 Okay, good morning. So we've got a bunch of stuff to cover today. We're going to start learning to solve problems that contain capacitors. Homework three should go up here in the pile, like ASAP. And let me just begin today with a brief review. All right, so again, concepts. What are the concepts that underpin the course so far? There's this thing called electric charge. There are two kinds. They exert forces on one another. They do this through an electric field that reaches out from the charges and fills space around the charge and exists whether there are other charges there or not. All right, so as long as there's one charge present someplace where you're looking, there will be electric fields. The electric field is a conservative force field. This is useful. It means it has an associated potential energy. So we can store energy in the field and then energy can be released later. It can be used to do work and thus add kinetic energy, for instance, to charges. The electric field comes along with an associated energy per unit charge. It's electric potential, which in many ways is actually far more fundamental than the field itself. As if one goes to more advanced courses in physics, one learns that really the language of nature is all about electric potentials. When you're talking about electric charges, the field itself can be derived from the potential. You don't actually need to start with the field. You can start with this and you can derive everything else. So by understanding how charges move in an electric potential, we can understand how energy is stored in the field. So those are the basic ideas we've sort of breezed through so far in the course. So what's your next assignment? You should finish reading the chapter on capacitors, so 25.4, 25.5. Finish watching the video that you started that you were supposed to watch 42 minutes of for today, 42, 43 minutes, until you hit the word dielectric, which I'll spend a bit more time on in class today. And then there is a video here on what you do when you encounter more than one capacitor. And this video also introduces you to the language of circuits. So a circuit is a closed electrical system. It contains usually a certain minimum number of components, like a battery conductor, so wires, maybe a switch, so you can attach or detach the battery. And the first device we're going to stick into this picture is a capacitor. Then we're going to stick two capacitors in. And at the end of the video, I kind of tell you how to handle many capacitor networks. As we'll see later, capacitors are actually really, well, you're going to start to see this today, but capacitors are really essential to an understanding of biology. And you'll begin to see this today, but to really appreciate it, you have to not just have capacitors that can hold charge and then just hold it there statically, which is what we're doing right now. We're not worrying about what happens during the charge up phase of the capacitor. We are worried more about what happens after some time has passed. There's no more charge moving in the system, so we've reached equal that bring up no charges are moving at all. What does the capacitor look like? What is its voltage? If you have more than one, how do you handle that? That's what you're going to see in the next video. So homework four will be assigned today. I haven't gotten it ready yet. I got behind on things the last couple of days because there were a bunch of unrelated fires to put out. So I'll get that prepped today, but the good news is it's not due for two weeks. So it's not like you have to rush to get this done. You have an exam next Thursday. So this is assigned today, sometime today, and it will be due 9.30, beginning of class February 26th. So let's focus on exam one because that's what I really want you to be turning your attention to now over the next few days. It's next Thursday, so it's a week from today. It's in class. You'll have 80 minutes to do the exam. These exams typically consist of about two problems that you have to solve. They could be parts A, B, maybe C, depending on the complexity of the problem or the number of steps I want you to go through. And then we'll have something of the order of five multiple choice questions akin to the ones you've been seeing in the exam, in the quizzes. I'm going to send around an example exam so you can have a look. This one will be from last semester, so you'll get a sense of what these are going to look like. And you'll get something completely fresh and brand new next Thursday. I will try to draw from at least a few of the quizzes some problems for the multiple choice, but you won't necessarily have seen every one of the questions in the form you've already seen them before. Next Tuesday, we'll do in class review and I prefer to review not like blathering, but by letting you work and then letting you see where you get stuck. Alright, so I'll have some exam style problems and we'll we'll have, you know, periods when you're working by yourself, because that's how you're going to take the exam. Alright, so I want you to get comfortable with the concept of working on your own. And there will be periods where you peer mentor each other. You won't necessarily all be solving the same problem. So your neighbor may be solving a different problem on Tuesday in class than you are. And then you're going to try to help each other out. So one person may be helping the other person cold and not have seen their problem before, but may have some insights that will help you if you've gotten stuck. And then you'll have to work alone again. Alright, so that'll be sort of the rhythm of Tuesday. There won't be any instructor demonstrations. Bring questions about the exam. I'll have a Q&A period either at the beginning or end of Tuesday. And if you're stuck on something, if you think other people have been stuck on something from homeworks one, two, or three, that's your chance to ask in class, okay? We will have a quiz at the beginning because you do have a signed reading and video. So there'll be a quiz on the assigned reading from today and the assigned video that's given out today. So this stuff up here. Okay. Alright, so grand challenge problem status. So thanks for all the minutes. All the teams have gotten me minutes. All the teams have chosen lead editors. The first team meetings with me will be the week after the exam. So the 23rd to the 27th, I have to put together a poll yet and I'll send it to the lead editors. So again, watch for my emails with team signups. What you should be doing right now is collecting one, you know, 30 minute time slots where all members of your team can be available during that week. If you're not getting responses from people that are assigned to your team, if you've had a hard time getting in touch with some people, they've never responded. Lead editors, please let me know by email. I'd like to understand whether or not everybody's participating or not. So don't cover up for the week links in your team. The lead editor's job is to make sure that the team is functioning like a machine. And you're going to tune up that machine over the course of the semester. So if you already have parts that aren't functioning correctly, I need to know now. All right. So this is a good time to let me know before these meetings. Okay, and that's so that's the status of the team. So apologies to team echo. In fact, Elizabeth had sent me the name of the crown jewels. I had to put a dollar in the jar for that because I had the email and missed it completely. So I've got everything from everybody that I've asked for so far. And what you should be doing again is meeting once per week as a team. Send lead editors, send me your minutes. So I expect minutes again by Monday 5 p.m. from the lead editors. Keep talking, jot down what you guys talk about, who comes up with what ideas. That's what I've seen in the minutes so far is who says what and little discussion points and things like that. So that's nice. I like that. And then we'll talk in more detail face to face in a couple of weeks. So again, you should be meeting once a week. You should be thinking about how the material you've learned in the interim period could be used to inform a solution. And basically by the end of February after we get to our first meetings, after that, I expect that you will have one semi-jelled idea that you could start calculating based on stuff we've done in the course so far about a possible outcome when that MRI machine gets switched on. Okay? It could be anything as long as you can back it up with mathematics. Okay? And then understand the mathematics. Explain the mathematics to me in your report. Okay. Any questions before we go to Happy Joy's Dancing Quiz Time? No? Okay. Great. Well, so, no books away, books away. Okay. So let's continue here. So let's take a look at the answers to these and see how people feel about them. Okay. So what is capacitance? This is something we're going to exercise today. Is it one, the constant of proportionality relating the charge on either plate of the capacitor to the electric potential difference voltage across the capacitor? One. Anyone for one? Okay. Two, the total amount of charge placed on the capacitor. Total on a charge for two? All right. Three, the energy stored in a capacitor. Number three. Number four, the constant of proportionality relating the potential energy to the work required to place all the charges on a capacitor. So nobody voted for anything on that one. It looks like it's a few people. All right. So it's one. It's the constant of proportionality. Okay. So it's the thing that tells you given a voltage placed on this device, how much charge magnitude will each of the plates store up in the capacitor? You could then detach this device, for instance, if you wanted to be really mechanical about this and plug it in somewhere else and have a short jolt of charge that you could use to provide to something else. And in fact, there is a device that you'll look at later today that does that. We've already talked about it, but you'll see kind of how it works now that we have a change, now that we've sort of seen capacitors a little bit here. Okay. Consider a parallel plate capacitor with plates of area A and separation D. What is true about the capacitance if I double the separation between the plates? Does it one, the remain unchanged? Does the capacitance remain unchanged? Number one. Number two, the capacitance, does it increase by a factor of two? If I double the distance. Does it decrease by a factor of two? If I double the distance? Okay, we got like one, two, great. All right. Three-ish. All right. Does the, and then the capacitance decreases by a factor of four? That's the possible outcome. No. Okay, well everyone's just like, this is the end of the week. I don't want to talk to you. I'm not giving you my answer as you dictator. Okay. All right. Capacitance decreases. If you increase the separation between the plates of a capacitor, however you do that, you cut the capacitance down. You decrease it. Okay. So that's one way to control capacitance. Capacitance is a property that can be tuned via geometry. And not only that, but also the materials inside the space between the plates and we'll explore that in a little bit. Okay. So what was true about the electric field inside the ideal, archetypal, parallel plate capacitor discussed by Mois in the lecture video? One, it is stronger next to the plate containing the positive charge. The field is stronger next to the positively charged plates. Two, it's stronger next to the plate containing the negative charge. Stronger field near negatively charged plate. Three, it's strong next to both plates but very weakened between them. And four, it's uniform in strength between the plates. Okay. Sort of a tiny Mediterranean sea of hands. Okay. It's four. Yeah. All right. So, boy, you're all burred out on participating in this, don't you? Well, your answer is on paper. I'm going to know what your hand actually meant to say when I grade them, right? All right. Okay. So, again, you know, this question comes up a lot, you know, these these slides do get posted online. The quiz question answers are all in the slides so you can always go back and review them anytime you like. Okay. Let's take a look at capacitors. Let's start learning to solve problems with capacitors. And let's go over the basic ideas. Okay. So again, quiz question one was meant to emphasize this. A capacitor is a device on which a charge is placed. And then in response to placing that charge and having it separated by some distance from the positive from the negative, it develops an electric potential difference. So there's an electric field between the positive charge and the negative charge and thus there is an electric potential difference. Or you could instead, you could place an electric potential difference across the device and build up a charge. Those two things are sort of symmetric in this device. You can put a voltage on and get a charge. You could charge on and get a voltage. And the relationship between how much voltage you apply and how much charge you get or how much charge you put on the device and how much voltage you get is controlled by a very nice equation. And this is the capacitor equation. Every capacitor that you encounter in a system and a system may contain more than one. Every capacitor you encounter has one of these equations associated with it. Whatever the charge on that capacitor, you can figure out the voltage across it alone knowing its capacitance. Or if you know the charge and you know the voltage on that capacitor, you can solve for capacitance. And in fact, this may be in an experimental way how one has to get C. You may not know exactly how the capacitor is built. But if you assume that the thing you're trying to measure is a capacitor and you find out how much charge is separated in its volume and what the responsive voltage is to that, you can figure out C. And in fact, doing this was a super clever way to measure something that you all take for granted now. And I'll come to that in a bit. Now, a very basic, simple, prototypical, nonetheless very useful kind of capacitor is one known as the parallel plate capacitor. You can make a capacitor out of two parallel thin plates on which charge can be, for instance, uniformly distributed. There are more complicated ways to make a capacitor. For instance, the one that you see up here is a cylinder. So it's actually, if you were to crack this open and have a look at it, it's a parallel plate capacitor that's very short but very long. And it's rolled up like a scroll inside this device. So this allows you to get more area in a smaller volume. If you wanted to make a parallel plate capacitor that was flat and had as much surface area as this, it probably would stretch a fair fraction of the way across this room. Very impractical. You know, you'd never put this in an amplifier. You'd never put this in some device that needs a capacitor, for instance. So instead, you take advantage of the fact that you can make two plates that are flexible, put some kind of barrier between them so they don't touch, okay? And then roll them up and roll up just like a scroll or a piece of paper. And that's in fact, in general, how a cylindrically shaped capacitor like this is made. You can also make your capacitor out of a cylinder of metal and another cylinder of metal that goes inside of it, okay? So that's two plates. You can put charge on both of them and they are separated by a distance. That's a capacitor. So any device in which you can place, one conductor on which charge can be placed, separated from another conductor on which charge can be placed, is in principle a capacitor. All right? So this illustrates the point area A, separation D for the parallel plate case. We'll come back to this thing, this so-called die electric in a bit, but you don't have to just put empty space in here. You could stick glass, ceramic, anything that doesn't conduct. You could shove in between there. You don't want charge to get across the gap. You want charge to be stuck, unable to get back to, you know, if you're positive charges, you don't want them to get back to their negative charges by jumping the gap, okay? We'll come back to this thing called the die electric in a bit. So in this equation, it is assumed it's actually implicit, and I'll go into a bit more depth about this in a bit, that there is absolutely nothing between the plates. This epsilon naught, okay? Epsilon naught we've seen in the book before, but we haven't really used it. That constant K, which has a value of 8.99 times 10 to the nine Newton meters squared per Coulomb squared, can be related to actually what is a more fundamental constant, epsilon naught, by this equation. K equals 1 over 4 pi epsilon naught. It occurred very early in the first chapter we looked at, 21, I believe, okay? And we haven't really dealt with it, but now it falls out when you start studying the capacitor with mathematics, okay? So it's much more convenient to write epsilon naught instead of a K and a 4 pi in ratio in this thing, alright? So that should have been in the lecture video, you should have seen how that happened. But anyway, this epsilon naught is a bit more fundamental, and it has a value of 8.85 times 10 to the minus 12 Coulomb squared per Newton meter squared. So you just flip the units upside down to get the units of epsilon naught. Actually, those units are quite profound, and I'll come back to that in a bit. Something very profound is going to happen in class today. I don't know how many of you will appreciate it, but you'll see later in the course why what happens today as we begin to study this silly little device is actually quite a profound statement about the universe itself, okay? So this equation represents a capacitor with plates area A, separation D, and then absolutely no material in between the plates, we call that empty space or free space or the vacuum, okay? There's nothing, no air molecules, nothing. There's literally nothing in between the plates, okay? And I'll come back to exactly what's going on with this epsilon naught in just a bit, okay? All right, so let's do a capacitor demonstration. To do this, let me get rid of that, get rid of this annoying guy and bring up this, and boom, okay? So I have here, see if I can get this to work. Okay, so I have here a capacitor. I showed this to you already, okay? This is a cylindrical capacitor. I have over here a source of electric potential difference. You can think of this as a ginormous battery. It's called a power supply. You have a small version of this, for instance, for your mobile devices. It's got a tiny little brick on one end, two prongs that go into a wall outlet, and then some small connector, maybe an Apple proprietary connector, maybe a micro USB connector that goes off the other end and that plugs into your device. And it takes 120 volts and it converts it into something much more friendly to the small electrical components inside of your mobile device, which can't take 120 volts that would blow them up, okay? So this does the same thing. It's just much bigger and it converts 120 volts from the wall into anywhere between zero and about six and a half volts. All right, so to demonstrate this, let me disconnect this for a second. Now, I have over here a voltmeter. Actually, this is a multimeter. It can read voltage. It can read the flow of charge per unit second, also known as electric current measured in amps. It can do what's called direct current, where you always have a plus side and a minus side, and they never, they never change. And it can do alternating current. Alternating current is generated when you flip the sign of plus and minus alternately. And in fact, alternating current is what comes out of here. We won't study that in this course. It takes a little bit of additional mathematics involving time dependence of charge and voltage and things like that to get the hang of it. But it's not that much more complicated than DC. It turns out to be a very efficient way to transmit power over long distances, which is why we use it in the United States, for instance, okay? So let me get this going here. So I've set this up so that it's capable of measuring an electric potential difference of up to about 20 volts. So that's the setting over here. And it's a direct, direct current voltage. So it's set to up to 20. And I have this power supply here. So what I'm going to do is I'm going to switch it about halfway or so on. And all I have to do is, you know, and I do kind of a mathy version of this in the next video you're going to watch, I'm going to measure the electric potential difference between two points on the power supply. One of them is known as ground, and that typically is represented by the black wire. So that would be our point of zero electric potential, okay? And then there's red, which is the hot, and it's the high potential point in the circuit. And you see, I'm reading if I take the probe out, zero, if I put the probe in and measure across these two points in the device, I measure an electric potential difference of about 3.4 or so volts. All right, I can crank this up, take this up to max. And as I said, this should give us something in the neighborhood of about six and a half or so. All right, 6.41. All right. So these are great little devices. You can buy cheap ones. You can check batteries to make sure they still work. They're still delivering their full electric potential difference and whatnot. Now, I have an electric potential difference, and I have a capacitor. And this capacitor is an extremely, let me see if I can flip this over without losing the thing. This is, it's a 10,000 microfarad capacitor. So it's a 10 millifarad capacitor. And I'll come back to farads in a bit, but farad is the unit of capacitance. So it is coulombs per volt. It gets its own name, the farad in honor of Michael Faraday. So one farad equals one coulomb per volt. So new unit, but based on units we've already been playing with. And it's much more convenient to carry a big capital F around in your equation than C over V, C over V, C over V all the time. So I have some wires. These are conductors. They're made of copper or aluminum. Doesn't really matter. They offer a very low resistance to the flow of charge. That's the whole point of a conductor. These are the plumbing of any circuit. Conductors allow charges to move relatively freely, motivated by electric potential differences. So this is like a pump. This is like your home plumbing tubing. And this thing is a place like a sink basin where we can store water charge in this case. So we have a pump. We have a tube. We have a basin. And this is basically a sink for electrons. That's all this is. And I like the mechanical analogy because it helps me to think about what's moving, where it's moving, where it's building up and so forth. So I'm going to plug this capacitor into the power supply and turn on the power supply. Very exciting. Like absolutely nothing happens. I don't know what you were expecting. I'm always afraid one of these old ones is going to blow up on me. That would be exciting. We have one in the back. It's a one Farad capacitor, which means it's capable of, if you put, you know, one volt across it, it can store one Coulomb of charge. Coulomb of charge is a lot of charge. If you divide that by the elementary charge, that's a big number. Okay. A one Farad capacitor, if you suddenly drain all the energy out of it by say, I don't know, taking a screwdriver and shorting across its leads, it can weld the screwdriver to the capacitor. That's how much energy gets dumped out of a one Farad capacitor. Don't f around with them. All right. You can kill yourself. So this one is only 10 millifarads. All right. So this one's not so bad. I'm still not going to stick my fingers across it though, just to be a role model, you know, because that's what I do. All right. So I'm going to measure the electric potential difference now across the capacitor. Now something I'm going to emphasize in the next video is that, you know, I'm going to pick a point that I define as zero potential and conveniently the power supply has done that for me. It's wherever the black cable connects into. So that's ground, that's zero potential by construction in the device. Okay. And then this will always probe another point in the circuit someplace and it will tell me the electric potential with reference to ground. So if I go ahead and touch the conductor here and the conductor here, low and behold, my hands in the way. Let me try that again. That was, that was a derp. All right, there we go. So, you know, 6.3 volts. And if I go back to here, well, it's a little hard to do, but I can get the probe in there, get the probe in there, just see 6.3 volts. Okay. So no big surprise. I'm measuring the same electric potential difference with respect to ground here as over here. But that's because one of the paths that takes me from the red to the black is through the power supply, where I measured the electric potential difference before anyway. The other path that takes me from the black to the red, or from the black to the red is through the capacitor. So it should be, if this is really stored up a charge, a charge induced by plugging it into this electric potential difference, I ought to be able to disconnect the capacitor from the power supply. And as long as no charge is leaking out of the system, I should measure the same electric potential difference across this energy storage device as I did while the power supply was still plugged in. So let's test that. So what I'm going to do is disconnect and there, disconnect. So now this is disconnected from the power supply. And I'm going to measure the voltage, 6.25, 6.24, 6.23, 22. All right. So it started out at the voltage when it was plugged into the power supply. But what's happening to it now? It's decreasing. This is what's known as a leaky capacitor. No capacitor is perfect. No capacitor is capable of exactly preventing all charge from staying separated once you take the external electric potential difference away. Now the ones we'll be dealing with in homework problems will typically be perfect capacitors. They will, in the absence of the external voltage that charged them up, they will hold their charge. All right. So you can always use Q equals CV. All right. In this case you see we've declined almost 0.3 volts from where we started in just about a minute. So the charge on this capacitor is slowly leaking away because this is the real world. There are free charges in the material inside of this capacitor. They're being gobbled up by atoms nearby that just happen to have room for an extra electron. Or it could be that water molecules in the air are coming in contact with the charges right here on this screw which forms one of the electrodes that I'm touching and is soaking up charges right here where I'm probing with the voltage probe. Okay. There are many ways that a system can lose charge and thus because it's a capacitor lose proportionally voltage over time. And this is typically known as the leaky capacitor. All right. So it's literally like a sink with a drain problem and this is slowly leaking all that water you've tried to save up. All right. Water can leave a sink basin that's been plugged by basically two means evaporation or it can just leak out of a hole because your plumbing hasn't been kept up in a long time. That's just the real world. You're never going to be able to keep all that water in the sink basin. And this is the real world for capacitors. You're never going to be able to keep all that charge there once you take the external electric potential away. And we're down to 5.8 volts now. But still, that's not too bad. I mean, I could at this point carry this capacitor over some place else that needs about 5 volts and plug it in. And for just a moment until all the charges drained off the capacitor by being pulled away by the other device, you know, it'll get about 5 volts, 4 volts, 3 volts, and then it'll drop to zero. And we're going to explore that time dependence later. Right now, let's just focus on the fact that an ideal capacitor can be charged up. You could disconnect it and it still has the same voltage across it. You could move it around, plug it into something else and have it do work. So this is a prototypical energy storage device. Batteries, in contrast, use a sustained chemical reaction to maintain the electric potential difference. So a battery doesn't change its voltage very quickly. It takes days, weeks, or months, depending on how power hungry your device is. My phone can last about 18 hours under normal usage on one charge. So that's good, but not great. You can do better than that. I think companies in general should be able to do better than that. But that's reality of batteries. The chemical reaction wears down. The potential drains. And then eventually, the phone can't be operated anymore. The iPad can't be operated anymore, and so forth. OK. And incidentally, why does an iPad, which is a much bigger screen and so forth, why does it have a battery that can last, like, a full day of watching video where if you watch video on your mobile phone, it may die in three or four hours? Any ideas? I'll blind your retinas while you're thinking. Sorry, Mooney. Bigger battery. iPad's a bigger device. And the reason Apple makes them so impossible to open is because they want to carve out every nook and cranny of that aluminum body that it's put into and pour battery into it. So if you take an iPad apart, literally every place there isn't electronics, there's battery inside that thing. This is just a smaller thing. So less battery, less chemical reaction per unit time that it can sustain. And that's it. It just wears down after the course of the day and you have to charge it back up. You have to reverse the chemical reaction and then let it run forward again to get your voltage back. OK. So that's what you do every day when you're charging your phone. Phones also contain capacitors. Just about every electronic device contain capacitors. There are places you can keep reservoirs of charge for emergency. And if there's a fluctuation in power from the battery, this thing can come to the rescue for a moment until the battery can restore itself and then the capacitor will slowly charge back up and wait until it's needed again. You can use these things in all kinds of applications. You can smooth out amplifier signals. You can build filters for passing high frequency sounds and low frequency sounds using capacitors because of the way that they respond to changes in voltage with respect to time. They're very powerful devices. OK. Questions? Because now I'm going to go solve a problem with these things. So that's just a demonstration. OK. So get rid of that. Put the idiot back up on the screen. Oh, there he is. OK. And there we go. OK. So you've seen the demonstration. Let's solve a problem. All right. So let's look at the defibrillator again. All right, the defibrillator is a really interesting device. I mean, not only is it a medical device, so it's probably something you care about more than a phone or a calculator or something like that. It's a device that saves lives, right? This saves lives all the time. Having portable defibrillators on planes, in malls, in your home, if you have a person that may have a heart attack and having something like this may be necessary to save their life or sustain their life until they can get real medical treatment, these are essential in the modern world. What they do, OK, because you don't have to have the portable defibrillator plugged in when you charge up the paddles and say clear, OK, you can plug it in and charge it and then carry it around with you. All right, so EMTs might do that. They might just have this in a case that they can carry with them. They could charge it up once back at the station and then drive around with it until they need to use it and plug it in again when they're done, OK? To make that possible, this device must be capable of storing charge for long periods of time. Now, there's no doubt a battery in this because even if you put a big capacitor in this, they leak. So you don't want to let this thing just sit with a capacitor with a stored charge in it all day. It won't have as much charge in an hour. And you don't want that to be the difference between saving a life and letting a person die. So you've got a battery, but you've also got a capacitor. And the beautiful thing about a capacitor is it can deliver its energy very quickly, nearly all at once. Getting a battery to do that is very difficult. You could blow the battery up if you do that. In fact, has anyone ever accidentally done what's called shorting a battery? That is where you plug one terminal of a battery into the other terminal of the battery? No one's ever done this? Don't. Yeah, you have? What happened? It just won't work anymore. Yeah, it won't work. Did it get hot? I forgot. OK, yeah. So a lot of people reported, for instance, battery failures in some mobile phones. The pockets got very hot, and actually they got burns. The battery, if it's ever shorted, will start running electric current, so charge through itself. And this will heat the battery up because it can drive a huge amount of electric charge through itself. And this will cause the battery at some point to explode. Car batteries, you must never, ever, ever, ever, ever, ever, ever short a car battery because it's a lead acid battery. And when it blows, guess what it's going to spray all over you? Not fun, sulfuric acid. Bad stuff. Don't short a battery. I can't emphasize that enough. They're not designed to deliver a lot of energy very fast. They're designed to deliver steady work per unit charge over long periods of time. A capacitor, on the other hand, can be designed to do a dump of charge very quickly. So that's what they're great for. So a portable defibrillator will have a capacitor in it that when you put those paddles on the chest and push the trigger, it closes a switch that now lets the capacitor do all the work. And it can dump its charge very fast through the human body. So you've got a power source in here that's capable of delivering something like 2.3 kilovolts. So inside this defibrillator, we're going to have some voltage difference, delta V, of 2.3 kilovolts, which we can write as 2.3 times 10 to the 3 volts. And to make this device work so that it delivers the right amount of charge to restart the pacemaker in the heart, you want it to hold 145 microcoulombs of charge. That is, you want the positive charge on the positive plate to be a plus 145 microcoulombs and the negative charge on the corresponding other plate to be negative 145 microcoulombs. The magnitude of the charge on either plate is 145. So that's what we write as Q for a capacitor. So 145 microcoulombs, which is 1.45 times 10 to the minus 4 coulombs. All right, part A, what's the capacitance required to achieve this? Well, what do I know? I know delta V. I know Q. And I know for a capacitor that these are related to each other by a constant of proportionality. Q equals C V, or C delta V. C is that constant. And it is the capacitance of this device. That's what I want to solve for. So it's a simple logic break exercise to answer part A. All I have to do is rewrite this as C equals Q divided by V. All right? And when I do that, I find out that the capacitor required to achieve my goals has a capacitance of 6.3 times 10 to the minus 8 coulombs per volt, also known as Farads. Coulombs per volt are Farads, F. That's our new unit for capacitance. And in fact, I can rewrite this in maybe a more reasonably sized unit. I could write this capacitance as 63 nanofarads, OK? So get used to converting all these powers of 10 that gets very commonplace in a course like this where you're expected to do things like that, OK? So 63 nanofarads, that's not a big capacitance. And think about it. It only takes 145 microcoulombs to dump through your chest in like a second to reboot the heart. Remember what I said, a one-farad capacitor is really dangerous? That thing can reboot your heart. And it's only using 145 microcoulombs to do it. So don't screw around with a one-farad capacitor. They are bad news. We have two of them to play with in the department. I'll probably do a demonstration using one of them later, not a welding demonstration, something a little less profound than that. OK, part B. If we assume that the capacitor is a parallel plate capacitor inside of this device and has plates that are 50 centimeters, so half a meter long, by 10 centimeters, so a 10th of a meter tall, in area, what separation is needed if the gap is just filled with empty space? There's nothing in between those plates, those conductive plates, all right? We'll get to the discussion in a minute. Is the answer I get feasible? And we'll talk about that in a bit. So for now, let's treat this capacitor as a parallel plate capacitor. So that means that this capacitor, if this thing is 6 tenths of a meter wide, which is about, let's see, that's about a meter. So that's about 6 tenths of a meter or so. That's not unreasonable for a suitcase-sized thing. So maybe there is a 50 centimeter wide, 10 centimeter high capacitor of the parallel plate variety lurking in this thing. OK, it would fit in that box. Let's see what happens if we assume that that's the case. So for a parallel plate capacitor filled with empty space between the plates, the capacitance is equal to epsilon naught times a over d. OK, well, epsilon naught is the constant. 8.85 times 10 to the minus 12 coulomb squared over Newton meter squared. And the area we can calculate, it's 0.50 meters times 0.10 meters, which gives us 0.05 meters squared. OK, so 0.05 meters squared is the area of either plate in the capacitor. We want d. We have c. We have epsilon naught. We have a. So all we have to do is a little algebraic rewrite. d equals epsilon naught a over c. OK, great. So we plug all the numbers in, and we find out that this is about 7.0 times 10 to the minus 6 meters or about 7 microns. So the gap between those two plates would have to be 7 microns if it was of the parallel plate variety with absolutely nothing in between the plates. Evacuate it. No air. Empty space, the vacuum, OK? Is this feasible? Any ideas? Could you build a capacitor that you could carry around with a plate separation maintained by empty space at 7 microns? OK, you're shaking your head. Why not? Well, it seems like if you're back close to each other, there's a vacuum between them. What would stop them from touching at that size? Yeah, yeah, what would stop them from touching? That's right. Now there are engineering things you could do. You could put little glass buttons in there. There are 7 microns thick to maintain that mostly empty space between the two. OK, so you could put little spacers in. That would be one thing you could do. That would slightly change the capacitor. But if you did only a few buttons and they were a small part of the total area, maybe you could say, well, it doesn't matter, right? Well, OK, you're all. I'm going to go check and make sure everyone's alive in there. Give me one second. OK, he's fine. Drawer parts all fell out of a bench. They were all metal tools, I think. So no glassware. We're good. All right, so you're all medical types. Give me something that is microns in size. Any ideas? I mean, you're trying to build a capacitor with a tolerance of a few microns to keep that distance constant. What has the size of a few microns in nature? Nothing. You guys know, I didn't memorize anything in biology class. No interests outside of your bacterial cells. Bacterial cells. Yeah, cells. Cells are typically like 10 microns in size. So you're talking about engineering a capacitor that has a gap that's roughly one bacteria in size between the plates. I know a lot of good engineers, but I don't know a lot of engineers that are that good, especially to make something that any person could carry around with them, bump around in a car, drop on the ground, have fall off a shelf, whatever, and still have it work when a crisis arises. You want this thing to be fault-tolerant. This thing has to work in a crisis. And it can't be that it doesn't work if somebody bumped it one day. That would be stupid. No one would buy that. OK, yeah, and just to give another maybe more common sense of scale, the average width of one of the hairs on your head is 200 microns. So it's tens of cells big in thickness, basically. Microns, you can see under a microscope. You can obviously see cells under a microscope. I would hope you've all looked at them at some point in your career. All right, so how could we improve this capacitor? How could we make it so that D doesn't have to be so tiny? We want to get a capacitance of 63 nanofarad. That's what we need. So that C has to remain 63 nanofarad. And we want D to be able to grow bigger. But we know as D gets bigger, C would have to go down. So what could we do? Julius, you seem to have some thoughts. Increase the area. Increase the area, right? Yeah, so there are many ways we could do that. We could roll it up into a cylinder and get more surface area in a smaller volume, so it fits in there. Yeah, absolutely. That's a good one. So that, if you were, now what you do is say, well, maybe parallel plates are a little impractical. Maybe we should go full on cylindrical with this thing. We're basically a parallel plate that's been rolled up into a cylinder like that. So that will definitely fit in a suitcase size thing. No problem. And you can get more area and roll it tighter. But again, now you're rolling this thing, and you're trying to keep what, hopefully, would be a gap that's at least engineerable, open, empty space. So what's the other thing we could do? What's the other thing we could do? Any ideas? What else could we try to alter in that equation? The constant. Yeah, which sounds crazy, but that's actually exactly what you have to do. You have to get that constant, epsilon naught, to change its value. Now, epsilon naught, it turns out, is a fundamental constant of nature, but it represents something very specific. And if you alter the conditions inside of the gap, you can alter the effective value of epsilon naught. So what you need to put into the device is something called a dielectric. And this will be covered a little bit more. Let me come back to that in a second. That'll be covered a little bit more in the rest of the video that you started watching for today, so the last 15 minutes or so if that covers dielectrics. So what we could do, get rid of this because we don't really need it anymore, so imagine the parallel plate for passers were viewing it from the side. So here's one plate. Here's another plate. And when I say epsilon naught, what I'm talking about is the ability for electric fields to travel through this space when it's empty. So if I make it not empty, I can change the electric fields that are propagating through that gap. So for instance, I could put a material in here that's non-conductive. I could fill this gap up with some material. This material has to be non-conductive. That is, it has to be an insulator. Insulator is a word for a non-conductive material. You've probably all heard it before, right? House insulation keeps heat from getting out, keeps heat from getting in in the summer and heat from getting out in the winter. Actually insulators, things that are good electrical insulators that prevent the flow of electric charge also turn out to often be good thermal insulators. And that's not an accident. It's because of the atomic theory of matter. But if you're used to thinking about good materials that keep heat from moving from one place to another, what's the insulation in your house made from? Anyone know? Whoever been in the attic of your house and accidentally brushed up against the pink stuff or the yellow stuff that's blown down or laid down in the attic? Fiberglass. Yeah, so it's spun glass threads. So glass, right? Is glass a good electrical conductor? Are wires made out of glass? No, not typically. It's brittle. That's one thing it doesn't have going forward. But also if you try to take a little battery and press it against a window, the battery will not explode. And that's because charge really is not free to move in glass. The silicates that are in there, they don't really have any electrons that are weakly bound that can be motivated by a low electric potential difference like a 9-volt battery. Actually takes a whole lot of electric potential difference to get current to flow in glass. I have a question. Yeah, sure. What about you increase the time, for example, 10 years later after adding all the charge? Would that explode? Oh, if you just left it sitting there? So because the glass will explore current in the next chapter, so it'll be after the exam. But because the amount of charge per unit time that the battery can actually drive through the glass is vanishingly small, it would never build up anywhere. So that chemical reaction can happily move a teeny, tiny little bit of charge every year and never wear down. The battery will never heat up. Because any heat that would build up is dissipated very quickly given the slow time, the long time scale required to move even one charge across the terminals in glass or something like that. So these materials, these insulators, are of a class of materials known as dye electrics. Basically, their structure is such that they're built from little dye poles. And what dye poles do is in the presence of an electric field, they rotate and they line up with the field. So if you go back and look at the section on dye poles in an earlier chapter, one of the things that happens is that when you take a dye pole and you put it in a uniform electric field, because of the way the positive and negative charges line up, in between the charges, it greatly weakens the external electric field. The field of the dye pole lines up in such a way as to slightly cancel out the external electric field in which the dye pole is now lined up. So if you put Avogadro's number worth of dye poles between one side of the capacitor and the other side and make the electric field go through this, it greatly is weakened by the dielectric material inside of it. And so it can contain a much stronger electric field generated by bigger charges on the plates because the field is weakened in the bulk between the plates. And so what we learn is that it's possible to modify space with regards to electric fields by turning epsilon naught into just epsilon, which is the original constant times the Greek letter kappa. And kappa is known as the dielectric constant. Dielectric constant. And basically it tells you the multiple of the vacuum, the multiple of empty space that this material represents in terms of weakening electric fields. Empty space is the easiest time that electric fields ever have traveling. If you put a material in the path of an electric field, it will be weakened by that, any material. And so you never will find a material with a lower value of epsilon than one like the vacuum, which is epsilon naught. All dielectric constants are value one or greater. So as an example, one could put ceramic inside of the parallel plate capacitor here. So if I instead stick ceramic inside of this parallel plate capacitor, I modify epsilon naught to epsilon a over d, which is just epsilon naught kappa a over d. So all I have to know is what's the dielectric constant kappa of the material? Ceramics can be manufactured to taste. So you can get kappas anywhere between a few hundred and a few thousand. And so for instance, I could put a ceramic in here with a kappa of 4,500. Very easy to manufacture that. And in fact, ceramic is a very common material that's used in capacitors that need to be able to have a reasonable size and still store a lot of charge. And so if you run the numbers on this and now go and solve for d, you find in this case for the ceramic capacitor, this comes out to be three centimeters. The gap that you need to have between those plates that are half a meter by a tenth of a meter is three centimeters. So that's reasonable. That can be engineered. You could put three centimeters of ceramic in there. No problem, keep those plates separated and still get your device to be about the right size and portable. And ceramic is nice and strong. So unless somebody really smashes it and kicks it, which in which case not much is going to survive that anyway, it's tough to break the ceramic up and damage it. Now the last thing I'll mention here is that there is too much of a good thing. If you put too strong an electric field on a dielectric material, eventually the field becomes so strong that it tears the dipoles apart. Dipoles are just electric charges that are bound in rigid, like water molecules. But if you put water in a big enough electric field, you know you can tear hydrogen from oxygen. In fact, if you ever expose water to an electric current, 12 volts, 13 volts, 20 volts, something like that, you can easily rip the hydrogens off the oxygens and you'll get hydrogen gas as a byproduct. Don't spark and don't let it match. Because obviously hydrogen gas will under the, once you put some energy into it, will recombine with oxygen. And when it does that, it releases a tremendous amount of energy. So I almost went deaf once because in high school, we had a chem lab course that was self-driven study. You could do one project for the whole semester. And my lab partner and I tried to build a hydrogen powered engine. So we thought that was an interesting idea at the time and there had been some German scientists that had made some reliable ones. We wanted to build one out of a little helicopter engine. And we made, the big thing we did was we just found different materials to try to make more hydrogen more quickly. And we made a lot of hydrogen and we made a big bottle of it one day. But we weren't sure if we had hydrogen in the bottle or not. So of course what we do, we put the bottle in a fume hood with a blast shield in front of it, bulletproof glass, okay. Ran a sparker clicker on two wires into the electrodes in the bottle and then click, click, click, click, click, click. Oh, there must not be any hydrogen gas in there. Adjust the wires. But click, click, click, click, click, nothing, nothing. And then finally I turned to, I just turned to my lab partner and I was about to say something about we should try the experiment again and that spark jumped the gap inside the bottle. And it sounded like a gunshot when it went off and I went deaf in one year for about a week. All right, so hearing did come back. But again, be careful. It doesn't take a lot to get atoms to dance for you. And you need to be careful of what atoms you make dance because when they break up and then want to partner up again they can release a tremendous amount of energy and you don't want to be there when that happens, all right. So do be careful with these things, all right. Let me tell you what the profound thing is and then I'll give you a problem to do. You know, we study the capacitor because it's the simplest thing, the simplest device that you can build out of conductor, a gap, and a voltage. So an electric potential difference. And so we study it, right, because it's easy. You know, you can say, well, I have big plates and there's uniform electric fields between them and then you can figure out what's the relationship between Q and V and you can say, oh, look, that's the capacitance and I can solve for capacitance in a parallel plate and it's got this epsilon knot in it which for empty space between the plates is what you're sort of forced to write there. But in studying the capacitor you actually learn something very profound about this constant K that appeared originally in Coulomb's law, right. F equals K, Q1, Q2 over R12 squared, R hat 12. Remember Coulomb's law? Do remember it, you're gonna need it next week, okay? There's that constant that had to be figured out experimentally. It's just the relationship between the charges, the distances, and the force that results. So it just seems like a number you have to go figure out, right? But what is that number? Well, that number, again, it turns out to be related to a more fundamental constant because you get a bunch of four pies when you start playing with K in certain situations like the capacitor, you wanna get rid of those four pies, they just look stupid. So you can rewrite K in terms of another number with the four pies so it goes away in your equations. So this epsilon knot turns out to be a number that actually tells us something extremely profound and deep about the cosmos. It tells us how the vacuum of empty space, empty space between the plates permits electric fields to move through it. So basically it tells us the ability of the vacuum to permit electric fields to pass for every meter. And in fact, if you look at what the units of this are, right, you have, here you have meters squared. Actually, let's look at this one here, right? So you have A over D is meters, right? So this thing has units of meters. You want ferrads over here. So this thing at its heart must have units of ferrads per meter in order to get the meters that are left to cancel out and give you ferrads on the left hand side, all right? So the units of this thing, 8.8510 by 12 Coulomb squared over Newton meter squared can be rewritten as ferrads per meter. That's what that is, that is a ferrad per meter. It tells you the capacitance of empty space. It tells you that empty space doesn't just permit electric fields to travel limitlessly through it. And that actually turns out to be quite profound and we'll see why later. There's a beautiful symmetry, as you'll see, between electric fields and magnetic fields. And that symmetry by itself, that relationship that appears to exist somehow between these two things has deep implications for the cosmos and our understanding of it, right? But we'll get there, we'll get there. I just wanted you to know that something profound is actually happening right now in the course. And that is, this number means something. It isn't just an arbitrary number. It's a fundamental property of the universe and particularly, it's a fundamental property of an empty universe. Nothing, okay, right? So, we'll get there. Here's your task. The cell membrane. Does anybody know roughly what the thickness of the cell membrane is? A living cell's skin, the lipid bilayer that makes up the membrane. Does anyone know how thick that is? Okay, good, you're gonna calculate it. This was assumed to exist for a very long time. You could look at cells under a microscope. That's not hard. Cells are microns in size. The wavelengths of light that your eyes are sensitive to are roughly half or so microns in size. So, seeing something that's microns in size with a wave, a light wave, that has a wavelength that's half or a tenth of a micron in size. That's not hard. You can resolve a cell with visible light. But the cell membrane eluded observation because it's so tiny. You can't see it with visible light. It's impossible. So, there were attempts to figure out, first of all, if it's there, what size is it? And then once you know that it's there, what's it made from, right? And it was assumed to be a monolayer of molecules. That was wrong, okay? So the original work that was done on this got the right answer for the wrong description of the cell membrane. The membrane is obviously not empty space. We know now that it's a two-layer thing of lipids, so fats, and it clearly has a dielectric constant. This is not empty space. So, it turns out that for a cell wall, that dielectric constant kappa is about three, all right? So kappa for a cell membrane, that gap, cell membrane gap, is about three, okay? And it's a dimensionless number. It just multiplies epsilon naught, all right? So it's the multiple of the vacuum that this thing represents. And it's about three times less permissive of electric fields than the vacuum is. Cap is three. The cell membrane is a capacitor. It's a spacer with a charge separation. There's more negative charge just inside the membrane and more positive charge just outside the membrane. And this is developed by pumping sodium out of the cell, okay? And it's much easier to, and I'm not kidding about this, to basically measure the electric potential of a cell than it is to measure the thickness of the cell membrane itself. It's also easier to measure the amount of charge moving in and out of a cell than it is to measure the thickness of the cell membrane itself. That thing is so tiny, okay? So in fact, measurements were done in the early 1900s before anybody knew how to actually see the cell membrane more directly. And discovered, right, that there's a potential in that potential is roughly 70 millivolts. And that, you know, the typical cell has to move something like 0.17 picocoulombs of charge. So the delta V across the membrane is 70 millivolts and the charge that has to be moved and separated in order to achieve that is roughly 0.17 picocoulombs, okay? It was much easier to do experiments to assess these things. You could take blood cells, you could dilute them, you could put them in an experimental apparatus and you could figure out the capacitance by making assumptions, all right? So first thing I want you to do, calculate the capacitance of the cell membrane, all right? Second thing I want you to do is I want you to take the fact that cells can be seen with microscopes and they have a radius of about five microns, all right? And you can think of the cell as here's a cell physicist's picture of a cell, it's a sphere, all right? And it has a radius R, R equals five microns. Again, microns in size, okay? Based on that information, what's the thickness of the cell membrane? So once you have the capacitance and you have this information, I want you to try to calculate the thickness of the cell membrane. Hint, treat the cell as a parallel plate capacitor that merely has the area corresponding to the surface area of that sphere. So imagine you took that sphere and you sliced it and you laid it out flat so that you get a flat surface with like that right there. So flat surface with a charge separation and its area is that of the corresponding sphere that the cell once was before you lized it and then opened it up, okay? So go forth and calculate, see what you get, all right? And if you held out on me, if you actually kind of know the size of the cell membrane but didn't say anything, see if the number comports with what you remember about the typical size of a cell membrane, okay? So pair up, triple up, whatever you like to do and work together, so yeah, that's a good question. So pico, pico equals 10 to the minus 12, yep.