 All right, so I'll just repeat this again because it bears repeating but the sum total of the behavior of atoms Equals the behavior that we see at our scale of the world. All right, so we experience as human beings The scale of the universe that we call roughly about a meter, right? So a meter is roughly the length of your arm If you stick it out straight So It gets very tricky it turns out to Visualize what's happening? Deep down in materials where you can't actually see what's going on and as it turns out if you get past a course like this You get into something that we call modern physics usually modern physics combines two things objects moving very fast and objects that are very tiny and I know that sounds ridiculous, but that's really what modern physics is The study of and the study of those things things that move very fast and things that are very tiny Lay at the heart of all of the technology that we take for granted today that makes our lives comfortable Okay, so how many of you are aware that the physics Nobel Prize was announced today raise your hand if you were wow Okay, one person. That's more than expected So what was it for? Okay, all right, so it was for the the Creation of the first what's called blue as in the color blue light emitting diode or led So leds are ubiquitous these days There's an led inside of this laser pointer that creates that very intense beam of Monochromatic that is very close to a single wavelength red light Led's are everywhere. They are used to backlight the screen in my laptop They're now becoming regular players in the light bulb industry and the reason that they're becoming regular players in the light bulb industry Is just two things one. They're really cheap to manufacture although the manufacturing of White lights for lighting your home is still an expensive venture and I'll tell you why in a moment And and also because they use very little power to emit light They're very efficient unlike these things which if you've ever grabbed an incandescent bulb after it's been plugged in for a minute or so You know what happens you burn your fingers Especially on a hundred watt bulb and a 40 white ball You might get away with it for a second or two before you let it go But a hundred watt bulb you almost burn your fingers immediately and that means if you feel heat coming off of a light source That means energy that's going into that system is being wasted in the form of heat and you want it to all Go into light because you want the bulb to light a room. That's all you wanted to do You don't want it to heat a room. You've got heaters for that Okay So your air conditioning has to work against these things because they're so inefficient Led bulbs on the other hand are extremely efficient. They have a very high efficiency for converting current into light and That light can be tuned very precisely to specific wavelengths And so the reason the blue led is so important is a it was very difficult to actually invent and then manufacture It was very the material. It's made from was not something that was in common usage. It had to be formulated first Once you have blue LEDs Red and green LEDs have existed for decades. I used to Okay, I used to play with them when I was in high school. I had no friends So I used to play with them when I was in high school. Oh, yeah, thanks. Sorry Anna. I appreciate that. That's really nice And so I you know so that was something easy You could go to like Radio Shack and you could buy those for 50 cents a pop now They're even cheaper the blue led on the other hand if you go to Radio Shack and buy it It's a couple of dollars. So by comparison to its blue and green counterparts It's far more expensive because it's far more recently that it's been invented and then mass produced So the price of that is going to go down over the next decade or so But the reason it's so great is once you have a red a green and a blue you can tune the frequencies to make white light All right, so white light can be decomposed Electronically into three colors red green and blue and so it used to be that for instance the cathode ray to television sets The way that they worked is they had a beam for green red and blue and they could sweep the beams and Everywhere those beams met they made a spot and you can control the color of the spot by having them meet or miss And that's how you control the color of a television set And it's actually very similar in an LED TV these days You have red green and blue LEDs and the way you control the color is you simply alter their the mixture of red Green and blue in each dot in the screen and you know They tout the density of pixels and those things like the retina display for instance on on an iPad. So yeah, Rachel Because it's much because just because of the material you have to You have to engineer the material so that when photons jump an energy gap Oh, sorry when electrons jump an energy gap and that energy gap has to be large They emit a correspondingly high energy photon So the way light works is that the higher the energy the shorter the wavelength There's a direct relationship between energy and wavelength and energy wavelength and frequency for light And so if you have a if you want to make a very high energy photon You have to correspondingly have a material with a very large energy gap between basically between its conduction band and its valence band And so you have to engineer that material Yeah, yeah the small energy gaps are more abundant in nature So humans had to engineer materials to give you Blue light, but at a low cost and that's the trip All right So it took a lot of physics effort to actually engineer that material you have to combine Atomic physics what's called solid-state physics. That's just the physics of what happens when atoms group in regular clusters. That's it and and engineering to make that happen so No red is a lower energy in a longer wavelength of the way around so red So for instance the reason that you get skin cancer if you spend too much time in the sun is because of ultraviolet light And ultraviolet light has just enough energy to break chemical bonds in your skin And so it's about four electron volts worth of energy and that doesn't sound like a whole lot Okay, but in order to break the weakest bonds the hydrogen bonds in the you know Molecules in your skin all you require is about four electron volts. So all the visible light won't do that It's all too low wavelength It's too low energy or too high wavelength too low in energy, but UV light is just right It's just at the cusp of where you start to get physical damage You create free radicals the free radicals interfere with DNA replication You can cause mutation and you can get cancers that result from this now your body's very good at removing mutations that are You know most of the time your cells are mutating all the time But your body's very good at eliminating them before they cause problems But every now and then you'll get a runaway Cell that replicates far faster than your body can handle it or might even fool the body's defenses into ignoring it And that's what we call cancer. It's a very difficult thing to evade So, yeah, Arianna. So they Yeah, well, they will get hot. I mean nothing is perfectly efficient. There is no such thing as a perfectly efficient device For the home right there are actually physical limits to how efficient energy conversion can be to understand that you have to study thermodynamics, okay, but They are far for okay So for the density of pixels that they provide if you've made a cathode ray-tube television set with the same density of pixels you Blow your house energy budget on that. I mean, there's a reason why TVs didn't scale up to be 40-44 inches 56 inches 72 inches, right when they were just cathode rays. Those things were very expensive You had to have a big running room for the electron beam to travel and you needed big magnets And you needed to sweep really fast across the whole screen and you had to do that enough So your eyes don't notice the refresh rate because otherwise you'll get motion-sick and headaches and things like that Okay, so there's an art to building those things and that's where the engineering comes in But it's just impractical. There were cathode ray-tube TVs that were that big but No one could really afford them. So and they were power hogs anyway Plasma TVs were also power hogs when they first appeared that they could go big LED TVs are the right balance of size and energy usage. And so they're much more popular now because they give you the big size at a Reasonable cost. Okay. So if you're just looking at saving money leds are great If you have to buy an LED light bulb, you know and versus a compact fluorescent right now You'll probably choose a compact fluorescent based on price But compact fluorescence come with a whole list of other things like the fact that they contain mercury and then they have to be properly Recycled and disposed of they're a chemical hazard So so there's all kind of risks and benefits that you have to take into account when buying a light bulb But right now on price alone leds are the most expensive lights you can buy On the other hand, they've made laser pointers extremely cheap by comparison to when I was buying them as a grad student I mean, I had to save up for my first one. Now you walk into a store and you can pick one up at checkout for like two bucks Okay, so Okay, so that's it. I just wanted to let you guys know that that's going on today Let's get back to the microscopic world for a moment So in the microscopic world, what's going on is sort of pictured in this This cartoon right here is you have some material made of atoms and for a conductor Some of the electrons in each atom one or more of them have to be loosely bound to their parent atom So that under the influence of even a modest electric field They can be removed and motivated to accelerate in a particular direction But what makes materials interesting is collisions the electrons might accelerate or short distance You know much like the ball bearing in this model here But they'll hit something as they are accelerated by gravity. They'll get up to some instantaneous speed That's actually quite high But then they'll bounce off of an atom and they'll have to be Re-accelerated by the gravitational field in this case and the situation is similar for a material with an electric field So if one puts an electric field across the material Okay, and let's just assume that they're a uniform for now to keep this nice and simple We'll just deal with uniform fields for these cases one can induce for instance an electron to drift Remember the electric field points that way electrons will drift that way so correspondingly it can be said that the positive charge is moving this way With the opposite direction but equal magnitude be driven Everything is done in terms of positive charge when you're defining your directions in a circuit. Okay, where does the positive charge move? So microscopically if we wanted to imagine for a moment that the electrons are standing still but the atoms are moving That's kind of what then Franklin has stuck us with at this point. Okay, so it's really the electrons that are moving But they're moving opposite the direction of the positive current flow positive current flows that way if electrons are flowing that way Okay, I know this gets a little backward, but again, these are conventions that we are hindered with by the history of our field okay, so Other charge is moving this way and this basically induces a If I can make that j better a current density, okay now current density is a vector and It points in the same direction that the positive v drift points So let's call this negative v drifts to distinguish it from the the Velocity with which the positive charge is moving to the right Okay, and then this current density will point in the same direction as V drift So the direction that positive charge is moving that is the direction of positive current density Okay, that's the only thing you need to define the sign of that vector as positive or negative and That should point in the same direction as the net electric field on the system So the positive charge is going to go in the direction that the net electric field is pointing All right, so that's what I've drawn here in this cartoon And so we kind of get a feeling that there must be some relationship between Electric field and the current density that's set up and that that current density will depend somehow on the properties of the material If the material offers a lot of resistance to the motion of of charge Then the you can put an electric field on it But you won't get a very big j and if you put more electric field on that same material You can increase j Correspondingly you could instead change your material you could put the same electric field on a material that offers less resistance to electric Current and that would allow you to set up a bigger current density. So there must be some relationship Which we can write as the electric field equals the The Electric field equals some constant of proportionality. So this is a constant of Proportionality that takes care of all the units right because this is in Amps per unit area. This is in Newton's per Coulomb. So whatever this thing is we'd have to figure it out for each material Whatever this thing is it will have units that correctly map one on to the other. Yeah, what's that row? Yeah, that's the Greek letter row That's how I draw a row. You can know sure people can do better than that okay so yeah, so this is the Greek letter row and It is known as the resistivity of the material Okay, so at the microscopic level there's some relationship between the current density that one can set up and The electric field that you place on the material to establish that current density in the first place So if we write that down over here, so here at the microscopic level We have Row okay, or correspondingly we can just write this in terms of magnetism okay, or for simplicity sake just equal for okay Just get rid of the vectors for a second and then at the macroscopic scale. We have the expression of Ohm's law Which is that a potential difference will establish a current? And that current will depend on the amount of resistance of the material. So this is the resistance And that's in in ohm's omega. That's the symbol for its Okay, and We can attempt to relate the two of them We want to find the connection between this row this constant of proportionality and are the resistance of the material So that constant of proportionality summarizes atomic physics What's going on with collisions down inside the material and this Summarizes the net effect of all of those collisions on the relationship between the voltage one applies to a wire For instance and the current that one is able to drive through the wire All right. Well, if we have a material whose length is L and We establish a uniform electric field through the material. How could I relate the potential across that material to the electric field? Any ideas we're going to try to map the microscopic the electric field to the macroscopic the electric potential across the material Very on any ideas. How do I relate voltage and electric field given that information? All right, so you're jumping ahead and trying to get row into it one step at a time We'll get to that. You can beat the head three steps. That's fine Voltage So he looks like you're going for the capacitor equation Let's go back even further than that Well, okay, what's the what's the definition of the voltage right voltage is equal to work done by an applied force per unit charge right, okay, and this is The work is if we do one over two here the work is the integral of the force Times the displacement Okay, which I can write as one over q e Let's see Q e Dot DX So my q's cancel and I just have the integral of e dot DX Well, I've given a nice simple case. I've got a uniform electric field and it's a length of material L And so in the end this integral is just gonna give me e times L. That's it Okay, so voltage is e times L nice simple equation and This is maybe a demonstration of how you can go back to the basic definition of voltage is work from the applied force divided by charge That the work through all your stuff. Okay All right, so the voltage in the system The voltage in the system is times L Okay. Well, let's remember the basic definition of current density This is the current divided by the area of the material through which it's passing So if we were to slice this if this was some kind of cylinder we have some some area a meter squared Okay, that this current is passing through that's the definition of current density current per unit area and now we can take that equation up there e equals rho j and We can rewrite it. So we want to solve for rho. We want to figure out what this thing is So it's row is just going to be e divided by j Well, I have things I can substitute in E is equal to v over L and j is i over a so j is in the denominator So that flips this relationship over Okay, and finally I can try to use ohm's law to figure out the relationship between Or and row So let's see if we can get this into something that looks like ohm's law Let's leave v on this side, but let's move current area and length to the other side So we're going to get L over a row I Equals v and in order to recover ohm's law v equals I are I now only have to make an Identity between that thing multiplying I and resistance So R is equal to row L over a And let's think about that formula for a moment. Okay, that's the identity that we can solve for from this little exercise Whatever this row is what we see is as it goes up resistance goes up and so that's why this thing is referred to as Resist So as resistivity increases so increases the resistance of the material if I put more material in front of in the path of the Charge if I lengthen the amount of material that it has to go through I offer the opportunity for more collision and correspondingly Argos up so if I take a material that's a very good Conductor has very good conduct or very it has very low resistivity. I Can make it a really terrible conductor by just adding more of it So the longer your house wiring for instance the more resistance there is in the wall to the flow of current in your house Okay, so there's a there's an art to engineering a nice short path for current in your house So that it's not looking wildly all over the place that wastes Energy basically because the more copper you put in your wall even though copper is an excellent conductor It has some resistivity and that will add up as you add more and more and more lengths of copper So you want a shorter path between where for instance the electric potential comes into your house and your blender Or your light as possible if you put too much copper in you basically just create a big resistor in your wall And you're now you're wasting energy in the form of heat from collisions in that material And then finally if one decreases the area of the material Basically, you're squeezing the charge now travel for a much smaller area And that will increase the number of collisions as well. And so that increases resistance as Overall, so if you want to figure out how to go from the atomic properties of a material the length that can the The charge has to travel the area through which it has to travel and the inherent Structure of the material which is summarized by its resistivity you have this equation. Yeah Yeah Current to flow with less resistance Right, and so this is why if you're driving a lot of current your wire thickness goes up Because if you have a small thickness and a high current You'll generate a huge resistance and that can heat up the wire to the point of melting So, you know, this is why you need to be very careful with driving more than say 15 amps or 20 amps Through house wiring that's rated for 15 or 20 so for instance The the ship evolved that my spouse and I drive it can be charged at a higher current But the company has explicitly limited the rate at which that car will charge to no more than 12 amps And that's for a couple of reasons one that's safely below the limit of the of the house wiring in any standard house That gets built today most of the house wiring is rated for 15 to 20 amps There are special circuits in a house usually for even higher current appliances like washers and drivers They can draw a lot more current The other reason is is that the company Chevy They don't know whether you're plugging your bolt into a new house Or a 40 year old house with 40 year old wiring which may be to hang and decrepit and actually have a higher Resistance as a result of its lack of good condition And so they don't want to put it at 14 amps or 15 amps the limit of the house wiring now They put it safely below that is for a margin of error because Chevy doesn't want to get sued for setting houses Right, and that's also why you have breakers in your house They're little switches when they overheat they trip and break the circuit and that's on purpose That's so you can't accidentally put 25 amps of raw on a 15 amp circuit and set your house on fire So the breakers are there to save you from yourself essentially or from a malfunctioning appliance For instance, we had a heating element in an oven. I'll bring it next time and It exploded one day and why did it explode it exploded because the resistance of the material in the heating element suddenly changed for a Catastrophic reason. We'll never know why Could be that there was just a cheap You know some problem with the material in one part it broke down the resistance changed and suddenly the power dissipating through an increase But it exploded with a bright flash and a pop and a trip to breaker because for just a brief moment as the resistance of the material Failed the current going through that part of the house suddenly exceeded 15 or 20 amps Whatever the stove is limited to and the breaker trip and it probably saved our house from burning down Okay, we still have to deal with smoke and and sparks and so forth inside the oven But at least nothing else bad happened behind the walls where we couldn't get All right That's what the fire brigade would have done if they had rolled into town to save our house from a house fire and electrical house fires Particularly nasty because it usually starts in the wall. So you have to tear the walls down again And that means massive amounts of damage to your home Okay So things to keep in mind if you're goofing around with too much stuff plugged into one wall socket Think about it carefully many of the wall sockets like this one may be on a different breaker than the one down here That I'm plugging my laptop into and that's why you should distribute your appliances across multiple plugs Because your wiring can only handle so much current Before you start wasting energy in the form of lots of heat and you can ignite the wall and fire or melt material or worse okay, so that's the connection between the Macroscopic and microscopic worlds and we're going to start exercising now ohm's law We're going to exercise ohm's law We're going to exercise in conjunction with conservation of energy and conservation of charge and start thinking about circuits Just out of curiosity would anybody like to see the demo of the The taser One more time but this time with audio from Rick Sanchez Yeah, Avery you didn't get to see this right is anyone mind if I play this again, I got the audio working this time All right, let's let's see so what I summer. Oh, yeah, I'm just gonna show this so you can look up resistivity of materials On the web Wikipedia has a great table. Here's copper for instance resistivity is measured in ohms times meters And you have to do it at a particular temperature. We'll come back to that later for instance copper has a resistivity of 1.68 times 10 to the minus 8 ohm meters and That's exceedingly small resistivity another convenient way of quoting resistivity or rewriting it is by taking one over the resistivity and This is known as the conductivity So if you have a big resistivity You have a low conductivity and vice versa if you have a big conductivity you have a low resistivity Okay, so this is something that depending on what table of numbers you're looking at if they give you conductivity You can get resistivity from it just by inverting conductivity. It's a very simple bit of math. Okay All right, so copper is pretty good Graphene which got a Nobel Prize a few years ago now. This is a very special material that's showing up more and more now in electronics I actually saw a great talk by one of the Nobel Prize winners who won for graphene's discovery When I was at the University of Manchester this summer. That's where he's located and He was talking about the now they've developed basically industrial scale 3d circuit printers based on graphene So if you would like to custom build a phone with certain characteristics They could print this thing for you in 10 or 20 years So you just go online you say I want this and with these features and one whatever I'm maybe I want a radio on it for some strange reason and they can just print that all onto a Single board for you in layers of graph and this are already industrial scale printers that can do that They're just not very common use for commercial electrons. Yeah, James Yeah It well the fact that they had so actually having more valence electrons You'd think would make them better, right? So what what is different about gold silver and copper gold is a great conductor? Platinum's even better. Okay So so I'm told by my spouse that this is platinum Alright, so that's we decided on platinum wedding bands for ourselves. I still hang on off when I was a postdoc So that was a bad idea. It seemed like a good idea at the time, you know And so yeah, what makes them different is actually the structure of the material the way the atoms are positioned Alters the way collisions occur and that increases their conductivity as a result So even though gold and copper have the same number of valence electrons available to move Their atomic structures are different from one another and you can alter those structures manually in many cases to improve their conduction level But that comes at a price that costs money to do that Yeah, so on this list here the lowest resistivity material is actually graphene and so you you're gonna see a lot more It's also really cheap to make the way to discovered it was They found a mono layer of graphite on a piece of scotch tape and when they analyzed it It was this amazing one atom thick layer of repeating carbon atoms and it turned out to have these incredible electrical properties Okay, and then you go down the list you know platinum has a Resistivity that's a bit bigger actually than copper and so forth Let's see here and then okay. I wanted to highlight these so seawater and drinking water So you'll notice that they have very different resistivity Sorry, yeah resistivities here and as a result of that's because in seawater you have a lot of salt So there's a lot of free Ions available to be moved in drinking water. It's been desalinated. It tends to have a lower mineral content There's less free charge to move the water dipole really holds on to itself in order to rip that apart You basically have to make hydrogen and oxygen out of water to get those charges to separate So they tend to have a much higher Resistivity as a result than then seawater You're kind of similar to seawater in terms of your blood conductivity and things like that what makes you a Worse conductor a better resistor than seawater is the fact that your skin is often dry and you know If you're not sweating you're in good shape But if you sweat you basically putting seawater on your skin and any current that it wants to flow across you will flow across You very easily and so this was sort of the the basic idea I got into last time where I was talking about This stuff useful numbers for human biology. All right, so if you Accidentally come in contact with a current flow So if you become part of a circuit where current comes in your right hand and it goes out your left hand Basically, that means it's traveling across your heart to make that path If you come into just half to two milliamps worth of current it's a tiny amount of current That's the threshold of human sensation that basically set your nerves Into notice you you're gonna feel that it's gonna alter electrical signals in your body You're gonna notice that there's electric current flowing. So I don't have one with me Does anyone ever touch their tongue to a nine volt battery? Okay, well you can calculate you can estimate how much current is flowing through your tongue It doesn't paralyze you but it it feels weird Okay, basically you're taking a very, you know salt sugar laden surface with other proteins and stuff mixed into Salivary amylase and so forth and you touch your tongue to it and you breathe the Contacts you'll feel that in your tongue it it feels both like You'll taste like blood in your mouth. That's weird and and then you will feel something akin to sort of a Very strong itching burning sensation on the tip of your tongue like like you've got a rash And it's a right on your tongue. It's not pleasant. So do it right out see how it feels Okay, I strongly recommend it at least once in your life to testing that out It shouldn't kill you, but if you have a weak heart, please don't do it because I have no idea what it's gonna do Okay, all right 10 to 15 milliamps is where you start to go into involuntary muscle contractions You'll notice there's a gap here Try not to mess too much with that gap because somewhere in that gap You hit this point where you now you have your you know start to your muscles to start to contract Strongly in response to the current flowing through them It's overcoming your your your own electrical responses that control your muscles and often at this point You can't let go anymore So somebody puts you in a circuit where if you accidentally put yourself in a circuit You may not be able to let go anymore and this is not a lot of current. Okay? Severe shock muscle control completely lost which means also involuntary functions like breathing They become difficult that happens between 15 and 100 milliamps 100 to 200 milliamps and you get heart fibrillation death occurs within minutes greater than 200 It's immediate cardiac arrest or breathing stops and you can suffer severe skin burns inside and outside. Okay So this is what I showed last time a taser is designed to put you into the it's designed to put a voltage Essentially across your chest that puts you into the range of about 15 milliamps of current That's in the range to paralyze so to incapacitate somebody and so Rick Sanchez who used to report for CNN Now he's on Fox news. He volunteered for this story to be tased By a couple of cops. So let's uh, let's watch those Now what it comes to technology many in law enforcement recommend stun guns over real weapons to show you how it works I'm about to see Of electricity, I'll tell you what he why why there's a difference in a moment Yeah, no doubt Welcome to the resistance Okay, so uh Yeah, I mean that that kind of made it almost look humorous But the the reality is it's a delicate subject socially right because if you have a suspect with an unknown heart condition And you taste them you can kill them that has happened on at least a few occasions So like any situation involving force of any kind of judgment calls involved And uh, all all the physics can tell you about is why this happens in the first place So he said 50 000 volts when that thing's flying through the air when those electrodes are flying through the air The potential difference across them is very high and the idea is that that way when they puncture the skin Uh, the voltage will actually drop in response to the change in resistance between the air and your skin And that will deliver about only 1500 volts to your body. So yes The taser is capable of creating a potential difference of 50 000 volts or so But what's delivered across your chest is typically only about Something like that enough to cause the involuntary muscle contractions He you know rick had to get caught by people because he lost control of his body um If you have enough determination and enough momentum you can still charge an officer shooting you with one of these But uh, eventually you will lose complete control of your body So, um, yeah, so this is just an example of why you want to be really careful with this stuff Okay, so we did all this stuff All right, let's go to simple circuits. All right So we're going to start to build up a toolkit to deal with situations that involve a source of voltage conductor And resistance and then eventually we're going to add capacitors into this now a preview of why this is Is important to do Uh, it's something that I mentioned earlier and I'll show a picture of it and probably not this lecture But maybe next one and that is for instance if one wanted to try to model The body as a large group of electric circuits You could start thinking about the smallest pieces of that circuitry and how it functions And so one of the things that actually has you know a long time ago I believe it won a Nobel Prize in physiology and medicine was the description of the firing of the neuron as a series of voltages resistors and the capacitors and with that model in mind one could grossly reproduce The features of the action potential that occurs in every neuron in your body and By changing the potential across the neuron transmits information The aggregate storage of electrochemical information is possible through the way that voltages and chemicals are controlled In the brain and this is something which is still not completely understood the brain is a is a huge mystery the Nobel Prize in physiology and medicine this year went to fundamental work on how the brain is able to determine spatial Location so how is it that we know where things are in reference to other things? That my hand is here that my hand is now here How is it that the brain does that and so this year's Nobel Prize in physiology and medicine went to figuring that out There's no application of it yet The hope is that you might be able to apply this information to understanding why in Alzheimer's patients They completely lose their ability to know where they are So I have family members that are going through this right now. It's very difficult It's it's a huge strain on the family But maybe it won't benefit them, but maybe in 10 20 30 years The basic understanding of how the brain locates in space Will have some application to solving the problem of getting lost when you have Alzheimer's so yeah This is related when we talked about like spacing of like How you know where you are in relation to other things how you how do you navigate? How do you remember that to get to your friend's house you turn left at this street right at that street? So it's both position. You know like where's the mouse in relation to me, but also where am I in relation to everything else? You know, I know I'm in this room. I know how I got here How's the brain do that and that's just a basic piece of information that that we didn't know until The people that got the prize that was contributed to that body of work Yeah, yeah, even though I don't have to see it. I know it's over here I didn't know that actually So is that actually how you can indirectly detect the presence of diabetes without doing a blood test like advanced diet? or All right, so basically they've lost their ability to know where their limbs are where sensations are in relation to themselves Yeah, I wonder if this is somehow also related to phantom limb syndrome too, right if you lose a finger a hand and so forth You still feel that it's there even though it's not for some period of time afterward Yeah, well, I mean all this is fascinating, right? I mean neuro neuroscience is a is a is really a It seems like it's advanced, but it's really quite in its infancy And that's why for instance There's a huge attempt to inject lots of federal dollars into this to try to have like a Shoot the moon moment with the human brain Europe is doing this too They have a huge brain initiative to simply try to answer basic questions about the brain And that requires synthesizing chemistry biology physics mathematics computation and a lot of other areas engineering Um, because I mean we're just wet wear, right? We're just a large computer with some software loaded into it Where's all that come from? How's it all functioned together? Nobody really understands that? It's a huge area of opportunity for discovery and money. No doubt. So Okay, so back to this boring picture by comparison Uh power supply battery. All right, so let me make a comment on batteries here So far we've been assuming that a battery is an ideal Provider of an electric potential difference Uh, and one does have to be a little bit careful, right? This is a this is the simplest circuit You could construct basically you take some conductor and here for the purposes of the schematics It's assumed that this conductor Carries no resistance and all the resistance of whatever's in this circuit is summarized by this squiggly symbol here, which is the universal circuit symbol for a resistor. Okay So there's some current that's driven by the battery and it's clockwise All right, so current is emitted the positive charge is emitted out the positive end of the battery It flows through the resistive material and then back down here And it's re-upped by the chemical reaction inside the battery which won't last forever But we'll ignore that for now and then this cycle just continues current just keeps flowing And we know from looking at the drift velocity last time that this is a very slow moving thing I mean in a typical house wire You can walk faster than electrons are drifting through this wire But nonetheless because the electric field is established immediately in the system by the battery All the electrons over here start to move even if it's only a little and they start doing work in the resistor by colliding with atoms And so that you know that for instance will give you light from a light bulb almost instantaneously All right, so this is our basic picture battery battery so a voltage source current driven by the battery resistor with resistance to motion of current in the circuit And we're going to play with this archetype as we go forward All right now there's a symbol here that is introduced in the chapter. It's an old term It's a vestigial term left over but nonetheless since everything Contains it when you look at circuits. You're sort of stuck with having to To uh adopted this bit of terminology, but We have a special symbol for the electric potential difference that's established by the battery and it's this curly e which is short for Electro motive force Or just em F It's an old term before we understood the batteries were actually doing so, you know When people were playing around with these cells back in the 1800s They knew that they had some electromotive force in them that would drive Sure charge through the system. It would do work somehow, but they didn't know what the force was until later They made the connection to electricity and magnetism and so on. Okay, so it's an old term But it's convenient because whenever you see that little curly e All right, that's a prettier one than the one i'm drawing but That means the battery voltage or a battery voltage. It could be multiple batteries from the circuit We'll look into that situation later on. Okay All right, so um one of the things that we'll have to deal with right away is The organization of resistance in a circuit Just like capacitors can be next to each other with each end at the same potential That's parallel Or just like capacitors can be one after another so that any Charge that passes through one has to pass through the other before getting back to the battery So called series. Okay, you can do the same thing with resistors. You can We have a battery here You can put two of them In the system such that right so here's our electromotive force Here's r1. Here's r2 You could put two resistors in so that they are parallel to one another That is that the voltage across them if i were to measure this here The voltage is the battery voltage. They both are at the same electric potential difference but The current that's flowing out of the battery i has a branch It can go through resistor one or it can go through resistor two And what you have to figure out is how the current is distributed through the resistors And your guiding principles on this as always are Energy conservation and charge conservation Any current that enters a branch in circuit No matter how it branches the sum of the branches must equal what went in And will equal what comes out. There's no place in these circuits where charge can build up yet We'll get to that later when we add capacitors Okay, capacitors store charge and so at some point when they oppose The voltage that's put across them by storing of charge with a separation current will cease to flow through a capacitor And that is something that we have to analyze by adding time into the situation right now We're ignoring time. All right, so purely current is established It flows through the resistors it comes out the other side goes back to the battery and so forth All right, so here you have a branch in any place you have a branch You can apply conservation of charge Okay Now in the case of series, which we'll get to in a moment You will half the current. Well, I'm sure let me just show it to you All right, so here's series. All right, that's why I drew this picture. So I wouldn't have to repeat it All right, so in series you have the voltage from the battery It is driving a current so here the plus side is on the right All right, so the current is going counterclockwise in this circuit Okay And it has to flow through r2 before it flows through r1 There is no way the current can skip r2 and go to r1 There are no branch points in this circuit So whatever current goes into r2 goes into r1 and comes out again All right, so whatever the current is in the whole circuit coming out of the battery It's equal to the current going through r2 and that's also equal to the current going through r1 All right, and that's written down here current is not split anywhere And by conservation of charge that means that the current must be the same literally everywhere in this circuit All right, and we're gonna we're gonna check that assumption in a moment. All right with a real example Okay, so the other thing to keep in mind here is that if I were to I know what the potential difference is coming from the battery This could be 9 volts 12 volts, you know, whatever the problem gives you The potential difference however is split across r2 and r1 If I were to make a measurement with a voltmeter or potentiometer here and here I would get the battery voltage because there's a path that connects directly back to the battery with no resistor in between But if I make a measurement of the potential here Okay, I am measuring the potential across that resistor And if I measure the potential here, I'm measuring the potential across that resistor And I know from ohm's law that v equals ir so if I know r and I know i I can figure out the v across each of those resistors All right, so what will be true here is not that the electric potential differences are the same across these two But rather that the sum of the electric potential differences on r1 and r2 will equal that of the battery Okay over here That's conservation of energy any energy changes that happen through here Have to be matched by the energy changes in the battery. This is a closed system There's no place for energy to go in or go out All right, so with those two principles in mind We can do the same trick that we try to figure we try to do with capacitors That is to find the equivalent resistance of these two resistors So we sketch here for a second What we would prefer Is a simple circuit With just some total resistance But we've got that picture So to reduce that picture into that simpler circuit We have to do a little algebra and we need to use energy conservation and charge conservation as our guiding principles And I sketch that out down there, but I'll just rewrite it up here So we know from energy conservation That that has to be true And we have ohms law for every Every resistor In the system ohms law applies All right, so there is a v1 equals i1 r1 and a v2 equals i2 r2 just like for every capacitor in a system of multiple capacitors There is a capacitance equation that applies to that capacitor Similarly, there's an ohms law for every single one of the The resistors in the circuit. All right, so that is also true for this r total that we're trying to figure out So v total here is just i total r total And that's equal to i1 r1 plus i2 r2 just subbing in with ohms law into this equation All right, so whatever v is equal to up here. It's equal to the current total current in the circuit times the total resistance of the circuit And then similarly v1 is i1 r1 v2 is i2 r2. We're just plugging in ohms law Well, the other thing we get to take advantage of now is that the total current in the circuit. All right, so i total Is equal to the current going through the first resistor and the current going through the second resistor There is no place in this circuit where current branches So in order to conserve current it has to be the same here Here here here here everywhere current has to be the same everywhere All right, so that's the last bit of information we need We now know that i total i1 and i2 are the same numbers So they cancel out of both sides of the equation And you're left with this relatively nice formula that for series series resistors The total resistance is just the sum of the individual resistances. That's it Now series capacitors was a little different in series capacitors The total capacitance was one over the total capacitance was one You know the sum of one over the capacitances of the individual capacitors So if you can remember the capacitor rules You can figure out the resistor rules by remembering that the rules that apply for series capacitors Apply for parallel resistors and the rules that apply for parallel capacitors apply for series resistors And they just substitute r's for c's. That's it. Okay, so if you can remember one of them You can remember the other one just by swapping them. Okay So I I know I find that tip helpful, but it may just be easier to memorize them all. Okay, I don't know It's sort of by your you know, it's up to the buyer, right? Okay, so that's the situation for the series resistance Now let's look at parallel resistors So in this case, I have my battery. It's driving a current I Have now a branch in the circuit So some current will flow through r1 some current will flow through r2 But the sum of those will be equal to the current driven by the battery through the whole circuit So I have i coming in here i1 going up through the top branch i2 going down through the bottom branch i1 plus i2 meet again over here, and I just get i So whatever goes in comes out conservation of charge Now I also have this set up so that the resistors are at the same electric potential difference This these sides of the resistors are both hooked into the same side of the battery These sides of the resistors are both hooked into the other side of the battery So whatever the electric potential difference is across r2 It's the same as r1 and the only one that's in the system is the battery So in this case v equals v1 equals v2 And I just have to use the fact that i will be equal to the sum of i1 and i2 whatever the total Current is driven by the battery It will be equal to the sum of the currents in the branch points So to sketch this out What I want Is I want to simplify this picture so that I have just some total resistance I have some total current and one resistor But I'm stuck with that picture to begin with so I'm going to try to relate the two of them And to do that I'm going to start with the the current conservation equation i1 must equal i i must equal i1 plus i2 so this is i total And again, there's an ohm's law for every one of these resistors Write that down All right, so I can make substitutions. There's also the total equals i total r total So I can make substitutions. I can rewrite this as i1 Is v1 over r1 i2 is v2 over r2 And i total equals v over r Total all right. I will now sub that into the conservation equation. So I have v1 uh, sorry v over again v over r total equals v1 over r1 plus v2 over r2 And now I get to use the last equation This one That the each resistor is at the same potential difference and that potential difference is given entirely in this case by the battery So v is equal to v1 is equal to v2 They all cancel out of both sides And I'm just left with a very familiar looking equation And this is the parallel resistor case that one over the total resistance Is equal to the sum of one over the individual resistors So if I had three in parallel here would be one over r1. What's one over r2? So wherever you see resistors in parallel in a complex circuit merge them together using the parallel rule Wherever you see them in series merge them together using the series rule Your goal with any circuit picture is to get it down to as much something resembling this as possible Maybe one voltage supply one resistor do the best you can Yeah Because regardless of how those are configured. I want to get a final picture that looks just like this That's my final picture. Yeah, it just turns out that in in this board I was talking about starting with two resistors in parallel and on this board I had started with two resistors in series. That's how I get r total for that picture That's how I get our total for the parallel picture Okay Okay We'll come back to yeah, we'll come back to that in a bit We'll come back to the internal resistance of batteries next time What I'd like to do right now is take the last 20 minutes of this lecture And talk about the light bulb game Okay, because something happened when we did this last week That maybe was a bit perplexing because you attempted to use intuition to answer the question, right? So What had I done? I'll reproduce what I had done So each of these is a just a light bulb and a light bulb is really nothing more than a resistor And what we're going to do is we're going to exercise resistors in parallel and resistors in series and owns law like mad And we're going to look at light bulbs and see I know this is so exciting, right? And we're going to see what happens if we can make predictions about what will happen in this circuit Okay, and these are great. I mean, these are getting harder to find but these are great demonstrations of resistors Okay, so to illustrate what we did last time Um, what I'll start by doing is just hooking up the I've plugged nothing in. I've just plugged in this really sketchy Circuit to wall voltage. All right, and what I'm going to do now is Hey, okay kill the lights Oh, sorry about that Morgan. There we go. Okay. So I'll try to do my best. There actually might be better with this on Let's see All right. So what I'm going to do is set this up so that it's capable of measuring a potential difference of up to 200 volts All right, and you'll see right now. It's measuring zero. All right, so that's terrible zero There we go So what I'm going to do now is I'm going to just hook this into the wall Yes, I have this on voltage Last thing I want to do sure with the building out Okay, so Okay, we'll let that kind of average up for a second and how much voltage do we observe coming out of the wall Yeah, about 125 volts. So that's a 125 volt potential difference that's delivered by that socket Okay Doing nothing right now because it's not hooked up to anything all it's doing is making my my screen display The potential difference. So it's doing some work to power this thing now. Okay, we'll take that out Unplug that because I don't want to die All right So now what we'll do is we'll start simply by hooking up the the Bulbs the way the manufacturer sort of intended this to happen. So one end will go black to black One end will go red to red. So what I've done now is I've hooked up a single bulb. This is a simple circuit I just showed you it's this you have a voltage difference You have a single resistor that thing. Okay. It's a 40 watt light bulb. All right So what I will do is now plug that in That uh There was light. Okay. So nothing exciting happens. There you go nice decently soft bulb you put a shade over that and it actually wouldn't be too bad to have in a room, okay Now let's hook up the other bulb. So this is a 100 watt bulb Exactly as the manufacturer intended it. I'm going to put 125 volts across just it Just like I just did the 40 watt bulb by itself a second ago and Even brighter can't even look at that thing right now. I've got my retinas seared like tuna steaks as archer would say Okay, so there all right. No one no one gets the archer reference. No, okay retinas seared like tuna steaks. No nothing You should watch more tv. I'm ordering you as a doctor okay, all right, so that was pretty bright and Let me just ask how many people think that the 100 watt bulb is the bigger resistor Raise your hand if you think the 100 watt bulb is the bigger resistor Okay, raise your hand high. I mean really commit. Okay. Thank you. All right. All right, so good The 40 watt bulb is how many people think the 40 watt bulb is the bigger resistor Okay, and some people aren't committing at all you have commitment issues You should get over that at some point. All right, that would be helpful All right, so okay, so fine. All right, so more more people tend to think the 100 watt bulb is the bigger resistor than the 40 watt bulb Let's just keep that in mind. All right, that's unplugged. I'm not about to kill myself. Good Now, uh, let's do the following. Let us start so I want everyone to start keeping numbers here. Okay We are going to figure out what the resistance is of these different bulbs So we're going to use them as the manufacturer intended. We're going to hook it up Singly across a single potential difference All right, let's start keeping some data. So get your calculators out and get ready to write some numbers All right, so v wall is 125 volts Approximately okay, give or take it's good enough for what we want to do The manufacturer says that the power of what I'll call bulb one Is 100 watts And that's the power of bulb two is 40 watts How can I calculate the resistance of the resistor using power and ohm's law any ideas? What's power equal to anybody remember? IV yeah, okay good. I heard another one in there. So power is uh current Current times voltage and we can substitute with ohm's law again I squared R. All right. So if we put in put in ohm's law We can get I squared R. Okay, so if we knew the current going through the bulbs We could figure out the resistance by knowing the manufacturer's rating for the power But we don't know the current. What do we know? What do we know in this situation when I hook up one of those bulbs to the wall? We've already measured it Voltage, right? So is there another equation that involves just voltage in R? V squared over R and these are just substitutions of ohm's law in for either I or or uh V in that equation. Okay, so if you take V equals IR And if you want to get rid of I because you don't know it you can write I equals V over R plug it in here You get V squared over R. Okay. Get used to exercise All right. That's why we're doing this Okay, great. So we know that the power is equal to V squared over R So we can solve for resistance of bulb one Right, that's just going to be equal to V squared over P1 and R2 is V squared Over P2 so calculate them somebody uh avar give me the do you have a calculator with you? How'd you get a calculator out? Calculate R1 Let's see calculate R2. Oh don't you get your calculator out? We'll get some numbers here But what do you already notice collectively the rest of you not the two of you who are calculating right now? What do you already notice about the relative resistances of? The hundred watt bulb and the 40 watt bulb if I put a hundred in here Is that going to give me a bigger or smaller resistance and if I put 40 smaller? So the brighter bulb Offers less resistance apparently Very good okay And we'll we'll go back. I I guess we'll this will bleed over into the next lecture because we got about 10 minutes left here But we'll go back and we'll revisit light bulbs using the microscopic model And a little a little smartphone wizardry to look at the relative power output of a good conductor versus a bad conductor Okay, but let's let's stick with this for now We're going to do some prediction See how powerful we all are now that we've mastered ohm's law. Okay. All right. So what resistances do we get avery? Do you have your number yet? R2 And then I'll just check because I did this exercise before class as well And I get 156 and 39 excellent. Okay, great so Let's start playing around with this. Okay, because we can actually do measurements now. We can compare them to predictions All right, so for instance What if I hook these up in parallel? All right, we saw what happened last time. Let me do that. All right So I will hook them up in parallel. What I will do is I will attach The ends of the these bulbs here both to the same side of the wall potential And These ends To the same wall potential Okay, and what happens if I plug this in do we get them both kind of at their expected brightness? Or is or is one really faint and one really brighter. They both don't come on. What happened last time They're both turned on. Yeah, so let's just verify that. Yep, and they're both pretty freaking bright Okay, that one's nicer to look at than that one All right That is the situation with a power strip if you buy go to walmart, whatever and buy a power strip That's got like six or seven or eight sockets on it. You can plug a bunch of things into it They in all the things you plug into it are resistors And you're plugging them in in parallel and that's why it is that your appliances can all function normally You know, you can have a hairdryer plugged into a power strip with a lamp And when you turn the hairdryer on the lamp doesn't dim suddenly And it's because you're putting them all all those devices at exactly the rated electric potential difference that the manufacturer intended About 110 125 volts depending on your your wall outlets. Okay So they both lit up But let's let's see if what we think is going on is actually going on So for instance, we could measure the potential difference. I'm gonna have to turn these on so, you know, don't stare too much And what I will do is Like that Okay, maybe maybe I can make the human readable way Yay, okay Excellent All right. So what I can do is I can measure potential differences across the bulbs. What do I expect them to be in parallel? The same and what value will it be? 125 okay, let's see Thank you phone pretty close Yeah, close enough for government work probably. Okay 124.5 All right, and you know, you're gonna start to see a little bit of pattern here as we go Uh, that some of the numbers might not be quite what we predict But this is good because if we fail we will learn and we'll see if we can fail in this exercise The failure is very important. All right, but that's basically 125. Okay. Let's try the other one now average up 124.5. Okay. So they're at the same potential. It's a little bit lower We may have five volts lower than wall potential. We'll come back to that later That's an interesting observation. Maybe it's just a glitch. Maybe, you know, maybe it's just that's the error in the instrument Or something like that. We'll come back to that in a bit. But yeah, they're at the same potential that much is clear Even if the potential is not quite 125. All right Now we can do another thing too here Oh man. All right, we can also Measure the current flowing through each of the resistors Now this is a parallel circuit situation. All right, so let me sketch this here And this will be the last thing we do today and we'll pick this up next time What I like about circuits Is that with a few basic things ohms law energy conservation current conservation You can feel very powerful You can suddenly start to understand complicated systems by breaking them down Surprise surprise pieces at a time and understanding each piece and adding it all up Okay, the same trick we've been doing the whole time in the class All right, so I have created this situation this way all potential v And here's r1 and here's r2. Okay So the battery in this case the wall socket is driving some current I Counterclockwise in the circuit What does it do when it gets to this branch point that I've now created right because current can flow in through the red wire And then it gets to this point here and it can either do what it can go through A bulb 40 watt bulb bulb number two so resistor number two or it can go through the 100 watt bulb resistor number one All right, and what's the relationship again between the currents going through resistor one and resistor two They add to the total conservation of current. Okay That's a prediction. Let's see if it's true. So what I will do now and this is going to beep a little bit Oh, maybe not. Okay. I've now set this up in a mode where it can measure up to 10 amps of current And so in order to make the measurement I have to make this thing part of the circuit So this is where things get a little dicey So what I'm going to do is I'm going to start it's not plugged in so it's good I'm going to start by inserting it here at the beginning of the circuit before we get to the bulbs Nothing's touching no metal touching metal. Okay, good ready Let's see what did I do wrong something is wrong Maybe it just wasn't making good electrical contact. I hate this part This word always gets a little dicey Hmm Oh Would be helpful if I actually plugged it into the current measuring part of the device Yay Okay, there we go The current measuring part has to offer as little resistance as possible I had it in a mode where it was offering infinite resistance So no current was allowed to flow if you want to go into the details of am meters, you know And current and volt meters you can we can do that some other time But the bottom line is to measure a potential difference that thing needs infinite resistance and to measure a current It needs zero resistance so that it doesn't become a big part of the circuit All right, so what do I notice about the current going into the circuit? What is the the current equal to? About what one point Let's see here i equals 1.2 amps Okay, so now There we go, uh, let's break there and uh, it's apparently the walking dead and uh, we will pick this up on Thursday and we'll keep analyzing this Uh, and we'll see if we can get the right answers out of predictions because what I need you to do next is calculate the current in Each of the resistors. Okay Thank you Yeah