have to impose a direction, so if we’ve got some circuit going like this.1046

Then we’re going to put some direction on it. We’re going to say arbitrarily this way is the way we’re looking at it. We’re looking in this direction.1056

We know right off the bat that current, since it goes on the positive side is going to wind up flowing this way. When we get from here to here, it’s all echo potential so no change in voltage.1069

When we get to this resistor it’s going to cause a drop in the voltage because it takes voltage to make it across a resistor. Otherwise you’re going to have no power; you’re going to have no way to push stuff across.1080

We take some of our potential to make a jump over. So every resistor we have is a separate individual step in voltage.1092

We’re going to lose some of that voltage but we lost voltage going in the direction of current so we’ll call this a positive thing.1099

This will be some v1 and it’ll be some positive amount. Over here whatever we have spawning the voltage, the voltage source.1106

Now if we go here, we’ve now completed a loop, but to get across this we went from a low to a high.1115

That means that we went in the unusual direction, we went in the negative…we went in the opposite direction with current.1122

Since we went in the opposite direction we’d get v1 – v2 = 0. If on the other hand we had decided to go like this as our current direction we could do the exact same thing.1128

This would come through here and we’d see, we’d go across but now the voltage is changing opposite to what we’re seeing so it’s going to wind up being –v1 and over here it’s going to jump up so it’s going to be +v2.1145

In the end we’re going to get the exact same relationship v1 = v2. If we use it to analyze a visual example using multiple resistances then whatever is here has got to be…it’s going to start off at high voltage and then it’s going to lose some voltage as it steps across this.1159

Then it’s still got some voltage because it’s got to be able to make it across this otherwise it can’t get back to the end. So now it’s gotten back down to whatever this voltage is because we know it’s got to be the same voltage everywhere on the line unless it has something interrupt it like a resistor.1191

This is one set of voltages, I mean this is one electric potential, this is one potential here, this is one potential here, and this is one potential here.1207

The voltage is the difference in electric potential. If we wanted to look at this one we’d wind up having v2’s going with direction, so it’s v2 positive plus v3’s going with direction; positive to negative.1215

V1 is going against direction in negative to positive, well it’s going with the direction but it’s doing the opposite so it’d be –v1 and that would equal zero.1228

This makes a lot sense. If we don’t have the loop get to back down to zero then that means there is a potential throughout the loop which means that if you were to go an entire loop you’ve managed to somehow gain potential.1237

That means that we’d be breaking our law of energy, we wouldn’t have conservation of energy because every time we loop we’d gain some energy.1251

If it were a negative then we’d go in the opposite direction, that means every time we went in the opposite direction we’d gain some energy.1257

So there would some way to gain energy every time we do a loop. That means that we’re not having conservation of energy because we can make one circuit and have more energy.1261

Make another circuit, have even more energy. So it would keep self-perpetrating and we’d get more and more and more and more, doesn’t make sense, doesn’t work, doesn’t jive with everything we’ve talked about.1269

Conservation of energy, thermodynamics doesn’t work. We can’t have that, we can’t have something where its gaining it so it must be the case that at the end it’s gone back down to zero otherwise there’d be some way to configure it so we’d have more and more and more energy every loop.1278

It wouldn’t make sense. Any loop, whatever loop we choose, is going to wind up having a drop to zero. Sorry, its’ going to be…if we sum up all of the voltage differences, all the voltages, we’re going to get zero.1294

With these laws we can now analyze the effect of resistance of resistors when we put them end to end in series.1310

If we wanted to look at this, first off we’d could say that if we go through this like this we’re going to get that v2 + v3 – v1 = 0.1317

What we just said. Well v2 + v3 = v1. Another thing to notice, there is only one path for the current to take.1330

I must be the same throughout, since there is no ways for the current to get to a different…to break its path, i has to be the same throughout.1340

Since in general v = ir, we can substitute based on the subscripts we have. So we’ve got the current times r2 plus the current times r3 has got to be equal to the v1 because v2 goes to that, v3 goes to that.1351

We pull out our current and we’ve got that the current times the sum of the resistances is equal to the voltage. That means that we can now treat this whole thing as if it were a special circuit that instead just had one equivalent resistance.1365

One resistance equivalent and we could forget about this stuff here. We could forget about all this stuff here and we just have one resistance equivalent.1384

That means we can combine it, we can figure out what resistance two of them put end to end or five of them put end to end is going to be.1392

In general the equivalent resistance of resistors in a series, when they’re end to end is just the sum of what all of their individual resistances was.1400

If we want to know how much a bunch of resistors stacked on top of one another is we just add them all up.1408

What if we put them in parallel instead? Instead of being stacked end to end, they come in parallel.1414

Notice here, this current has the chance to split off. It can go one of two ways. That means each one is going to experience a different amount.1420

However if we were to start doing loops we’d be able to get some more information. First thing we want to do is we want to figure out how we can treat this whole thing as some r equivalent.1430

How can we break those parallel resistors into just one resistor? Our rules are really easy if we just have one resistor.1443

If we could treat it as one resistor that’d be awesome. What would that look like? We want to find some r equivalent, some resistance equivalent....resistor equivalent such that v1 divided by that resistance equivalent is equal to the current.1448

What we’re used to is v = ir. We want to have some equivalent resistor that is going to allow us to fulfill that.1462

We want to figure out something we can treat this whole thing as. First thing to notice we can do two loops.1469

We could go a loop like this, that’s a loop, it gets us back to where we started or we could do a loop like this.1476

One loop where we don’t repeat anything, as long as we don’t repeat but we make it back to where we started, we’ve got a loop.1486

If we do that way then first off we’d see that v1 has to equal v2 through the red, I should use the color red just so we can see that.1493

v1 has to equal v2 through the red and simultaneously v1 has to equal v3 through the blue.1501

Otherwise those loops wouldn’t be following that voltage law. Next up we know that the current sums have to come up together.1509

i1 has to split into two different things; i2 and i3. I1 must equal i2 plus i3. Then they recombine so it must be that whatever comes out on this side is whatever i2 and i3 was together, which we already know is i1.1517

We’ve got the current flowing down this side, flowing up this side and it’s going to split into two slightly smaller currents, or maybe much larger current.1531

Definitely going to split, who knows what the sizes are, that will vary on the resistance and that’s what we’re working to find out now.1540

In general we can put these two things together and we can see using i1, i2, i3 we know that since v = ir we can solve and we have v / r = i.1546

Whatever our little subscripts are here we get v1 divided by the resistance equivalent is equal to v2 / r2 + v3 / r3.1560

We’re looking for something like this. We’re looking for that r equivalent to show up. So as we know current one is here.1568

We want that v1 r equivalent, we plug that in here and we know i2 and i3 come from this here, so we’ve got that the voltage of whatever our voltage source divided by the equivalent resistance of the whole thing is got to be equal to the voltage of the second resistors divided by the second resistor resistance.1577

Plus the voltage of the third resistor divided by the third resistors resistance. We now realize ‘oh yeah’ v1 = v2 = v3, so we can cancel them all out.1600

We divide the whole thing by v1 and since v2 and v3 are also v1 we’ve got 1 over r equivalent is equal to 1 / r2 + 1 / r3.1610

In general the inverse of the equivalent resistance, the inverse of the equivalent resistance for our parallel set is equal to the sum of the inverse of those parallel resistors.1620

This would work if we had 50 of them as well. The equivalent would be equal to 1 over the first resistance plus 1 over the second resistance plus blah, blah, blah, plus 1 over the 50th resistance.1631

All of them added together, but those inverses added together when we’re dealing with parallel.1642

What this means is the current has more options. Since it’s easier, less current has to flow through it’s going to take less voltage.1648

If we have it splitting over two of them it’s going to wind up being less equivalent voltage for it. Real quick, if we had just some resistance, if both resistances were r then we’d have 1/r equivalent = 1/r+1/r which means that 1/r equivalent would equal 2/r.1656

Which means that r equals 2/r equivalent, which means that if they’re all just the same it’s going to wind up being half of it because the current has double the options.1678

If you had 5 of them, it would be a 5th resistance to get through that parallel section because the current has 5 options.1690

The current doesn’t have to work as hard to get through one resistor because it can only some of it current there and give some of the current to somewhere else.1697

It can be a little; it’s easier at every location because it gets the chance to split up. It has more options.1704

If the resistance are not equal it becomes a little more complicated, we have to do a little algebra but nothing too difficult.1710

What if we want to physically measure this stuff? What if we want to find out what’s the voltage in a section of the circuit? We want to find out what the voltage over resistor is.1717

Then we use a device called a volt meter. It’s a device for measuring voltage.1724

Meter measurement, volt, volts. If we want to measure the voltage, we connect it in parallel.1728

Why do we connect it in parallel? Remember voltage anywhere on a line is different. Here’s one potential, here’s a second potential.1733

These potentials are the same until they get to this resistor. Then they’re some voltage change, some change in the voltage. The voltage dropped; the potential difference.1744

So this volt meter is going to see v1 over here and it’s going to see v2 over here. It’s going to also be able to read that same potential drop.1752

That same potential difference, that same voltage. We’ll be able to read that voltage by putting it on either side in parallel to what we want to look at.1763

Notice if that volt meter were to allow current through it, we’d change the circuit dramatically. We’d be able to allow current to go through it so that means that less current would pass through here, so we’d need less voltage to push it through.1771

It has to be the case that a volt meter has extremely high or effectively infinite resistance, otherwise current will flow through it and it’s going to have an effect on the circuit.1785

We always put it in parallel and it doesn’t affect the circuit because it’s resistance is so high that the currents like “Heck with that, I’m not going to flow through there. I’m just going to take the path I normally would have taken.”1795

On the other hand if we want to find out the current we’re going to use ammeter. Am, amp, meter, measuring. It connects in series to the circuit.1806

Why? If we’ve got some current flowing through then we’ve got to have all that current flow through. If we put it in parallel, why would the current have to flow through it?1814

It wouldn’t necessarily decide to flow through that section, so it wouldn’t be a good idea. However, once again we’re going to have to choose this things resistance based on making sure it doesn’t affect the circuit.1824

If there’s resistance here less current is going to flow through the circuit because it’s harder over all to get through it.1835

An ammeter has to have effectively zero resistance. Something that has such low resistance that from the currents point of view it doesn’t even notice going through the ammeter so it’s not going to have an effect on what we’re seeing in it.1842

An ammeter allows us to measure the current by putting it in series. A volt meter allows us to measure the voltage over some section by putting it in parallel.1855

In general modern electrical analysis tools are able to do both. There is a volt meter and ammeter function on your multimeter since it has multiple tools.1866

It can even do many more things in addition to just volt meter and ammeter functions but being able to measure voltage and being able to see current, those are both really, really useful. Those are really important things to have in our multimeter.1874

Another idea that we should talk about is that direct current is what we’ve been talking about so far. We’ve talked about voltage as if it’s always a single constant unchanging value.1885

This is called direct current because it provides us with a steady direct source of current. Makes sense, but that isn’t always the case.1894

Sometimes it’s possible for the voltage to vary. The voltage in a wall socket will flip between positive and negative many times a second.1902

If you’ve ever heard about the voltage, the current in some country being 60 hertz or 50 hertz, that’s because it alternates per second 60 or 50 times.1908

It manages to flip between the positive and the negative. One of the lines in that wall socket, the neutral line stays at 0 volts, also sometimes called the cold line.1919

The other, the hot line, varies from positive to negative. It flips up to positive and then down to negative.1930

If you live in the US you’d see positive, actually you wind up seeing higher than the number given because that’s the average that it comes out being for the purposes of using electronics and the amount of energy.1937

But there is extreme values pass what we see. We call it 120 volt but it actually has a peak of +170 down to -170. It averages out to effectively being 120 but it winds up having peaks that are higher and lower.1948

If you’re living in a different country, like Europe, you might see an average of 240 or 220 but it’s going to vary depending on the country and there’s also the peak voltage that goes passed that.1963

For our purposes if we get a problem dealing with that we can treat it as that if we want to know what power dissipation is because that’s how it works.1972

That’s what the point of having what that average value is. We call this alternating current because it alternates between the positive and the negative.1979

We’ve got the hot line flipping between positive to negative while the neutral gives that always continuous return path, whether it’s positive or negative, it’s something for it to go along.1988

Sometimes positive charge will be flowing from the neutral to the hot, other times it’ll be flowing from the hot to the neutral.1998

It depends on whether we’re negative or if we’re positive. In any case we’ve always got that return path going on.2003

We can see this visually by the two different voltage graphs. DC just has a straight line continuing out, it doesn’t change it voltage, with respect time always stays the same.2011

Alternating current, AC on the other hand though, it’s going to flip up and then flip down. Flip up and then flip down. Flip up and then flip down. Every bit of time that we move across it’s going to wind up changing its voltage.2021

It’s going to have its own regular pattern like when we talked about waves. Finally ready to talk about some examples.2033

What voltage would be read by the volt meter in this diagram? The first thing to notice is remember, we don’t have to worry about this taking anything off.2041

It has no effect. So what we have to do is figure out what’s the voltage change here.2048

What would that voltage change be? IT’s not just the voltage change from here to here because we go all the way from 9 to 0 volts, 9 volts to 0 volts.2053

Because here echo potential all along the line. Since these are echo potential all along the line we know we have to be 9 volts over here because we’ve got the positive 9 volts.2064

Then down here we have to be negative which we would normally just make 0. We know the important thing is that they have to have a difference of 9.2073

It’s not just figuring out what’s the 9 volts applied over that whole thing because each one of these is going to take is own change in voltage.2079

It takes some amount of voltage to get that, to get pushed over it. We need to figure out how much voltage gets put into each one of these resistors.2086

What we could do is we could use the various laws we have or remember we talked about what resistors in series.2096

If we want to figure out what the equivalent resistance of that whole thing is, well resistance equivalent series. Resistance equivalent is equal to the sum of the resistors.2102

If we want to know what this is. First one, 10. Second one, 30. Third one, 50.2120

The sum of our resistances are equivalent resistance from the point of view of that voltage source is going to be 90 ohms.2130

If that’s the case, how much current flows through? Well the current that it’s going to put through, we can see what it would do that equivalent resistor.2137

That’s going to be a 9 volts divided by our equivalent resistance of 90 equals 1/10 of an amp or 0.1 amps.2145

We’ve got .1 amps in there. If we want to know how much voltage has to go through here. Well we know we’ve got .1 amps.2160

The voltage drop over each one of these is going to have to vary based on how much current has to get through. The 10 ohm resistor will use less than the 30 ohm resistor will use less than the 50 ohm resistor because it takes more and more push to get a given amount of current through with a higher resistor.2168

If we want to know how much goes through the 30, what that change is there. We know what the current going through is, it’s 0.1 amps.2187

We know what the resistance is; now we can figure out what the voltage drop has to be. What that voltage across that resistor if it’s going to be able to have that much current flow through it.2193

We’ve got v = ir. We know what the current is; we know what the resistance is, so the voltage is equal to current, 0.1.2203

Resistance, 30 ohms. We get it must be a 3 volt drop over it. It drops down here from positive down to a lower one.2212

We can see here it’s going to be 9 and then same idea, 10 ohms is going change to a 1 volt. It’s going to be 9 here, let’s erase just a little bit so we can see what’s going on.2223

9 volts here because it’s on the line, then here it’s going to drop to 8 volts. Here it’s going to drop to 5 volts, here it’s going to drop to 0 volts, which is great because then it matches up to what it should be originally coming from.2234

That means the volt meter is going to see 8 volts to 5 volts so it’s going to see a change of…sorry, a delta v. The voltage that it’s going to read is going to be 3 volts.2247

Next one. If we have our complex diagram that we saw before and now we throw in some resistances, what would be the ammeters current flowing through it?2263

How much current will flow through the ammeter if the switch is open? If that’s the case, current flows like this.2272

It can’t make it up through this switch, it gets blocked. So we don’t have to worry about anything making it through this line.2280

Going to have to split over this and then come back together like this. We can use those current laws but remember we could also figure out what’s just the r equivalent for this whole thing.2286

Well r equivalent for this whole thing, 1 / r equivalent = 1 / 40 + 1 / 5. Convert to common bases, 1 / 40 + 8 / 40.2295

We’ve got 9 / 40 and since it’s 1 / r equivalent = 9 /40 we flip both of them and we’ve got that the resistance equivalent seen by this is going to be 40 9ths which turns out to be 4.44 ohms.2317

Notice that means it has less resistance there than either of the resistors because the current has more options to flow over.2339

If we know what the equivalent resistance is here then this is effectively, we can treat this as effectively…we can forget what it came from and we can treat it as one effective resistor that just connects here and here.2348

Then that means we’ve got 1, 2, 3 in series. R equivalent for the series, so let’s make this r equivalent parallel, r equivalent series is going to be each one of those added up.2361

We’ve got the 4.44 ohms first then it adds to the 100 ohms, then it adds to the 5 ohms. The total resistance for this entire path is going to be 109.44 ohms.2377

109.44 ohm. So if we wanted to see how much current flows through this path. Voltage equals ir. v /r = i. We sub in our voltage; we’ve got a 20 volt difference going over this path.2394

We’ve got 109.44 resistance, 109.44 ohms. We pop that into a calculator and we get 0.183 amps equals i.2407

The ammeter is going to read .183 amps running through it because we’re able to…we want convert the parallel into one effective resistance and convert everything.2422

It’s basically a way being able to figure out what do I have to change into, what do I have to suck into one piece that I can treat it as one big resistor because it’s really easy to work with one big resistor that would give us what it is.2432

Then once we know it’s one big resistor with a current flowing through that big resistor is, we can apply that throughout those same places.2443

Notice this and this would have different numbers of amps. They would not each be .183. One of them would be some portion of .183, one of them would be some other portion but they’d add together to make .183 because it has to split around that point.2448

Which one would get more current? The lower resistance because it’s easier for current to flow through it. Once they recombine both the 100 ohm and the 5 ohm will wind up seeing that .183 amps because they have to be getting the full current flowing through it.2466

How much power would be dissipated in that same circuit if the switch was open? Remember power equals current squared times resistance.2484

That was one of the ways we had it. When it was open we knew what the current was, the current was I = 0.183 amps.2497

If it’s 0.183 amps, we chuck it in and we get that the power is equal to 0.183² times the resistance. How much is the resistance for that resistor?2511

Its 5, so that comes out to be 0…..let’s write somewhere a little bit lower. Equals 0.167 watts.2522

That’s what the power would be when the switch is open. What happens if we go and we close the switch?2536

If we close this switch, we see a very different circuit all of a sudden. All of a sudden the current, it can flow through here and up here or it can split and go this way.2547

If it splits and it goes this way, it has to go across these resistors. But if it splits and goes this way, well it’s going to split and go both ways, if it goes this way, it dodges those resistors.2561

What does it take to make it across a resistor? It takes a voltage. You have to have a potential difference. It’s going to take some pop to get over these and then another amount to get over these, over that final resistor.2575

To get over each of those is going to take some voltage. We know voltage here is equal to voltage here is equal to voltage here is equal to voltage here because they’re all connected by wire.2588

They’re all connected by echo potential wire. The voltage here and the voltage here is the same thing.2600

The only place we’re going to wind up seeing different voltages is when we make it to the other side of the resistor.2607

Since there’s all just pure wire connecting all of these locations, here and here have the same voltage.2615

They have the same potential, if they have the same potential there’s not voltage across them. There’s no difference in potentials.2621

Potential difference makes voltage. There’s no voltage to make it across all those resistors. Why would the current choose to go through a hard path when it’s got this nice well paved road to just go through?2628

It can either hack through a jungle of those resistors in the bottom or it can just walk on the well paved freeway.2639

Maybe it takes a Lamborghini on the well paved freeway. It’s really easy for it to get through the well paved freeway, through this middle section right here.2644

When the switch closes it forgets about those resistors on the bottom and all of a sudden the only resistor it’s going to see is that 5 ohm resistor.2653

Now we’ve got voltage equals ir. 20 volts divided by 5 ohm resistor equals 4 amps of current.2661

What happens if we check this for power? Power equal i²r equals 4² x 5 = 16 x 5 = 80 watts.2672

That’s a whole lot more power because now we can have way more current flow through since there’s’ way more current flowing through we’re getting the chance to dissipate more power.2689

When that switch closes we manage to jump from .167 to 80 watts. We managed to jump 600-700…probably like 500xs more power is being dissipated all of a sudden.2699

That’s a lot more power that we’re jumping up. Think about that. Example four.2710

We’ve got a two way switch. Remember how I talked about how there being other switches, this is one of them.2717

A two way switch looks like this diagram. What that mean is when you switch it, it flips to the other line. A normal light switch in a wall is this kind of switch.2722

It has…it depends. For the most part this would be a reasonable thing to think. A two way switch is going to look like this.2731

When you pop the switch it doesn’t go to disconnect it, it pops down to here. If you pop the switch, it flips to the other one.2744

If you pop the switch again, it flips back to its original. Every time you pop the switch it flips to the other line.2755

It doesn’t go off it just flips between the two lines. We’ve got this flip flop here. This is an important element in circuits.2763

We want to be able to have other ways to connect things and this is a really cool switch that’s going to let us do some interesting stuff now.2771

Here’s the question, here’s the idea we’re going to try and figure out. If we’ve got two of these, I’m going to hand you two of these switches and an arbitrary amount of wire that you can easily connect.2778

I want you to design a hallway light switch circuit. Where flipping either one of the switches will turn on the light but flipping them both will turn the light off.2789

This is just like what we’re used to at home. They both start down, you flip one of them and pop the light turns on.2799

You flip it down, pop the light turns off. You flip the other one on, pop the light turns on. You flip this one back down, turns off.2805

You flip them on and on, the light goes off. That means you only have to be at one end of the hall or either end of the hall to be able to turn on the light.2811

This is handy in a hallway because we don’t want to have to walk to one end before we can turn on the light.2820

As opposed to most of the stuff we’ve wound up working through so far, where we’ve been like, let’s figure out how to apply our formulas, let’s figure out what the best thing to do is.2826

Then we just methodically go through it. Designing something like this, engineering problems, a lot of them wind up having math going on for a long time.2835

At some point, if it’s going to be an interesting bit of engineering, it’s a riddle. It’s a puzzle for us to solve.2844

This is a puzzle and now I can tell you what the answer is because I know the answer. It’s like a riddle, once you know the answer you know the answer.2850

You won’t get the chance to experience this riddle if you don’t wait for a second and think about it.2857

I would encourage you; pause this video, take a piece of scratch paper and screw around for 2-3 minutes trying to figure out how could you connect this thing?2861

In just a second I’ll give you a hint so you can go think about that hint and try it one more time before I finally give you the answer. I’ll wait.2869

Assuming that you took a little bit of a look or maybe you just skipped up to the answer, oh well. Assuming you took a little bit of look but you couldn’t figure out.2881

Here’s the hint. Try it but try putting the two switches near one another but don’t put them end to end, put them so that they face opposite directions. Then try thinking about the connection.2888

Remember you want something where that when you flip one it’s going to cause it to see something opposite. They’re going to have to talk to each other because they’re going to have to somehow see what the other one is doing in a manner of speaking.2899

There’s going to need to be some information communication going on between their states. They have to connect to each other in some way.2909

Think about that, think about trying to turn the way you’re looking at them around. Give it another minute, give it another shot. It’s a really cool idea and if you manage to pull it off, it’s a really great feeling.2917

Solving puzzles to me, is one of the most satisfying things there is. Give you another second, pause me.2927

We’re finally ready for the punch line. The trick is like I was saying; we’ve got the lamp up here and the negative line here.2935

We’re going to wind up connecting the negative line directly to the lamp. There’s actually multiple ways to do this but this is a general idea.2943

This one is a very good way to wire such a switch. Now if we’ve got one of these switches over here and we put another one of these switches over here so they’re facing each other.2952

We can connect this switch like that. We’ll connect this switch to the power source. Now we need some way for them to talk.2971

Say this switch is originally like this…that was a little crooked, let’s make it straight. This switch was originally like this and this switch is originally like this.2982

If that’s the case then we can take this and draw straight lines and at first they don’t talk to each other. They don’t talk to each other when they’re starting off.2994

If we go back and flip one of these two, hey look, we’ve not completed a circuit. We’ve got a way for energy to run through.3011

If then we come along and we switch the other end, we’ve broken the circuit because now it’s seeing the other side. It’s a question of do you guys both see the same thing at the same time?3022

You put them in so they see different things at first and then they flip between the two states. If their two states are in agreement, power flows.3033

If their two states are not in agreement, power does not flow. By putting them…so that they look at each other in opposite ways, they start off looking at different things, then you just flip which thing they’re looking at.3040

You change the bit of information they have, you’re able to have this communication of what the other one is doing. Once they’re working in tandem, if they both have the same piece of information.3051

They both say on, it’s on. They both say off, it’s off. If it’s on/off or off/on then we’ve got offness.3060

It depends on how we do it. We could also look at it as being on/on being off and off/off being off.3071

It just depends on how we’ve named it. The important thing is if we’ve got these…it’s about controlling how these states are talking to each other.3077

It’s a really interesting idea and this bit of circuitry is actually probably in your house or your apartment, wherever you live.3083

It’s almost certainly in something you’ve ever interacted with. Is in some way able to just flip it and so they have to do is they have to wire to other one before they wire to the light if you want to have in this method.3089

There are other ways to wire this and that might be one that you figured out, but this one good way to wire such a switch.3099

Hope that made a lot of sense and we’ll have our final lesson on magnetism where we’ll get the chance to see what’s going with generators.3107 it is that we’re able to have such a great supply of energy; how it is that a motor can run work on electricity -- all these cool ideas.3111

See you on later.3121