 Hi, so let's go ahead and get started with just my little time-wasting verbal intro before I do the reading quizzes. Tests overall pretty much landed the way that I expected. There are a few surprises, but positive and negative for me. I'm not going to hand your exams back because I have two makeup exams that I have to do at the end of this week. So if you want to see your exam, come meet with me during office hours and we can talk about it. I'll keep it copied until everybody's had a chance to actually take the equivalent of the first exam and then I'll hand it back with solutions. So again, I'm not going to hand them back today. If you want your exam back, just come and talk to me during office hours. I'll show it to you. We can talk about it and then I'll actually hand it back next week after everybody's had a chance to do the first exam. Did everybody watch the lecture? Heck, I had people not in my class watching the lecture hoping to learn something. So that's on you guys. I put something up in the social media and I get a bunch of hits. Well, I'm going to build on that today and what I'm going to do is I'm going to demonstrate some of the things that I blah blah blah about in the video lecture. Actually using a camera and some actual capacitors. So I have some capacitors here today. These look really nasty and mean. These are like pathetic little capacitors. They can barely hold charge. They're really weak. They're old. There's what's called a one farad capacitor back there. That's capable of holding one Coulomb for one volts worth of potential difference. That'll kill you. We'll talk a little bit about electric current in the human body as we go through the lectures this week. But it doesn't take a whole lot to kill a human being when it comes to the movement of charge through the body. And well, I'm going to have some disturbing slash entertaining videos that we can look at including a Taser demonstration. I just have a question about homework. You said that we would have to essentially double the homework. Yeah, I lied. I just wanted you guys to sweat it. You're done. Just do homework four. Homework four is due Thursday. I think I got everything updated on the course notes website last night because it still had homework five is listed this Thursday. Homework five will be next week. So everything just proceeds. It's like we skipped a week and then we just keep going. Okay. All right. So deep breaths. I'm allowed to lie occasionally as an instructor. You shouldn't trust everything I say. You should take my critical thinking course. Okay. Who wants a quiz? Yay. I want a quiz. All right. Fine. You're getting special paper. That's beautiful what you want. I think that's boring. Okay. So flip the quizzes over. Hand them down to the end of the row. I'll pick them up. Today, we're going to use capacitors and I'm going to Demons. This is for me as an experimental scientist. This is a lot of fun because I actually get to show real things in the real world. Now, these are a bit exaggerated. The capacitors that are that are in the, you know, microelectronics like your phone and so forth. Those are really funny. Your screen is actually a great example of a big capacitor. I mentioned this in the video lecture, but the touch screens of things like Android and Apple phones are what are called capacitive touch. And what that means is that they sense changes in capacitance as your finger touches the screen. And based on those changes, it's able to convert that using software into position information. So a couple of things that were introduced in the video lecture. We're going to use a lot of symbols going forward as we talk more and more about circuits. So you should really think about this as building up a Lego like tool kit of pieces that you can string together and do stuff schematically. So this is the schematic symbol for a battery. It can have usually has at least one large plate and one small plate. And the large plate may or may not be labeled plus. I'll try to be consistent about that. But remember that the longer of the two plates is supposed to be the one that is the source of positive electric charge. And a battery's job in an ideal situation is to maintain a constant potential difference for its part of the circuit. So if all you ever remember about a battery is that it's a source of electric field. That electric field doesn't change in strength in any appreciable way. And that sets up a constant electric potential difference across the terminals, the ends of the battery. That's about all you really need to remember about batteries. So that's what those batteries are doing in your phones, your watches, your keyboards, your mice, your laptops. Their job is to maintain as much as possible a specific constant electric potential difference across the entire device. Now there may be changes inside the device in electric potential. But because electric potential is just another way of saying work per unit charge done in this case by the device. An energy is conserved in a closed system. Any changes in electric potential inside of the circuitry of, let's say, the laptop. All those changes should sum up to the big change across the battery. Otherwise, energy is not conserved. I just have a general question about the capacitor. Well, when you change the distance between the two, I'm not sure how you could increase the amount of charge stored on the plates. Because if there was a fixed voltage, wouldn't it have to stop at some point? Well, that's the feature of the capacitor. So a couple of things. I haven't gotten back to the capacitor yet, but I'll jump ahead here. The capacitor is a device with a physical geometric area on which charge can be stored. And those are the plates. So the top plate and the bottom plate. And the idea is that there's an uncrossable gap in between the plates. There's no way for a charge unless you tear the material apart inside the capacitor and turn it into a perfect conductor. There's no way for, let's say, a positive charge up here to get down here, jumping the gap. The only way it could do that would be to move back through the circuit somehow through the battery and then go to the other side. Okay, so why is it that the amount of charge changes as you change the, say, the distance between the plates or the areas of the plates? It really has to do simply with the fact that the source of the electric field here is a surface charge density. And so if you increase the area, you can increase the amount of charge to maintain the surface charge density and keep the electric field constant. So the electric field in the circuit, the one that the capacitor will eventually mimic and oppose, is driven by the battery. So that's creating an electric field. So in response, once you hook a capacitor into that and charge starts moving in the circuit, then this will slowly build up an electric field. And eventually that electric field will reach the same magnitude as this one and oppose it and no more charge will move. There will be no net electric field left in the circuit. So does that just mean that the voltage cumulants on the capacitor, that that happens more quickly? It can. Yeah, so if you alter the capacitance of a device, you can alter the speed with which it charges up. We'll get to that eventually. We're not there yet. Okay, so if there's a greater or more charge, which means that it will become the same voltage as the battery more quickly? It could, yes. Yeah, we'll explore what's called the time dependence of the capacitor in a bit right now. What I just want you to focus on is that you plug it in, you walk away, you come back a little while later, and whatever that little while is, it's enough for all the charge to have moved, gotten to the point where it's separated, opposed to the voltage of the battery, and now there's no more motion, and then we're analyzing the circuit under that situation. So this is what's called a static analysis. Okay, there is no flow of charge. There's no electric current that you have to worry about right now, but we're about to get into that. Okay, so that's sort of leading a little bit, but it's a good sneak preview of what's to come. Okay, but right now, I mean, if you go back to the beginning of the capacitor video lecture, and I talk about the electric field from a disk, and that disk could be a circular disk. It doesn't matter. It could be a square disk. I chose the circle just because they talk about the electric field from a circular disk in your book. If you look at, if you're very close to the disk itself, then there is absolutely no dependence on the strength of the electric field with height above the plate. It only depends on the charge density. And so if you increase the area, you have to increase the amount of charge on there in order to maintain the same electric field, for instance. That's the only way that that will work. And again, that's all because of energy conservation. In order to conserve energy in the system, the only way to do that is to move more charge until there's enough charge that it can oppose the voltage of the battery and it stops. And that's it. And you reach what's called an equilibrium situation. There's no more movement. Jenna? Yeah? Yeah. If you have a capacitor and you're increasing the distance, doesn't the charge stay the same? Because it's not going anywhere. You're just kind of moving. If you, okay, so, okay, let's go and look at the capacitance equation. So capacitance is A over D epsilon naught. And then there's this kappa, which comes from changing the material inside the capacitor. I didn't write this equation explicitly in the video lecture, but it's such a simple modification of the original parallel plate capacitor system. And this is for parallel plate. Okay, this is the area of the plates. That's the separation. So if you keep the area fixed, okay, and you do something like increase the separation of the plates, the capacitance decreases, okay? So since the amount of charge is equal to C times V, okay, if the voltage across the capacitor is fixed by the battery, and that doesn't change, and the capacitance decreases, the amount of charge stored will also do what? Decrease, right? Because if C goes down and V is constant, Q must go down. So, in fact, as you change the separation between the plates and that little simulation I showed you, it does that. It puts more or less pluses or minuses on the plates. So it really does affect the amount of charge. Basically, as you decrease the separation of the plates, in order to get that same strength electric field in between the plates, you don't need as much charge anymore, because the charges are getting closer. So the strength of the electric field can be maintained by having less charge. So as you decrease the plates, charge will actually move back through the battery to the other side, again until you reach equilibrium and then it will just stop, and it will reach just the static situation where nothing is moving anymore. Okay, now if you disconnect the battery and plug the ends of the capacitor into each other, which I'll do, you can get the charges to move back again until everything neutralizes one more time and you're right back to restart it. Neutral capacitor that you could charge up by putting a battery across it. And I'll do that, okay? Actually, let's do that. So this is not a parallel plate capacitor. It's sort of a three-dimensional parallel plate capacitor. This is a cylindrical capacitor, and what has basically been done is that conducting sheets of material have had some kind of dielectric material put in between them so that they can't make physical contact with one another. And the dielectric material is not a conductor. It doesn't allow charge to move freely through its volume. So you just take a big sheet of this, maybe long but thin, and you put your conductor down, you put your dielectric down, you put your conductor down on top of that and make a little sandwich, like an ice cream sandwich, and then you roll it, and that's what you get. So you can put a lot of area in this little volume because you've taken a really long thing and rolled it into a cylinder, much like you do with paper as a kid or something, that if you get a poster or something, you want to store it more easily, you roll it up and you put it in a tube. Same idea. Okay, so that's all this is. This is a particularly unimpressive, I guess this is going to be 4,000 millifarad. So this is a, well, you'll see, this is a little bit better than this 10,000 microfarad one. So they use funny units like this. Micro and millifarad are sort of the things that engineers like to work in, and so they'll put these really big numbers in micro to indicate the size of the capacitors, except when you get to a farad, then they just write a farad capacitor on it. The one farad capacitor we have in the back, which is capable of storing, I guess this is 4,000 microfarad, actually. So this is 4,000 microfarad. This is capable of storing, you know, something like 1,000 times more charged than this is actually about, it's the same area here, but it's only about this thick. So, you know, this is an old one. The joke used to be when the new grad student in the 1960s or 1970s joined the group, you'd send them into the storage room in the back to look for a one farad capacitor, because back then a one farad capacitor would take an entire room, but technologies marched on since then, and that's not really a funny joke anymore, and actually I would be very low to let anyone handle a one farad capacitor charged. I once did, and I well did a, I actually, I accidentally, I was told not to do this, but I did it because it was an accident. I was holding on the leads of the capacitor, and I shorted them. And when I did this, all the charge on one side of the capacitor is now free to go back to the other side of the capacitor, and it well did my screwdriver to the leads. I could now no longer remove the screwdriver, and I just had to throw the whole thing down on the table and get away for fear of it melting or exploding. It's very bad to do what's called shorting an electric device. That is where you create a path of almost no resistance between lots of charge, because charge is going to do what it, what's needed to do to neutralize the system again, and that may mean melting metal and then now creating a permanent short that you can't undo anymore, and then this can explode. So that's also very bad. One farad capacitor is blowing up or like bombs going off, and I can probably find some demo video of that, but there's plenty of stuff on YouTube. Usually if you're going to short a one farad capacitor, you put a bulletproof glass up first so that no one gets shrapnel through their head. So if you're in lab, and you're given a one farad capacitor, hand it back to the person who gave it to you and said, no, thank you. It's much better that way. All right, so let's charge one up. I have a, what's that? Yeah, so if Mr. Garino hands you a one farad capacitor, walk away. That's the best advice I can give you, okay? It's a trap. Get out. All right, so I have this 10,000, so this is a 10 millifarad capacitor, and it's got a labeled plus side, although it really doesn't matter what side I hook up to plus, what side I hook up to minus. This is just so engineers don't screw things up. So it's got a plus side on this side and a minus side on that side, and I have here a voltmeter, so let me bring this thing to the front. Okay, so how many of you have seen a voltmeter before or an ammeter, a current meter? Okay, a few, more than a few. I'm just going to shock to you. This device is, this is actually a multimeter. It has many settings on it here, and I've got it set so that it can read up to 20, a potential difference of 20 volts across a system right now. And my system is going to be this DC direct current power supply. Okay, so it has a little dial on it, which I'll hold up here because I can't get everything in frame. It's got a little dial. It's set to zero right now, but I can increase this, negative end in here and the positive end in here and then no shorts, no metal move on. Okay, and I'm going to switch on the power supply and absolutely nothing interesting happens. This is just noise in the meter. There's always an uncertainty in these devices and it's usually in that last decimal place on the meter. So you shouldn't really trust that last number as it kind of flicks around, but I can actually give it a voltage to measure. If I raise this a little bit, you see I can get this up to about one volt or so and if I keep going, I'm going to take this up to about 12 volts. I'm going to crank it up past 11. There we go. So 12 and a third volts, roughly. So that's about the equivalent now of a 12 volt battery. So 12 volt batteries are roughly what you find in cars, right? So your car has a 12 volt battery and that's a lead acid cell battery or something big like that. You can use your gas engine, power your radio, your other electronics, charge up your devices plugged into the what used to be a cigarette lighter, but now it's just called the power outlet. So this is now roughly equivalent to the voltage across a car battery. Great. Well, now, that's nice. All I'm doing is I'm measuring the electric potential difference across the terminals. So nothing really exciting is going on here. What I'm going to do now, however, is I am going to hook this power supply, let me switch that off, into a capacitor and we'll select silver here. So silver is 10,000 microfarad. Okay. And we'll go up plus to plus, although this part doesn't really matter so much. Plus to plus. Minus to minus. Okay. And now, if I switch this on, what I'm going to do is I'm going to measure the electric potential difference again across the power supply. So what should that be? 12. It should be 12 volts. It's still delivering the same voltage it was before. So I'll just hook that. Let's see here and here. Okay. And we see again about 12.3 volts. Now, if I measure the voltage difference across the capacitor, what should I measure? Anyone? What's going to be the electric potential difference across the capacitor now that it's hooked into this battery or power supply? Well, that's the capacitance. That's its ability to store charge which is proportional to the voltage. But what's the voltage going to be? I heard it from somewhere. No? Yeah. Yeah. It'll be 12 volts. It's not a trick question. Energy is conserved in the system. There's no other source of energy in the system. So the potential, once this thing is charged up, the potential difference across it has to be the same as the potential difference because that's the only source of energy in the system. So this is just energy conservation and I'm going to really just kind of hammer this in. Okay. There are two major things you need to think about when you're analyzing systems like this and they're all based on conservation laws. Conservation of charge. That is the net charge in the system has not changed. It's just been separated into different places like across the plates of the capacitor and the energy conservation. That the changes in potential difference in the circuit will net to zero overall. Okay. That is energy is conserved. Okay. So let's measure the potential difference across the capacitor. Let's go this way. 12.3 volts. Okay. So we can test this. We can test this claim based on energy conservation and charge conservation. Specifically here, energy conservation. That the voltage, the electric potential difference across the capacitor will be the same as the battery and so it is. Now here's the neat thing about capacitors. If I disconnect the power supply, I can switch it off. Okay. The leads are now over there. What's the electric potential difference going to be across the capacitor when I measure it now? It's been disconnected from the power supply. Same. It should be the same. Or roughly the same. And you'll see. Okay. So it's a little lower. Why is it a little lower than it was before it was plugged in? And what's happening to it as we sit here and watch it? It's just moving. Yeah. So it's not a perfect closed system. There's always some leakage, right? In a real world system, there's no device invented that perfectly prevents charge from moving. There's a little bit of leakage of charge off the end of the lead here, for instance, into... These leads are exposed to the air. There are water molecules in the air. Humidity has a way of soaking up additional charge. So if any of the charge is being soft off of this metal by water vapor in the air, then sure enough, this is eventually going to drain down. Even the material inside is not perfect at preventing the motion of charge. But it's not bad. I mean, we've been sitting here now for about a minute, and it's lost about 2 volts of electric potential difference across. So what happens if I short this puppy? It drains completely. Okay? There we go. Let's measure it now. I know it's not supposed to explode, but there's no way I'm going to go explain that to my spouse today. All right, so we've got it down almost to zero now. Okay? So that's one capacitor. What happens if you have multiple capacitors in the system? This is where things seem to get tricky, but if you keep charge conservation and energy conservation in mind, it's really not quite as bad as it looks. All right? So what would happen now if I created a circuit involving a battery and two capacitors that look something like this? All right? So I have my battery, plus side and the minus side, and I'm going to start with two capacitors in what are called parallel to one another column. So, again, all these lines in between the devices are meant to be perfect conductor. They offer, as you'll see in a bit, no resistance to the flow of motion of charge. That's an approximation. There are perfect conductors that humans have learned how to make, but they're not cheap, so they tend not to be used in typical applications. But there are very good metals that you can rip out of the earth and refine, and they actually are pretty good conductors overall. They offer very little resistance so we have our battery, we have our two capacitors, and they may not even have the same capacitances. So we'll label them C1 and C2. Okay? So those are the capacitances of each of those capacitors. Now, without doing anything really novel here, we can simply write down a few bits and pieces. Okay? And I'll go for this here. We have the voltage across the battery V. Okay? We have the capacitance of capacitor 1, the capacitance of capacitor 2, and we know a few things. For any capacitor in the system to label it I, the relationship between its capacitance, its voltage, and its charge is given by the very basic capacitor equation. That the charge stored on the capacitor plates on either one of them, the magnitude of that charge is equal to a constant times the voltage across the capacitor. Alright, so there's going to be some potential difference across capacitor 1. We may or may not know what that is yet, and there's some potential difference across capacitor 2. We may or may not know what that is yet, but it does allow us to write down a few things. The charge stored on capacitor 1 is just C1 times V1. And the charge stored on capacitor 2 is C2 times V2. Okay? Now, the name of the game with any circuit analysis problem, and this is where we're going to really begin circuit analysis. The name of the game is when you have repeated components in a picture like this, your goal should be to try to reduce the number of components to the minimum number that you can get. So if you have multiple capacitors and they're connected in this case in what's called parallel, and I hope you see why. It's because they're in parallel next to each other hooked up to the battery. Each of these terminals is connected to the same plus end of the battery. Each of these terminals is connected to the same minus end of the battery. They're parallel to one another. So that's where this arrangement takes its name from. The goal with this or the other arrangement I'll talk about today is to reduce the number of capacitors to as few as possible by doing energy and charge conservation and using that to simplify the system. Okay? So, a couple of things here. We know that the charge on this plate is going to be plus Q1. Oops, the charge on this plate is minus Q1. And this is going to be Q2. And minus Q2. Okay, so we can begin jotting things down in the picture that are supposed to be true for the capacitor. And our goal is to write a single equation Qtotal, that is the total charge stored in this system is equal to some total capacitance of one whopping capacitor in here, not two times the total voltage across the system. So our goal is to start with the two separate equations and try to use energy or charge conservation or both and rewrite those two parallel capacitors as if they were one giant capacitor and figure out what Ctotal is so that we can plug it into that bottom equation. Okay, so a couple of things here. Let's think about electric potential difference. Let's start with energy conservation. You have the top sides of the two capacitors plugged into the same side of the battery at the same point in the battery, right? So if I was to put a voltmeter here and here, so put the leads in the voltmeter here, what voltage would I measure? Yeah, the voltage across the battery V. What if I put them here and here? Same. What if I put them here and here? Same. What if I put them here and here? Same. So my prediction is that because if I were to take a voltmeter and stick it here and here, it's equivalent to putting it here and here, here and here, here and here. I kind of did this in the video lecture, right? The electric potential difference across these points will be the same here because there's a clear path back to the battery. There's a clear path with no other circuits, no other capacitors in the way back to the battery. So by energy conservation, whatever the electric potential changes across one and two are, they're the same. And since the only other source of potential in this battery in this circuit is the battery, it's passed to be V. So energy conservation rides to the rescue in this problem. So from that energy conservation we have the following. We have the V1 must be equal to 2 must be equal to V. That's a prediction. Let's test it. Okay, that's just math on a chalkboard. So I have two different capacitance capacitors here. One 4,000 microfarad 1, 10,000 microfarad so they're different by almost a factor of 2. I have a source of potential difference, 12 volts here. So what I'm going to do now is I'm going to hook these capacitors up in parallel. So to do that I have to take the negative side of this one and I have to hook it to the negative side of this one. Okay, and then I'm going to hook that to the negative side of the let's see if I can do this without touching any other metal. That looks good, okay? That goes to the negative side of the voltage source. Now I have the positive side. So I've got to hook the positive side to the positive side and let me just double check. Yep, red plus, good. That's supposed to be the positive sides. Now I've got to hook this up to the voltage source. Come on, you. Okay, didn't fall over. That's all I can ask for. Alright, let me switch this on. Give it a second. Okay, so we can very easily just check if I hook right into the leads of the power supply. Okay, we can check the oops, I'm going to get my hand out of the way. Alright. Oh, yeah, that would be helpful. Derp to derp. There we go. Oh, that's terrible. Is that okay? Okay, great. Thanks. Alright, let me make sure I don't screw this up now. So, negative side of the battery and positive side of the battery. Okay, 12 volts. Well, that correspondingly also happens to be the voltage across this capacitor, right? Because it's, I have the battery voltage coming into this side of this capacitor. I have the battery voltage on the other side going on to this side. So, touching the leads of these two capacitors, I get 12.3 volts. So, let's see what happens over here. Alright. So, here we go. And 12.3 volts. Okay, so that's good. We have a prediction and it's actually born out in the real world. We have a device that's capable of holding charge. It's got plates separated by some dielectric material that doesn't allow charge to move. So, two of them in parallel, that is, I put them both hooked into one side of the potential difference and both hooked into the other side of the potential difference so that they're effectively joined together like this. And the voltage across them is the same. Great. So, we can use this. We can use this. This prediction is real. So, let's go ahead and use it. So, we have that V1 and V2 are going to be the same. There is something else that we can use here. Okay. What's the relationship between the charge I put on capacitor one, the charge I put on capacitor two, and the total charge in the system that's been separated? How do I relate those? You can add them. And how? How would you add them? Like, you wouldn't do like the reciprocal or anything? No, right. So, I'm just using charge conservation. Yeah. Right. So, Qtotal must be equal to what? Q1 plus Q1 plus Q2. Sorry. I heard something. Starts and then stops and then it faded out. So, Ethan? Would it be 2 times Q1 or 2 times Q2? No. Q1 plus Q2. Yeah. Charge conservation is that if I have a charge stored on device one and I have a charge stored on device two, the total charge stored in the system is Q1 plus Q2. So, that's Qtotal. Okay. So, that's charge conservation. So, Qtotal must also be equal to Q1 plus Q2. Okay? Well, now I can actually start using the capacitor equation. So, I can simply rewrite Q1. Well, actually, I can just plug this right in here, can't I? So, this is going to be equal to C1 V1 plus C2 V2. Well, V1 and V2 are both equal to V. So, I can just rewrite this again as C1V plus C2V. And now with a little bit more algebra, we have actually the exact equation we were looking for. Qtotal we want to find out what Ctotal is. Vtotal is just the voltage across the battery and that's just going to be C1 plus C2 times V. So, for a system of parallel capacitors like this the total capacitance so for parallel capacitors Ctotal is equal to C1 plus C2. Nice easy equation. And again, it's all borne out of energy conservation and charge conservation. Okay? So, that's one example. And you can use that in homework. You know, you'll be given some awful looking set of capacitors in parallel all with different capacitances and be told to find the equivalent capacitance of this mess. C1 plus C2 plus C3 plus whatever if they're all in parallel. Okay? Where the tricky bits come in is when you mix parallel with what we're going to do next, which is called series. So, we'll do series on its own and then I'll leave the homework to see if you've grasped the core concepts. Okay? So, you're coming out of there and then charge off. Okay? So, series is the one that I think people think is a bit more daunting, but again if you remember basically if you remember your training, if you remember energy and charge conservation you'll be able to handle this no problem. And eventually it just becomes a couple of rules based on energy and charge conservation that you have to apply, apply, apply. Alright, so here we have our capacitors. Now, this is what is called series. So, series is that you have one capacitor in the circuit that's in front of or behind of depending on how I want to look at it, another capacitor in the circuit. So, they're in sequence in the conductor path. So, now, again, you would expect that there's going to be some plus Q1 here, some minus Q1 here, some plus Q2 here, some minus Q2 here. There's going to be some potential V1 and V2. Let me put a semi-colon here so that those aren't multiplied. Okay, so you can just write that down. And then, of course, we have the voltage across the battery V. Yeah, Rachel. This might be just tedious, but on the other diagrams I know you're raised over that. You only wrote like plus Q1 or plus Q2, you didn't write minus Q1, minus Q2. I did. You did? Okay, I've said that. Fair on the other place. It was just on the other. Okay. Yeah, so because the top of both capacitors was hooked into the plus side of the battery, both of those were plus Q1 and plus Q2. The bottom side is minus Q1 and minus Q2. That's all. Okay. No, no, no. It's a good question. Alright, so this one we have to analyze as well. And let's start with energy conservation again. So, again, if I put a voltmeter on the system here and here, I'm going to get V. The voltage across the battery. Here and here? V. V. Okay. What about here and here? Am I going to get V? Should be. Okay, so some prediction. That's going to be the same voltage as the voltage across the battery. Okay. Any other predictions? Can you give me half? You think it would be half? Well, different. It's certainly different than V. I mean, half is a bit specific. We'll see. But... Are, like, proportional to C? Yeah, somehow related to the C's and how they relate to one another. Something like that. Okay. Alright. We have a prediction. One that this is the same voltage as the voltage of the battery and one that this is something other than that that's related to the capacitances. Alright. Let's check. So, again, I have capacitors. So, this time I'm going to hook the minus side of one of them into the plus side of the other. So, you are my victim for this one. Okay. And let's see. So, this is the plus side of the power supply. This will go here. Okay. And then this is the minus side. Everything's off. This will go here. Okay. So, now I have the series configuration. I have let's go from the plus side here. So, plus side hooks into the plus side of this capacitor. The minus side of this capacitor goes into... There's a little plus right here. I'm trying to see it in the image actually thanks to that reflection. And then the minus side over here goes to the power supply. So, just like in this picture here. Alright. So, now I will switch this on. Okay. So, we can do... we can check the first thing, right? Which is that the voltage across both capacitors had better be the same as the voltage across the batteries. So, let's do that. So, here's one end of the system and here is the other end of the system. 12.3 volts. Okay. Now, let's check the next part. So, what I'll do first is I'll measure the voltage difference across the black capacitor and then the silver one. Okay. So, all you have to do is put this here. Put this here. Ah. Six volts. Okay. And then let's check this one. So, this is the plus side of this one. Now, what do I expect the voltage across this one to be? About six volts. Yeah. Yeah. The other one was 6.3 something. This is 5.9 something. Okay. All right. So, they're slightly different. And that's... Oh, yeah. Yeah. Okay. So, in the parallel plate system, let me see if I can show this here. All right. So, in the parallel system, what you do is you connect the lead, let's say, from one side of the power supply or the battery, to the same sides of the capacitor. So, this plus lead should also go to the plus side of this capacitor in parallel. But here it doesn't. Here, the plus only goes into one of them, then the side of one capacitor is connected to the plus side of the other, and then the negative side of the power supply connects to this capacitor. So, rather than both of them feeling the voltage from the negative part of the power supply and the positive, only one of them gets the voltage in from the positive side and only one of them gets to the negative side. Yeah, exactly. So, when you go across this capacitor, you experience some potential difference of E1. Okay, in this case, it was about, see, 6.3. Okay, 6.5. Again, there's a little bit of measurement error here, just because this is an imperfect device. So, 6.5, 2, or so, and then over here it should be less, and it's 5.68, something like that, and the sum of those two should be about 6.3. Okay. So, all right, so, we had a couple predictions, and this is the beauty of experiment, is you can test predictions and see which ones are reliable and which ones are not. And so, we now we know which one's unreliable. It's the one where they both have the same voltage in this configuration, but the reliable one is where they have different voltages. Rachel? I just want to make sure I'm understanding this. So, you just hooked up two capacitors to each other, like the one from the other. Yeah, the back end of one goes into the front end of the other, and then they each connect to the power supply. Is the power supply the battery? Yes, the power supply is our battery. It maintains a constant voltage of 12.3 volts. Yep, okay. You can do this with a 9 volt battery, you can do this with a 1.5 volt battery, you just get different voltages in that case, so. So, positive end to negative end capacitor to capacitor, 12.3. Across the whole capacitor system? Yeah, just one, basically. Like this to this, that's 12.3. Can I assume the inside one, like the mid-lines? Oh, if I do this? That one, but to the other one. Just trying to get what the mid, the connector Oh, here to here? Yeah. That's a good question. Zero. Because there is no battery in between the path connecting these two points. Yep, so there is so that's good, that means the conductor isn't providing any additional electric fields that we have to worry about. Yeah, so that's a great question. Exactly. That would be the same as me taking this bit of wire and hooking the voltmeter into itself. I'd expect 0 volts because there's no source of electric field anywhere in here. Yeah, Ethan. Here? No. No. The equation for the series that we write down based on energy conservation is that V1 plus V2 equals the total voltage across the system. So, here in the parallel case, the total charge was equal to Q1 plus Q2. We'll get to charge in a second. In the series capacitor system, the total voltage is V1 plus V2. And you'll see this affects the total capacitance. This system has a different total capacitance than when you put the same capacitors in parallel with one another. Yeah. So, since these are in series that the capacitance would decrease, but why would you... You're begging the question, but what's that? I was just wondering why you would want to decrease the capacitance since the whole problem is to store charge. Right, but here's a great example. You're like MacGyver. You're locked in a room. You have two capacitors. Each of them is too large to solve the problem that you have. But if you could combine them in some way, you could reduce the total capacitance and build a circuit that involves half the capacitance of the two you were given. Okay. So, then it comes in handy to be able to cut the capacitance down in some way. Engineers have to do this all the time, right? You can't build a custom capacitor for every situation. But what you can do is you can combine capacitors to solve problems. Maybe in a prototype. You can always custom build it later. Right? But you don't have to custom build every little capacitor that you need. Yeah. So, do you necessarily need the mid connector or would they just store capacitors anyway? That's a good question, right? So actually, let's look at the charge and then we'll think about that question, okay? So, we have a charge Q, positive Q1 here, negative sign with same magnitude, negative Q1 down here. We have positive Q2 here and negative Q2 here. But let's think about this picture right here. You've got this plate with negative Q1 and you've got this plate with positive Q2. So, what must be the relationship between Q1 and Q2? Is this charge moving? Let me start with that question. No, the charge is sitting on the plates. It's not going anywhere. What would happen if Q2 were bigger than Q1? What would the charges on Q1 do? Move. They'd move, right? And then so this thing would keep reshuffling charge. So, these must be equal. Yeah, equal in magnitude but opposite in sign. So, what's happened here is that you put this potential difference across these two ends of different capacitors. And you start depositing positive charge up here. So, maybe you start by putting just a little bit of positive charge on the top plate and a little bit of negative charge down here. And in response, this material in between which also begins as electrically neutral it feels a little electric field from this charge and this charge and its charges separate. And so, they separate in equal amounts. And so, whatever the charge is positive Q1 here it's also the same as the plus Q2 here. So, from charge conservation Q1 equals Q2 and that's going to be equal to Qtotal this time. So, unlike the parallel system the total charge in the system is equal to the charge stored on either of the capacitors. Okay, and so from this we can begin to salt. So, let's do that. So, we have this equation and again these are four I should have written this down first series capacitors. So, these are in series. They're in sequence in the circuit one after the other. We have two equations. We have this equation from charge conservation and this equation from energy conservation. And so, we can begin to substitute in with our capacitor equation. So, let's go ahead and do that. So, V total is going to be equal to, let's see, V is going to be equal to Q total all over Ctotal. V1 is going to be equal to Q1 over C1 and V2 is going to be Q2 over C2. So, I'll leave those and get rid of this. And again, you can always write down a capacitor equation for every single individual capacitor in the circuit. And that's the first thing you should do when you have to tackle these problems. Just start with the fact that every single capacitor in the system will have its own capacitor equation. Q1 equals C1V1. Don't worry about what Q1 is. Don't worry about what V1 is yet. Just write it down. Write down an equivalent equation for every other capacitor. And then you want to start thinking about which ones are in series with one another, which ones are in parallel with one another, and then how can I combine capacitances. So, let's do that here. Okay, well, we have the energy conservation equation. So, we have V equals V1 plus V2. And if we substitute in with our capacitor equation, we have Qtotal over Ctotal equals, and again, substitute in with our capacitor equation. So, we have Q1 over C1 and Q2 over C2. And we're almost there. We have to now use this equation. The Q1 is equal to Q2 is equal to Qtotal in this situation for series capacitors. Well, we've got Qtotal here. Q1 is the same as that. Q2 is the same as that. So, what happens to the Q's on all sides of the equation? They all cancel, right? And we're left with, for the series case, this equation 1 over Ctotal is equal to 1 over C1 plus 1 over C2. And so, then you would put in your C1, do one over that, put in your C2, do one over that, add them, and do one over the result to get Ctotal. So, you have to invert this equation eventually to get Ctotal. And then in parallel, let me write down the result we got from that. So, in parallel, we had equal equal C1 plus C2. Okay? And that's it. Every circuit that you can design is basically going to have capacitors either in series or in parallel in some way. And so, the goal that you'll be put through in homework, not this, not homework 4, but in homework 5, will be to try to reduce a complex looking circuit down to a single large capacitance. Why is this useful? So, a good example of this is analyzing the action potential of a neuron. So, the neurons in the brain, they are capable of holding a potential difference of about what, does anybody remember? Yeah, negative 70 millivolts. And what happens is that when you want to transmit information through the axon, it actually causes an increase of the potential and then it falls, undershoots, and comes back to its original resting potential. That release of charge that causes information to move down the neuron, that release of charge is essentially modellable as a capacitor storage and discharge system. So, I had a student in this class many years ago. She went on to minor in physics, Holly Howard. We have a poster down the hall where we tried to reproduce the action potential just using simple resistor and capacitor circuits. We were unsuccessful which is good news because I would expect that the neuron is a bit more complicated than just throwing a few capacitors and resistors into a power supply in a circuit. But we learned a lot about how to try to sculpt the voltage from capacitors while we were doing it. So, this stuff has applications for instance in doing electrical analysis of information storage in the brain and how information is transmitted, how the action potential is realized, how it's changed in a neuron. All of that can be controlled with, you can model actually, I believe this actually won a Nobel Prize, but there's an old now model of the neuron and its action potential and how it changes that simply uses capacitors in a circuit to demonstrate it. And that's essentially what we were trying to reproduce in the lab to see if we could actually get the behavior we saw. So, questions? So, how the series is the Q1 and Q2? I guess I'm confused from the Q1 and Q3. So, why are the charges related to one another? Well, just ignore the bottom capacitor for a second. It certainly will be the case that if this top one was the only capacitor in the system that once you build up enough charge you can oppose the voltage of the battery these charges will be the same magnitude which gives you the electric field inside the capacitor and then no more charge moves. When you add another one in you're now putting the voltage across this entire system, so the battery voltage is over this entire pair of capacitors. So, if you just one way you can analyze this actually is just to imagine what would happen if these plates were to move closer and closer and closer to one another and get thinner and thinner and third thinner and eventually what would happen is that the negative charge on the top here and the positive charge on the bottom would come together and they'd merge and it would be as if you had one single capacitor with no plate in between. And so, the only way that can happen is that these charges exactly cancel each other. Which they did. Which they did, yeah. So, plus Q1 minus Q1 this will also have to be plus Q1 and that will be plus Q1. That's the only way that you can keep charge from moving in the system once you've charged up the capacitors. The book may do a better job of explaining this than me, but they do this thought experiment where what happens is if you shrink the, bring these inner plates of the capacitors very close together so that you're basically melting their conductor together until all the charge is now sitting on one single block of conductor in between the plates here and here. And in that case the charges, the negative charges and the positive charges are basically being forced to come back together and neutralize and you get one big capacitor with a plus Q1 up here and a minus Q1 down here. So you like did those two examples to show how to find capacitance in the series? Right. Exactly. Yeah, and it was just using charge conservation that the net charge in the circuit starts zero and it has to end zero. And so the only way to do that would be if we know that these two have to cancel each other, then it better be true that these two also cancel each other or there's net charge left over in the system and we don't know where it came from which would violate charge conservation. So that's another way to look at it. And then voltages have to add up. So you have to look at this and figure out, well are the voltages across these capacitors going to be the same or could they be different? I know that whatever happens in that system at the end the total had better equal what's coming from the battery and that's just energy conservation. So that's where all this comes from. That's what allows us to analyze the system of capacitors in the first place. It's those two things. Charge conservation, energy conservation. That's why they're so central to physics. Everybody. This is probably going to seem very elementary. I said I'm going to practice a question with that. Because what is the point? What's the point? Yes. The point is that when you are designing electronics you have to be able to figure out what the voltage changes are in the system and where the charge is being stored and how much is being stored. So as a simple example actually, here's a great example. It does it using a slightly different technology but the principle is the same. You go to Europe. How many people have traveled to Europe or outside of the United States? Okay, you bring a hairdryer with you. And it blew up, didn't it? Why did it blow up? Right. What's different about their circuits? Okay, so mechanically they're different. But electrically what's different about them? Different volts. They use about 220 volts. So if I plug in a hairdryer which is basically it's just copper wire into a high resistor that then when it heats up causes heat and it's got a fan that blows the heat into your hair. If I just plug that into a 220 volt outlet I will melt the resistor inside of the hairdryer and it will either catch fire or simply electrically fail. So what you need to do is you need to change the voltage that's coming from the wall and then going across your hairdryer so it doesn't melt. Now the way that this is actually done is because it's a transformer and it uses magnetism. But you could do it using capacitors and in fact this is done using capacitors in microelectronics. You have a battery. It puts out 12 volts but you have a sensitive microprocessor that only needs one and a half. If you put 12 across it you'll blow the expensive microprocessor up. So you need to devise a way to split the voltage to turn 12 and the capacitance is until the voltage difference across this one is 1 and this one is 11 and then you can plug your microprocessor into this. So this is how the human body regulates voltage for instance. You looked at a toy example using the cell membrane but this business with using capacitance effectively to alter voltage is the basic working mechanism by which the brain works by which cell membranes work and charge across the cell membrane. You have to be able to analyze these systems in general because they're useful and you want to use them for something. Nature's done it and there's no reason that we as part of nature shouldn't do it either. It's a great advantage, right? The fact that I have a microprocessor in here that can't take the full voltage of the battery is saved by the fact that I can use capacitances to drop the voltage down. What about capacitors for stability? Right, so another thing I mentioned this earlier, but because you can keep a reservoir of charge here if somebody were to maliciously disconnect your battery, right, you don't necessarily want your computer to be power off and you lose all your work, right? So there are capacitors in these devices anyway for a variety of other reasons but they can be used to hold charge for just a few seconds maybe just enough time to plug the battery or plug the wall plug back in before your computer completely shuts off. So you can use them for practical reasons like that but there's a whole bunch of circuit design reasons that you would want to do that in general to soothe out the amount of charge or current that's moving through a circuit. So capacitors are often used to regulate electric currents so it doesn't fluctuate wildly in a circuit which can damage microelectronics. So once the capacitors are drained that's in the battery and you can restore the charge? Right, because they only give you a finite amount of time and we'll look at how long that actually is given the voltage and given the capacitance, you can determine how long it will take to discharge the circuit and the resistance of the circuit. So how much resistance does the circuit offer to the flow of charge? If you know those three things you can figure out how long it'll, how long you have basically. And then use that on the wall? Yeah, microprocessors don't need a whole lot of voltage to run. So one thing uses? Yeah, well it'll give it one volt right away and it'll give you 0.99 volts a moment later and then 0.97 volts and then 0.92 volts and it'll discharge according to a specific pattern that we'll see. You don't have a lot of time it depends on how you design your circuit in the first place. And if you design it carefully enough you might get seconds which could be enough time to save yourself. The bigger problem is not so much what the microprocessor is doing but what the memory in the device is doing. You know when you're working on a document if you're not saving it to disk it's called RAM. And that RAM is volatile. If you disconnect power from it the state of the memory is lost. I mean in the same way that if you disconnect oxygen from your body your brain death will occur within how long? Minutes, right? 8 minutes, 10 minutes something like that. You need to be a vegetative state if you go without oxygen for too long. Same thing for electrons battery voltage or wall power RAM, that RAM requires voltage to maintain its current state its memory and if you pull power from it you'll destroy the current state of the RAM which means you're losing your document. So you'll get data corruption at the very minimum and data loss at the very maximum just under data loss. So the way you can resolve that is by keeping a capacitor or bank of capacitors handy just in case something bad happens to the voltage across the RAM the capacitors can come in and save it for a moment so you're saying if there's a low battery or something because if it's fully charged then that shouldn't happen right, right and it's a bit of a catch 22 because the battery is both storing charge in the capacitors and being used to operate your electronics at the same time so as it begins to wear as its chemical reaction wears down it can no longer maintain that voltage anymore so it can no longer maintain current in the circuit as we'll see and that causes all kinds of problems so that's when you begin to basically go into fail modes with electronics you know they just they can't maintain their screen power they can't maintain their memory state they can't maintain active processor calculations anymore it's the equivalent of rubbing you of oxygen you will stop functioning very quickly within a minute you'll be unable to move and within a few minutes several minutes you'll be brain dead and your organs will begin to shut down so you know humans have oxygen and food and those things have electrons coming from the wall but the outcome is the same if you rob them of their power supply you can't operate the electrical systems anymore and they power down and we're just a big bag of electronics we're wet electronics, those are dry electronics maybe one day they'll fuse and we'll be cyborgs, that'll be cool I could use more RAM, that's for sure so with your hair dryer example, why do you have to bring those adapters because I brought one because I do have time that was not a good idea and I had to talk my spouse down off a cliff about not plugging her hair dryer into an outlet this summer and I managed to win that but only barely because I knew what was going to happen when she plugged that in she's a physicist, this makes no sense to me why? because you need to transform the voltage into something that that hair dryer can actually handle so what does it do? what it does is it we'll get to what that kind of does later but the voltage comes in one side and there's a big wrapping of wire inside of it around a magnet and the current from the wall plug creates a magnetic field so energy is now stored in that field and you can induce a voltage on the other side of this device that's less than the one that comes in by robbing energy out of the electric field and this is called a transformer in that little transformer that little thing that hums and gets really hot the reason it hums and gets really hot is because it's taking that charge and storing it in heat it's wasting energy in heat as it transforms the voltage but it's primarily storing energy in a magnetic field so rather than an electric field which is how this stores energy there are devices called transformers that store energy in a magnetic field so it turns electrical energy from the wall into magnetic energy in the transformer and then it turns that back into less voltage so that's why they get hot and that's why they tend to fail because to do that requires that a lot of work happen in the device and that results in heat friction because of the resistance in the material and those adapters tend to only last a few years with regular travel because they just melt they're not going to Europe every day unfortunately I go several times a year so I burn through those things ridiculously fast but yeah maybe the adapter was bad or it's possible to transform to the wrong voltage I just bought a European one they do have switches on them so they're really good ones that you switch between voltages but yeah I don't know it could have been that thing was ready to fail to begin with or it could have just been that you happened to be unlucky and had a transformer that failed or it was bad when you bought it that's the risk if it's not well designed then it could just fail right away yeah yeah just to be safe well yeah that can cause fires obviously you don't want to do that because it will cause problems this is just to illustrate the kind of thing that you're going to see on homework so you'll be given some problem involving multiple capacitors in parallel or just in series or both and your goal will be to try to get that circuit into an equivalent circuit with only a single capacitor in it and you have to figure out what that equivalent total capacitance is that's the game you'll be playing so that's an example of 3 in parallel that's an example of 3 in series and you should always start by analyzing them pairwise so take one pair try to compress it into a single capacitor now use that paired with the next one try to compress that into a single capacitor and keep going it's a stepwise process it's just like solving problems involving models in many charges break it into pieces, attack each piece one at a time and then build it up to a big thing so same strategy as always one last comment I wanted to make and then I'll do a brief introduction to current before we get into Ohm's law join the resistance on Thursday alright my goal is to make that joke even moderately fun to any of you energy capacitors or die electrics in capacitors I mentioned in the lecture that you can shove material the capacitor you saw that demo using the simulation where you take the block of material and you shove it, it was glass you shove it into the capacitor and the capacitance goes way up there are all kinds of materials that we've developed over long periods of time that turn out to have various what are called die electric constants if I write the capacitor equation one more time or the parallel plate capacitor so for a parallel plate capacitor this is equal to a over d epsilon not kappa and this thing here is the die electric constant okay and so that's just a number it's always one or greater than one one corresponds to the vacuum of space, empty space no material at all anywhere anything else has a larger die electric constant that you can't be more permeable than the vacuum the vacuum perfectly permits electric fields to propagate other materials do not and I'll show you why from the atomic perspective in a moment alright so air is actually pretty good at one atmosphere air's die electric constant differs from the vacuum die electric constant which is one with an infinite number of zeros after it sort of at the level of 0.05% or so so air is a bit of a die electric and that's why you can put air in between two plates of a capacitor and it works fairly well but you don't always want to have to keep increasing the area of the plates or decrease the separation of the plates to get your capacitance up if you want to custom build a capacitor you may want to use other materials to improve your capacitance so polystyrene paper transformer oil, transformers I mentioned before for changing voltages that's present in that you can use that pyrex pyrex glass cooking glassware so it's a kind of glass ruby mica, porcelain, silicon germanium, ethanol water at different temperatures and these are the really good ones so like ceramics these nice ceramics that are built for aircraft and cars and things like that strontium titanate that's got a huge die electric constant and this comes from where this comes from is this picture picture materials as being formed from they're made from atoms and atoms build up into molecules and so the fundamental building block of all material that we deal with on a day to day basis is atoms and that material contains equal numbers of positive and negative charge and it's usually just that they're so close to one another that everything appears pretty much electrically neutral unless you get very close to an atom well if you were to expose a material like water where we did this I can do it again but I have, I do just carrying this crap around with me now alright so you can expose a perfectly electrically neutral material and I might even be able to you're going to have a pleasure of seeing some of your faces on screen okay so if we charge this up I can create a very non-uniform electric field from this around the cylinder and I can bend the water stream using that and that's because water is a little dipole it's positive charges and negative charges are slightly separated from one another okay and the consequence of that is that when I expose them to a non-uniform electric field I can get them to rotate and accelerate at the same time so the oops there you are so if you think of materials as always having the possibility of having their equal amounts of negative and positive charge separated by exposure to an electric field that's the basic building block of dielectrics any material in principle you shove it in the presence of an electric field and the little dipoles the little atoms or molecules their charges will move away from one another but if they're bound to one another they won't go very far so atoms are held stable by the Coulomb force and that Coulomb force is quite strong so if you put atoms and molecules in an external electric field they will separate a little bit and then line up like good dipoles in an electric field and that's basically what's going on because you're now separating the charge and making these dipoles line up with their positive ends to the right and their negative ends to the left in the electric field they begin to diminish the external electric field they weaken it and by weakening it they allow you to store more charge on the capacitor in order to get more electric field into the capacitor to oppose the battery you must put more charge on the capacitor to create a stronger electric field to fill the capacitor you can greatly increase the amount of charge that can be stored there because in order to get the same electric field through that glass you have to put a lot more charge on the plates for the same voltage so that's the basic operating principle of dielectrics now where this goes south is when you put such a strong electric field on the material that you actually overcome the Coulomb force that holds atoms and molecules together and you can turn the bonds apart or even tear atomic bonds apart now you've separated the charge and you've freed them from one another and now they will move and they will move fast and you can turn a dielectric into a conductor by doing that but you'll irrevocably change the material lightning strikes are a good example of how you get lots of charge built up in the clouds an equal magnitude but opposite sign charge is the electric field between the cloud and ground system so thunderstorms are giant capacitors and if you have parallel thunderstorms that come together what happens to the capacitances they act and you get a bigger capacitor capable of storing even more charge so you begin to see why it's important to think about this stuff if you have storm systems merging get the hell out of the way to be around when that electric field overcomes the dielectric constant of air and breaks it down that's what causes lightning strikes and those things will kill you or set things on fire or both and that leads neatly into electric current so in the last few minutes of class let me motivate what we're going to do next and start to begin to define some very basic terms this is a beautiful pristine loop of conductor in the top and it's copper colored because a lot of conductor that's commonly used is the metal copper and you'll see why as we go into resistance and resistivity in the next lecture so you have this little loop of conductor no sources of voltage whatsoever perfectly electrically neutral when it's just sitting there absolutely nothing interesting happens this is about as boring as it gets now if you were to clip the copper take out a section and plug a battery in and now you've put an electric potential difference into the circuit and again the plus end of the battery here the minus end of the battery here this is the source of positive charge and it will try to go around and get to the negative side of the battery the chemical reaction inside the battery will then shuffle charge back from the negative side to the positive side and the whole thing will repeat so you can think about this the battery is if you're thinking about a water analogy a water through a pipe this is the pump and the pump gets the water back in from the other side it uses some source of energy in this case a sustained chemical reaction for a battery to drive the charge back up to high potential and then drop it down again so the idea here is now that you're no longer thinking about charges just sitting there we already started to get into the movement of charge a little bit in my video lecture but now we're really going to start thinking about what's going on when you move charge and a couple of important things come into play so you have this symbol I and I is what is known as the electric current it is just if you were to slice through this conductor and just count the charges that go by you know one charge, another charge there goes a third there's a fourth, there's a fifth and then you divide the amount of charge that goes by in say 10 seconds that would give you the electric current it's just the amount of charge that passes a fixed point in the system in some time so delta q over delta t or dq over dt if you're talking about a continuous distribution of charge okay dq over dt is current that's it, coulombs per second nothing magic about it and that gets a nice name that gets its own unit you can get a unit named after you that's yay because there ain't a lot of money in science so you gotta get something the ampere which is named after somebody we'll meet later in the course the amp, amp one ampere is one coulombs per second okay so we'll pick that up next time and we'll talk about the fact that that material is not perfectly allowing the passage of the current it comes at a cost called resistance thanks everybody and again just in case