 So, lesson four, back voltage, back EMF. Recall how an electric motor works. An electric motor works when we send a current through an armature through a moving coil. In this case, we're sending the current upwards on the left side and down the page on the right side. So just to get a feel for which way the force is acting, on the left side here, point your thumbs up the page, which way is the magnetic field? Magnetic fields always point from what to what? So from north to south, the left side would get forced downwards, yes? Now what about the right side? Point your thumbs down the page on the right side, magnetic fields still go from north to south. I'm having to bend my hand like this kind of crooked. But the right side would get forced upwards and this is what caused it to spin. This is your electric motor. However, let's look at a single positive charge right there. Now this positive charge is actually moving in two directions. It's getting forced upwards because of the battery. But as soon as this motor starts to spin, which way is this positive charge moving also in the magnetic field? Downwards, right? So point your thumbs downwards, fingers in the direction of the magnetic field. Which way will this positive charge also feel a force? I think along the wire back towards the battery. So once the positive charge starts to move down, comma, it experiences a force towards the battery. Evan, there is a current in the opposite, yeah, you with me now? Okay. Bonson Park after school, start then, I don't care, but right now I need you here for the very last lesson. There is a current as soon as the motor starts to move in the opposite direction of the source current. We call that a back voltage or a back EMF. And that's today's topic. We call this a back voltage or a back EMF, which means your net voltage just decreased. If you have a 12 volt battery and you're generating two volts from the spin, your net voltage is 10 volts. And that current then also decreased. We should elaborate on the concept of back EMF. So here are the key facts about back voltage in an electric motor. Back voltage is created by the spinning armature, the coil that spins inside of an electric motor. And the amount of back voltage is proportional to how fast the armature spins. The faster you spin it, the more back voltage, the lower your net overall voltage. This is why electric motors cool off when you rev them up. Because the faster you spin it, the higher your back voltage, which cancels out your source voltage. And ideally you reach a point where your net voltage is zero, no current is flowing. Now it's as cool as it's going to get. Now, when the motor starts out at rest, what's the back voltage? It's a trick question, Ian, our symbol for back voltage, V back. When the motor is at its maximum operating speed, the back voltage is its maximum. Ideally in our perfect frictionless magic physics world, at maximum operating speed, the back voltage would equal the source voltage and that would mean your electric motor would never get hot. While they even at maximum speed, there's still friction and that is not perfect. So electric motors, when you rev them up, there's still something generated. But nowhere near as much as when they're under load, barely being able to turn. So compare back EMF to supply voltage. These supply will always be bigger than V back. Or airy in our magic physics world, we might be able to get an equal to V back. Black back voltage will never be bigger than your source. Turn the page. The mathematical analysis is fairly straightforward. Here's your battery or your plug powering the motor. Here's your supply voltage. As soon as it starts to spin, it says, though, you have a battery pointing in the opposite direction, make it mathematical. The motor itself becomes a battery. And the arm itself, that's your resistor, your internal resistance as it were. So you have current going this way. But the positive is facing this way in the opposite direction. You have a secondary current pushing against your initial current, which lowers your net overall current. And if we apply Kirchhoff's law, we get this, the source voltage. Now, if I go from here all the way through to here, I have to be able to end up at zero. How can I do that? Well, let's see. I would lose voltage going through here. I would lose voltage going through here. How do I want to end up, Mr. Dewick? Source voltage is going to be, you lose voltage going through the back. And you lose voltage going through the armature. Is that what I want, Mr. Dewick? Let me pause for a second and think about this. Sorry, that's a plus, because we're going in this direction. The current is still flowing in this direction. So it's going to be this takeaway that gets you back to zero. This is not the formula we're going to use. This is the mathematical analysis. The formula we're going to use is this. Back voltage equals your source EMF minus whatever voltage is left inside the armature itself. And this is on your formula sheet. This is on your formula sheet. And since it's on your formula sheet, oh, I have a box over here. Of course I do. Don't I usually have a box? The back equals EMF minus, what is I times R? What is I times R? Voltage. Source voltage, take away whatever's left inside the armature. Everything else must be back voltage in the opposite direction. That's how the ski hill works in that one. This is supply voltage. So I'll put a little E right there. And key ideas. If you're at rest, you know your back voltage. Nothing. I is the current through the motor. R is the resistance of the turning part of the motor, the armature. It's the fancy word for that. Going to make it airy? Here's a classic question. OK? A motor is connected to 100 volts. Initially with the motor at rest, we know the current running through the motor is 5 amps. When the motor is running at maximum speed, the EMF is measured at 20 volts. The back EMF is measured at 20 volts. Find A, the resistance of the armature, and B, the operating current for the motor when it's running. A. Here is how you can find the resistance of your motor with the electric instruments without taking apart the motor. At rest, Dan, what's the back voltage at rest when we're not turning? Yeah. Did you get that, or did you get the whisper? You with me now? You're back? You're OK? We're with me? What else have they told me? Well, they've told me my source voltage. This never changes. Dan, what are we plugged into? No, how many volts are we plugged into? 100. Did you say 100? Yep. And I also know the current at rest. We have an ammeter that's running through our motor, and we know the current at rest, Dan, is 1. 5. So the equation for back voltage is this. B back is source minus i times r. 0 equals E minus i times r. Dan, A wants us to get the resistance of the armature, get the little r by itself. You know what? I wouldn't minus the E. I'm actually going to plus this over, and then just divide by i. The resistance is your source voltage divided by the current at rest. It's V over i. What's my source voltage? 100. What's my current at rest? 5. The resistance inside this motor is 20 ohms, and that's a physical property, Brandon, that never changes. No matter how fast or how slow you're running the motor, the resistance is the thickness of the wires. It's 20 ohms. What does part B want us to find, Brandon? Now we're running. So when we're running, I read the question, now my source voltage is still 100. And I just figured out in part A, the resistance inside the motor itself is 20. That's not going to change. And they told me something else when we're running. Troy, what? The back voltage that we measured, 20 volts. Probably smokes that ran out of room. OK, I thought I had a bit more room to write here. We're going to get this. Back voltage equals E minus IR. Troy, they want us to find the operating current, get the I by itself, close. V minus E, I think divided by negative R, is it not? Because there's a negative there I've got to deal with too. Yeah? What's my back voltage? 20. What's my source voltage? 100. What's my negative R? 20. If you have a back voltage of 20, how many currents is your motor drawing? No, nothing there, eh? 4? 2 sig figs, 4.0 amps. Sorry, I ran out of room. Bad space management. OK? Let me pause because some of you are zoning out. So the back voltage equation, V back equals EMF minus IR. When you're not turning, what's your back voltage? Which means you can solve for one of the other three quite often. And then when you are turning, they'll either ask you to find the back voltage, which means they told you the current, or they'll ask you to find the current. Usually they won't ask you to find the EMF because they'll tell you the source voltage in the question. Example four. The resistance of the armature of a motor is 12 ohms at operating speed. When connected to 120 volts, the motor draws six amps, find the back voltage at operating speed. Well, back voltage equals source minus I times R. Megan, do I know the source voltage? 120? Do I know the current when we're running? Six? Do I know the resistance of the actual armature? Oh, this is straight plug-in chug. The back voltage is going to be 120 volts minus 6 times 12, also voltage, I times R. What's the back voltage that this motor is going to be sending back down the armature? Sorry, I can't hear. 120 minus 6 times 12 is what? Someone needs to crunch the numbers. 48? And your net voltage would be 72. 120 minus 48, your net voltage is 72 volts, which also happens to be what's left inside to turn the motor. Oh yeah, that makes sense. When an electric drill is prevented from turning, the motor heats up. How can we cool the motor off? Grab it as fast as possible. And the reason Brandon is this, if you're prevented from turning, what's your back voltage? If that's zero, the current is maximum, and it's current that heats up a resistor. So spin it. This gets bigger. This gets smaller. It's not the resistance that gets smaller. It's the current inside the motor that gets smaller. Your motor will cool off. Handy trick for those of you that do any household repairs with electric drills and things like that. There you go. Will that cool it off quicker than letting it sit? I wouldn't be surprised if yes, because you'd have air that would be pulling the heat off. I think the differential would be better that way than just letting it sit still. Ready? Try example six on your own, boys and girls. I need to get you out of your stupor, your lethargy, your drool running down the side of your face as you're zoning out, because getting sunny in to a better day. And cannot skit. Shut up. When do you grad? Not for three more weeks. Stay focused, right, Evan? Absolutely. Quiet, please. No. Physics. Not socialization, physics. Or I'll move you. I got a lovely seat right here that our friend seems to have vacated for the rest of the year for some strange reason. Try this. Good, go. I got a resistor of that. Can always find the resistor by remembering that if it's not turning, you know the back voltage. It's zero, right? That's the key concept. Otherwise, it's a straight plug-and-chug formula. You shouldn't get a negative. Check your signs. Yeah, there is a built-in error check. You won't get a negative resistance. If you invent one, you may win a Nobel Prize. We have superconductors, which have zero resistance. But I don't, because a negative resistance would somehow imply that, yeah, it would essentially be an accelerometer for particles without requiring energy. Invent one, but mention my name. And then for current, I got that. Yes? I like number six. I like number six. Number six is a nice question. I like number six. Back voltage. Applications of this, so in electric brake systems for the Prius and things, they're bleeding this back voltage off to recharge the batteries. That's why when you stop, it actually recharges the batteries. Very clever. Some other way cool applications. And I may finally buy one this summer. Turn the page. Does anybody here have an induction cooker? You do? Wow. So what's an induction cooker? It's a stove that boils water with no heat. See? Ice next to boiling water. Now, what does it do? Underneath here, there is an oscillating magnetic field, solenoid, just like our speakers, which means in this metal ring, there is an oscillating flux, which means you have a very rapidly changing alternating current. You have particles moving back and forth, back and forth, back and forth inside the metal. And just like when you rub a rope back and forth, back and forth to generate friction, you're generating friction inside the metal. And what will particle friction create? Heat. Ah, but here's the thing. Heat with no heat wasted from the stove element. These are huge in Australia. Why would these be huge in Australia? Hot kitchens. These are becoming big in college dorm rooms because you can have a single element and not have to worry about the fire hazard aspect. So you guys have one? I really do want to see if they make a standalone one. I tell you, on a hot day in the kitchen, great. Most of you don't do a lot of cooking. Once you start cooking for yourself, when it's 35 degrees out, there's a reason people like to grill outside. And it's not just because, hey, the food's good. It's because, hi, it's 35 degrees in my kitchen and I'm standing over a hot stove with more heat. Doesn't work very well. So negatives, however. Not all cookware will work. The cookware, for it to work, it has to be magnetic. In other words, it has to attract the magnet. If it does not, and most non-stick stuff does not, then it's not conductive and it won't actually generate the changing, oscillating current. So what works great is a cast iron skillet, though. And there's also induction cookware that you can get. I just bought a new set of cookware about two years ago, which is why I haven't bought an induction cooker. But they're fast, they're efficient. I think they're faster than a regular stove element. Certainly more efficient. If you've done any cooking, how much heat does not go into heating up the pot? Lots, lots. Yeah, which is why the ice can sit there and not melt. The heat is inside the pot. Just fine. Also, for safety, if you have toddlers or children, okay, Troy, we gotta be careful. I imagine some heat would get conducted down from the boiling water down to there. But I don't think it's anywhere near as like, you're not gonna scar yourself burning. I mean, the ice is just sitting there. So I imagine the ice would probably be experiencing some heat, but I would imagine it would not be enough to, it might even be enough to give you like a first degree owie, but not a third degree. I gotta, which hand is it now? This one. I got a permanent scar, you can barely see it now, but when I was about seven years old, my mom asked me to take a baking pan out of the oven. And I didn't know that the baking pan was on a cooling rack. I grabbed the cooling rack and I tilted it and the baking pan slid off and sizzled against my wrists while I screamed because I didn't wanna drop the baking mummy, mummy, mummy, come take this off. And for honestly, about 15 years, I wouldn't take anything out of the stove. That's one of my most, I still can vividly remember standing there for about a second as my wrists sizzled until my mom managed to sprint across the kitchen with a pot holder to grab this baking pan off my wrists. And I have, I think it's, you know what? I'm just realizing my scar has finally, finally faded. It's right there. I finally outgrown it. But boy, that's one of my worst childhood memories. Now, they don't make induction stoves, oh, they probably could. Although I don't know if you have as much control over the actual temperature. No, you would because you would just increase or decrease the current. It would give you exact control over the temperature. I'm impressed. This is the first student finally that's got an induction cooker. I think they started to make their way to North America about four or five years ago. Yes, but again, your cookware would have to be metal that would attract a magnet. That's how you know that it will conduct the current. Yeah, that would work. Sure. Okay. So how does an induction cooktop work? Induction cooktops have many advantages over other cooking methods, including efficiency, controllability, and safety. So each hob, each plate here contains one or more coils made of a ferromagnetic material, some type of iron. When an alternating current is passed through the coils, you get an oscillating magnetic field and this acts essentially like lens's law. It will create a magnetic field opposing the magnetic field that's causing the current in the first place, as long as your magnetic field is oscillating, you're gonna have the charges going back and forth, back and forth, back and forth, and that's friction. Once the pan is removed from the cooktop, the energy transfer stops, the result is a flameless method of cooking in which it's nearly impossible to start a fire by forgetting to turn off the stove. You could leave the stove on 24 seven. Really, it'd be a waste of power. Okay. And at least once in your life, all of you will forget to turn the stove off. And they're done that. Came back six hours later. Why is my sweet old warm? Whoops. Okay. No, it was actually, it was the power went out while I was cooking and I forgot to switch the stove off and I was cooking. Yeah, hungry! Drove out to get some food somewhere, came back, the power had come back on again and the stove was, you know, cooking hot. Parents won't have to worry about their child touching a red hot burner because the cooktop surface remains relatively cool. Changing cooking temperatures is achieved very quickly because there's no weight for the actual element to heat up as soon as you change the current. All you're waiting for is the pan to heat up and that happens pretty quick. Since there's no transfer of heat energy between the hob and the pan, less heat is lost into the air. So more efficient and a more agreeable cooking environment. A neat, very cool application. There it is, physics 12. That's the end. Well, it's not quite the end. Nope, I hit the wrong button.