Lec 1 | MIT 6.002 Circuits and Electronics, Spring 2007

January 16, 2008

39 Comments

Watch at: 00:00 / 00:00:20So, one question to ask ourselves is,what is engineering? How do we define,what is engineering? Well, the definition I like touse is one put forth by Steve Senturia, one of our professorsWatch at: 00:20 / 00:40who is now retired. He defined engineering to bethe purposeful use of science. All right, so what is 6.002about? So, 6.002 is a first course inengineering. And I like to view 6.002 as theWatch at: 00:40 / 01:00gainful employment of Maxwell's equations.Many of you have seen Maxwell's equations before.Most of you should have. And they are hard stuff.6.002 is all about teaching you how to simplify our lives,make things simple. So, if you can gainfully employWatch at: 01:00 / 01:20Maxwell's equations, gainfully employ the facts ofnature to build very interesting systems.So let me show you how the transition is made.So, there's a world around us, nature, so we made someWatch at: 01:20 / 01:40observations in nature. We make measurements,and we can write down large tables of measurements.So, for example, we can take objects and measurethe voltage across them, and look at the resultingcurrent through the elements. So, we may end up getting aWatch at: 01:40 / 02:00bunch of values such as [CHALKBOARD].So, we start out life with making measurements on whatexists. And we build a bunch of tables.Now, we could directly take these tables,and based on observations of these tables,we could go ahead and build very interesting engineeringWatch at: 02:00 / 02:20systems that help us out in day-to-day lives.But that's incredibly hard. Imagine having to resort to aset of tables to do any kind of useful work.So what we do as engineers, we first layer a level ofabstraction. We look at all the data,Watch at: 02:20 / 02:40and somehow layer abstraction such that we can simplify ormuch more succinctly put in a simple equation or a simplestatement what these numbers are telling us.OK, so for example, our physics laws,so laws of physics for example are simply abstractions,Watch at: 02:40 / 03:00the laws of abstractions. So, these sets of numbers canbe codified by Ohm's law, for example,V is equal to RI, the voltage current,relates to the resistance of the object.So, V is equal to RI is a law that succinctly describes a setof experiments, and replaces a large number ofWatch at: 03:00 / 03:20tables with a very simple statement.You could call this the law, or you could call it anabstraction. OK so you see laws of physics,call them abstractions of physics if you like.Similarly, there are Maxwell's equations and so on and soWatch at: 03:20 / 03:40forth. So, this is what is.This is what's out there. OK, and a law as an abstractiondescribe the properties of nature, as we see it,in some succinct form. Now, if you want to go andbuild useful things, we could take theseabstractions, take Maxwell's equations,Watch at: 03:40 / 04:00and go and build things. But it's hard.It's really, really hard.And what you learn in, at MIT is this place is allabout simplifying things. Take complicated things,build layers of abstraction, and simplify things so that wecan build useful systems. Even in 6.002 we start life byWatch at: 04:00 / 04:20making a huge leap from Maxwell's equations to a coupleof very, very simple laws. OK, I'm going to show you thatleap that we will make today. So, the first abstraction thatwe layer is called the lump circuit abstraction.OK, in the lump circuit abstraction, what we do is weWatch at: 04:20 / 04:40make a set of simplifications that allows us to view a set ofobjects as discrete or lumped elements.So, we may, I will define voltage sources.We'll define resistors. We'll define capacitors,and so on. OK, and I'm going to make theWatch at: 04:40 / 05:00jump, and show you how we make the jump in a few minutes.So, on that sort of abstraction, we then layer yetanother abstract layer. And let me call that theamplifier abstraction. OK, remember,here we are absolutely down and dirty.Watch at: 05:00 / 05:20We are setting the probes, measuring objects,and building huge tables. We abstracted things intosimple laws, and life got a little better.OK, I'm going to show you can abstract things further out andbuild discrete objects, and, you could build even moreinteresting components called amplifiers and begin playingaround with amplifiers. OK, so when you are usingWatch at: 05:20 / 05:40amplifiers, you don't really have to worry about the detailsof Maxwell's equations. OK, I'll give you some verysimple abstract rules of behavior for an amplifier,and you can go build very interesting systems withoutreally, really knowing how Maxwell's equations applies tothat because you will be working at this abstract layer.Watch at: 05:40 / 06:00However, since you're engineers, and you are good atbuilding such systems, it's very important for you tounderstand how we make this leap from the laws of physics intosome of our very primitive engineering abstractions.So, once we make the amplified abstraction in 6.002,by the way, 6.002 starts here. We start from the laws ofWatch at: 06:00 / 06:20physics and then proceed all the way out.So, once we talk about amplifiers we will take twopads. On the amplifier,you will build the next abstraction called the digitalabstraction. OK, and with the digitalWatch at: 06:20 / 06:40abstraction, we will build new elements such as inverters andcombinational gates, OK?So, notice we are building bigger, and bigger things,which have more and more complicated behavior insidethem, but which are very simple to describe, right?Watch at: 06:40 / 07:00So, following the digital abstraction, we will superimposethe combinational logic abstraction on top of that,and define functional blocks that look like this:some inputs, some function,some outputs. The next abstraction on top ofWatch at: 07:00 / 07:20that will be the clock digital abstraction, where we will havesome notion of time introduced into the system.There will be a clock, and this will be some function.And there will be a clock that introduces time into the sort oflogic values that functions operate upon.Watch at: 07:20 / 07:40Following that, the next level of abstractionthat we build is called instruction set abstraction.OK, now you begin to see things that consumers get to look at.Can someone give me an example of, or name an instruction set,Watch at: 07:40 / 08:00or instruction set abstraction? Bingo.So, x86 is one set of abstractions.And in fact, in many universities,education could well start just by saying, OK,here's an abstraction. These are the x86 instructions,OK? Some MIT gurus have designedWatch at: 08:00 / 08:20this awesome little microprocessor,OK? So you just worry about,you take this abstraction layer here, the assembly instructions,and you go and build systems on top of that.OK, so this is an abstraction layer called the x86 layer.There are other abstraction layers.Watch at: 08:20 / 08:40In 6.004, you will learn about, I believe, the alpha or thebeta, OK, and various other abstractions at this point.So, 6.002 kind of goes until here.6.002 takes me from the world of physics all the way to theworld of interesting analog and digital systems.Watch at: 08:40 / 09:00OK, 004, the course on computation structures,will show you how to build computers all the way fromsimple digital objects all the way to big systems.Following that, you learn about languageabstractions, Java, C, and other languages,and that's in 6.002. And there are several otherWatch at: 09:00 / 09:20courses that will cover that. Following this,you learn about software system abstractions,and software systems, you will learn about operatingsystems. Any example of an operatingsystem abstraction that people know out there?Watch at: 09:20 / 09:40What's that? Linux.What else? I'm just wondering how longI'll have to go before I hear what I want to hear.[LAUGHTER] OK, so we have a bunch of softwaresystems. So, if we have a bunch ofsoftware systems, these are nothing butabstractions. Linux simply implies a set ofWatch at: 09:40 / 10:00system calls that the programs must adhere to.Windows is another set of system calls.That's it. And see how much money theymade out of it? OK, it's all about abstractionlayers, that all start from nature.All right? Build abstraction uponabstraction upon abstraction upon abstraction,Watch at: 10:00 / 10:20and someone out here are lots of dollars.OK, so based on these abstractions,we can then build useful things for human beings.We can build very useful things, video games,so we can send space shuttles up, and a whole bunch of otherWatch at: 10:20 / 10:40systems. But it's based on theseabstraction layers. What's unique about educationat MIT? What's unique about 6.002 andEECS? Is to my knowledge,there are not many other places in the world where you will getWatch at: 10:40 / 11:00an education in everything going all the way from nature to howto build very complicated analog and digital systems.OK, we will show you layer upon layer upon layer upon layer,peel away the onion until you are down to raw nature,OK, through Maxwell's equations.Watch at: 11:00 / 11:20So, 6.002, 004, this is 033,OK, 6.170, and so on. OK, the whole EECS is aboutbuilding abstraction layers, one on top of the other.So that's one path. There's the analog path.The analog path would take an amplifier, and build anabstraction layer called the op-amp.Watch at: 11:20 / 11:40See how similar they all look? You know the amplifier,the inverter of the digital world, and the operationalamplifier in the analog world, just different ways of lookingat the same devices. So, to build an analog system,to build an operational amplifier, and then,Watch at: 11:40 / 12:00here we go end up building a whole bunch of differentinteresting analog system components.OK, and these components might look like oscillators.They might look like filters. OK, they look like powerWatch at: 12:00 / 12:20supplies, a whole bunch of very interesting abstract components,which pulled together can then give you the next set ofsystems. And these systems might betoasters, or say for example other analog systems like theWatch at: 12:20 / 12:40various control systems for various power plants and so onand so forth, and ultimately,fun and dollars. OK, so 6.002 is about goingfrom physics all the way to this point.We will build interesting analog systems,Watch at: 12:40 / 13:00and take you up to interesting digital system components,from which 004 will take you all the way to building computerarchitectures. So that, in a nutshell,kind of gives you a feel for the space of EECS.Watch at: 13:00 / 13:20OK, this chart here is almost a vignette of what EECS at MIT isall about. And this is the world accordingto Agarwal, because he's teaching 002.OK, so this is 6.002, and the rest of EECS issomewhere out there. OK, so I'm going to do now isWatch at: 13:20 / 13:40throughout this course; I want you to think about whichpart in this vignette we are in. So, right now,I'm going to start here and take you here.OK, and as you get closer and closer, things get simpler,and simpler, and simpler.Still, the final abstractions are pedal, brake,Watch at: 13:40 / 14:00steering wheel. I mean, that's the abstractionto play a game, right, four or five very simpleinterfaces, and that's all you need to know.And everybody in the world can play stuff.So remember, this stuff is complicated.This stuff is very, very simple.Watch at: 14:00 / 14:20OK, and the more we build abstractions and come to thisside, things get simpler and simpler.So, a large part of what I'll cover today is make the biggestsimplification. The biggest simplification wewill make his go from Maxwell's equation to some very,very simple algebraic rules. OK, I did Maxwell's equationsmyself. And I tell you,they were very interesting stuff but complicated.Watch at: 14:20 / 14:40I can't imagine building efficient systems usingMaxwell's equations. So, let's take an example,OK? So, let's say I have a battery.Just switch to page three of your course notes.And let's say I connect that to a bulb.Watch at: 14:40 / 15:00OK, and this is a wire. And, the battery supplies somevoltage, V, and I ask you a simple question.What is the current through the bulb?OK, so here is something that I can build using objects.Watch at: 15:00 / 15:20I can pick a round from stores and so on.And I can collect them up in this way, and ask the question,what is the current, I?Now, if all you've done is learn about Maxwell's equations,you can roll up your sleeves and say, ah-ha!The first step is to write down all of Maxwell's equations,Watch at: 15:20 / 15:40and you can say, del cross E is minus del and goon, and on, and on, OK, and write out all ofMaxwell's equations and say, now how do I get from there tohere? OK, it's very good.You can do it. OK, you can do it,but it's very complicated. OK, so instead,what you're going to do is take the easy way.Watch at: 15:40 / 16:00So, what I want to remind you is that this course is actuallyvery easy. OK remember,we're going to be building abstraction upon abstraction tomake your lives easier. If you think your lives aregetting more complicated, then you are not usingintuition enough. OK, just remember the big IWatch at: 16:00 / 16:19word. It's all about making thingssimple. OK, so let me give you ananalogy. So, suppose you have an object.OK, and I apply a force to the object.It's an analogy, OK to get some insight into howto do this. So, I say here's an object.I apply a force, and I ask you the question.Watch at: 16:19 / 16:40What is the acceleration of the object when I apply a force,F? So, how would you do it?OK, and eighth, or ninth, or tenth grader cando this. OK, they would ask me,what's the mass of the object? OK, I ask you what is theacceleration? You would turn around and askWatch at: 16:40 / 17:00me, what is the mass of the object?I tell you, the mass of the object is M.And then you say, oh sure, A is F divided by M,done. It's as simple as that.OK, I could have gone into all kinds of differential equationsand so on to figure that out, but you asked me for the mass.Watch at: 17:00 / 17:20And you gave me the answer, A is F divided by M.So, you ignored a bunch of things.You ignored the shape of the object.You ignored its color. You ignored its temperature.OK, and you ignored the soft or hard or whatever.OK, you ignored a whole bunch of things.Watch at: 17:20 / 17:40You were focused on one thing. OK, you're focused on its mass.And, it turns out that the process really was developedfrom a set of simplifications. That is called,does anybody remember this? Point mass simplification.Watch at: 17:40 / 18:00OK, so, in physics, you've done this before.OK, you've simplified your lives by viewing objects ashaving a mass at a point, and force is acting at thatpoint. OK, M is that property of theobject that is of interest to you.Watch at: 18:00 / 18:20This process is called, in physics, point massdiscretization. OK, now using an analogy,and I'm going to show you a similar simple process to do theWatch at: 18:20 / 18:40problem with the light bulb. OK, so take my light bulbagain,Watch at: 18:40 / 19:00And I focus on the filament of the light bulb.OK, all I care about is the current flowing through thelight bulb. OK, I don't care about whetherthe filament is twisted, whether it's hot.I don't care about its shape. I don't care about its color.All I care about is the current.Watch at: 19:00 / 19:20OK, so to do that, what we can do here at a veryhigh level is since we just need the current and don't care abouta bunch of other properties, we will simply replace the bulbwith a discrete object called a resistor.So the discrete object is a resistor, much like the pointmass simplification that we did earlier that replaced the bulbWatch at: 19:20 / 19:40filament with a object called a resistor, a discrete objectcalled a resistor. Or a lump object calledresister, and put a value next to it just like the mass for theobject, a resistance value, R.OK, now what I can do is in the same manner, replace the batteryWatch at: 19:40 / 20:00with an object called a battery object, and connect that here,the voltage, V, applied to it.V falls across the resistor, and I get my I simply fromOhm's law as we divide by R. So, notice here,Watch at: 20:00 / 20:20to replace this complicated bulb, this really twisty,weird old thing with this discreet thing called aresistor, and its only property of interest was its resistancevalue, R, direct analogy to what we did there.So, since R represents the only property of interest,we can simply ignore all the other things.Watch at: 20:20 / 20:40So, notice here, we've done things the simpleway. And remember,in EE, in the electrical engineering, we do things thesimple way. OK, we could go the hard routeand do Maxwell's equations, and get PhD's in physics,and so on. But out here,we are looking to do useful, interesting systems in theWatch at: 20:40 / 21:00simplest way that we can. OK, we do things a simple way.All right, so we just did this, and boom, I found out what thecurrent was. Now, I cheated a little bit.I've cheated a little bit. R is a lumped abstraction forthe bulb. So, you look at this resistorWatch at: 21:00 / 21:20here. That is simply a placeholder.It's a stand-in for this complicated thing called a bulb.It's a discreet object. It's a lumped object,and represents the bulb. Now, so most of 6.002 will takeoff from here, OK, and that's it.To very simple stuff, like V is equal to IR,Watch at: 21:20 / 21:40it's a simple high school algebra to take off in thatdirection. But before we go there,it's important to understand, why was it that we were able tomake the simplification? OK, we did something else.Something's going on under the covers here.On the one hand, I say let's use Maxwell's,and then I jump out and say, hey, we can just use thisWatch at: 21:40 / 22:00simple thing. I did something that allowed meto go from here to here. And you need to understand whyI did that and how I did that. Understand it once,and then you won't have to need that information again.You just need to understand it. So, let's take a closer look atthe bulb filament, and look at what we really did.Watch at: 22:00 / 22:20So, here's my filament, A, and let's say that thesurface area here, I label that SA,and the one down here SB, my voltage, V,applied there, and this is what I call myWatch at: 22:20 / 22:40black box that I've replaced with a resistor.Notice that, in order for this to work,V and I need to be defined. So I needs to be defined,Watch at: 22:40 / 23:00and V needs to be defined. OK, if I give you a randomobject, and I don't tell you anything else about the object,it's not clear I can do that. OK, if it's a much more generalsituation, I have to write down Maxwell's equations,and this is what I would write down.Watch at: 23:00 / 23:20Write down J dot dS as a function of the coordinate hereintegrated over the area minus, OK, I would have to start fromthere from one of Maxwell's equations.All right, notice that this becomes IA, and this becomes IBin our simplification. But, if I don't tell youWatch at: 23:20 / 23:40anything else, you have to start from here.You will have some varying current here by point.You might have some other current coming out here becauseI may have some charge buildup happening inside.If charge is building up inside the filament;Watch at: 23:40 / 24:00then I would have to put del q by del t out here,right, the current in minus the current out must equal chargebuildup. Whoa, where is this and whereis that? So this is reality.This is really, really what I have to do.But how did I get there? How did I get there?Watch at: 24:00 / 24:20The key answer is, as engineers,when in doubt we simplify. Remember, we are engineers.Our goal in life is to build interesting systems.OK and some are motivated by money.OK, so our goal is to build interesting systems and do goodto humanity. So, as long as we can build agood light bulb, we are happy.Watch at: 24:20 / 24:40So what we can do is we can say, look, all I care about isbuilding interesting systems. So I can say,hey, this stuff is too hard. Let's make the assumption thatall the systems that we will consider will have this thing bezero. OK, in other words,if I take a complete object, if I take an element like aWatch at: 24:40 / 25:00resistor or a capacitor, the box around the entireelement, OK, and I want to just deal with those systems in whichthis thing is zero. You can come and beat me up andsay, but why? Why not?Why am I doing this? And I am saying the world isarbitrary. I'm an engineer;I want to build good systems. By making this simplification,Watch at: 25:00 / 25:20I eliminate this squiggle thing, and so on.I don't want to deal with it. I want to make my life simple.So this is gone to zero because, why?Because I have said that in the future I will only deal withthose elements for which this is true.Watch at: 25:20 / 25:40I'm going to discipline myself. I'm going to discipline myselfto only deal with those systems. OK, Maxwell is turning aroundand, you know, mad at me and all that stuff,but tough. So this, what I've said aboutmaking a simplification here, and this is one of theWatch at: 25:40 / 26:00simplifications I'm making. And I give a name to thesimplification. And that's called the lumpedmatter discipline. OK, so I'm saying I will onlydeal with elements for which if I put a black box around it,Watch at: 26:00 / 26:20this is going to be true. And if this is going to betrue, then notice, there is no charge buildup.Current in must equal current out.Ah-ha! So this becomes IA.This becomes IB. Yes.OK, I can now deal with IA's and IB's.Watch at: 26:20 / 26:40And IB and IA are equal because this is zero.Notice that there is a whole bunch of depth here in the jumpfrom here to here. As MIT graduates,you really, really need to understand why it is that wemade that jump, and then go and use that,Watch at: 26:40 / 27:00and do cool things. All right, this allows us todefine I. We have a unique I associatedwith an element for the current through the element.We still have to worry about B, and I won't go through that indetail. The course notes have somediscussion of that and so does the textbook.Watch at: 27:00 / 27:20So V, AB is defined when del phi B, the rate of change ofmagnetic flux is zero. So, if I take the element and Itake any region outside the element, this must be true.And you say, why should that be true?Watch at: 27:20 / 27:40That's not true in general. Absolutely.It's not true in general. But I, because I choose to,I going to deal with only those elements.I will discipline myself. But these are only thoseelements for which this is true, and this is true.I'm going to limit my world. I'm going to create a playWatch at: 27:40 / 28:00field for myself. You want to play;follow my rules. OK, and that's called thelumped matter discipline. So once you say that I'm goingto adhere to the lump matter discipline, and this is trueinside your elements. This is true outside theelements. You can define VA and VB,and good things happen to you. OK, let me show you a fewWatch at: 28:00 / 28:20examples of lumped elements. But remember,a large part of what we're doing is based on these twoassumptions. And to just go through thebackground on that, I would encourage you to go tochapter 1 of your course notes and read through just as howWatch at: 28:20 / 28:40this came about, that comes about.So, by doing that by adhering to a lumped matter discipline,we can now lump objects. We could lump a bulb into aresistor. OK, so to be clear,a certain number of lumped objects, and now,the universe is going to be comprised into lumped objects.Watch at: 28:40 / 29:00OK, so before this, when he went home,we talked about eggs, and omelets,and light bulbs, and switches,but once you come to MIT, and after you've taken 6.002,you begin talking about lumped elements, you know,resistors, voltage sources, capacitors, little inky-dinkyobjects that follow the lumped matter discipline.Watch at: 29:00 / 29:20OK, they stick to very simple rules, and the math that youhave to do to analyze them is incredibly simple.What could be simpler than V is equal to IR?So, let me give you an example of interesting lumped elements,and then show you a couple of really nasty lumped elements.Watch at: 29:20 / 29:40OK.OK, so what you see out here, so we characterize lumpedelements by the VI characteristics.OK, you apply voltage, measure the current.OK, so what I can do is I can plot I here, and V here,Watch at: 29:40 / 30:00and see what it looks like. OK, I can characterize elementsby their VI relationship. And there are a bunch ofelements that I can create based on the VI relationship.So let me show you a few examples.Watch at: 30:00 / 30:20So for the resistor, since V is directlyproportional to I, and R is a constant,I get a straight line. That's the I axis,the V axis, and this is the resistor.What I actually have is a variable resistor,so I'm going to change the resistance value,R, and the curve will also change slope.Watch at: 30:20 / 30:40OK, I changed the value of R because it's a variableresistor, and the changes slope because my R is different.OK, next, let me go to a fixed resistor, and this guy here onthe screen to your left is a fixed resistor.And you see that its IV characteristic is a line of aWatch at: 30:40 / 31:00given slope, 1 by R, and that's it.I can't change it. Number three,I have another lumped element called a Zener diode that youwill see in the fourth week of this class, and thecharacteristics for the Zener diode look like this:IV. If my voltage goes across theWatch at: 31:00 / 31:20Zener diode goes up slightly, the current shoots up.But if the voltage becomes negative I don't have anycurrent flowing into it until the voltage passes on thethreshold, at which point my current begins to build up.OK, so I can increase the voltage a little bit,and it can show that the current starts building upWatch at: 31:20 / 31:40again. So that's another interestinglumped element called a Zener diode.Let's switch to the next one called a diode.So a diode looks like this: IV.As the voltage across the diode becomes positive,around .6 volts, or thereabout,the current begins to shoot up. But when the voltage is belowWatch at: 31:40 / 32:00that threshold of .6, then my current is almost zero.It's another lumped element called a diode.And you will begin using these elements in your 002 lives tobuild interesting systems. The next example is athermistor. A thermistor is a resistorwhose resistance varies with temperature.Watch at: 32:00 / 32:20OK, so this is a very expensive little hairdryer,and what I'm going to do is blow some hot air at myresistor, and you're going to see that its value is going toWatch at: 32:20 / 32:39change depending on how much I heat it.So as it cools down, let me cool it down,so you can see it's coming down.I can zap it again. I could do this all day.Watch at: 32:39 / 33:00This is so much fun. OK, so that's anotherinteresting lumped element. As the temperature rises,its resistance changes. The next thing is called aphoto resistor. It's a resistor.It used to be a resistor; Lorenzo?Watch at: 33:00 / 33:20Oh OK, that's fine. So this is a photo resistor.And notice that it almost behaves like an open circuit.But what I'm going to do is shine some light on it.When I shine light on it, it begins to conduct andbecomes a resistor of some value.There you go. OK, so that's a photo resistor.Watch at: 33:20 / 33:39So now I'm going to show you a battery.Notice we did talk about batteries before.I'll show you a battery. So before you show a battery,just thinking your own minds, what should the IVcharacteristic of a battery look like?IV. A battery supplies a constantWatch at: 33:39 / 34:00voltage. You know your little cell,the AA battery, 1.5 volts?So, think of what the IV characteristic of a batteryshould look like for three seconds before it shows you.This is the one I showed, Lorenzo?.It's a straight line. This is a good battery.Watch at: 34:00 / 34:20It's a straight, vertical line,but says that the voltage is 1.5 volts, or thereabouts.No matter what current it supplies as an ideal voltagesource, it has a fixed voltage, V, and no matter what thecurrent going through is. Now, I'll show you a dud,a bad battery, and this is what the badbattery looks like. So, many of you have had yourWatch at: 34:20 / 34:40car batteries die on you. When you go to the store,they check your batteries. They use exactly thisprinciple, that dead batteries have resistance.By the way, you see slopes here.You're thinking of resistance. OK, they can use this propertyto figure out that your battery is dead.Watch at: 34:40 / 35:00So that's a dead battery. And finally,let me show you a bulb. We started with a bulb,and so I need to end, OK, we started with a bulb,so I need to end with a bulb. And what you will see is that abulb simply behaves like a resistor.Its IV curve is going to look like this.Watch at: 35:00 / 35:20OK, notice this is my bulb. And guess what,it behaves like a resistor. It's a very interesting kind ofresistor, so I won't go into details for now.But notice its IV characteristic behaves like aresistor. OK, so those are some prettystandard lumped elements. You deal with a lot more setsWatch at: 35:20 / 35:40of lumped elements, switches, MOSFETs,capacitors, inductors, a bunch of other fun stuff.But before we do that, what I wanted to tell you,don't go berserk on this abstraction binge.Too much of anything is bad for you.So what I'm going to show you is, abstractions or models areonly valid provided you work within a set of constraints.Watch at: 35:40 / 36:00Notice, we have already had this tacit handshake which saidthat we follow the discipline. Even after we follow thediscipline, there are ranges to how well physical elements canbehave like ideal lumped elements.OK, for example, what we will do is show you theresistor. And it's going to look like aWatch at: 36:00 / 36:20resistor. And I'm going to keepincreasing the voltage around it.OK, what's going to happen at some point?I just keep doing that. If it's an ideal element,if you're a theorist, you say, oh yeah,the curve will keep extending until I reach infinity.Watch at: 36:20 / 36:40But this is a practical resistor, so people out here cancover your eyes or something. OK, so you're abstraction can'tpredict that. All it says is the current isan amp. It can't predict the heat,light, or the smell. In the laboratory,Watch at: 36:40 / 37:00even, you get the smell. You know what somebody has justdone. So that's one example of thelumped abstraction breaking down.So, if I really believe that my own BS, anything is a lumpedelement. So here's a pickle.A pickle is a lumped element. I can choose it as a lumpedWatch at: 37:00 / 37:20resistor. But this is a very interestinglumped resistor. Don't try this at home.This is a standard pickle into which you are pumping 110 V AC.I promise you, this is a standard pickle.So, it has a fixed resistance, but your lumped abstractionWatch at: 37:20 / 37:40cannot predict the nice light and sound effect.OK, so the last two or three minutes what I want to do,so remember, don't get carried away byabstractions. There are limits.OK, you can't predict everything.Watch at: 37:40 / 38:00OK, that's the smell of a pickle.OK, so let me give you a preview of some upcomingattractions, and show you one more quick simplification in thelast few minutes. So what we can do,once we build these lumped elements, we can connect them inWatch at: 38:00 / 38:20circuits. OK, so I can build a circuit,of the sort. So here's a voltage source witha bunch of resistors. I can connect them with wiresand build a circuit of the sort. One interesting question we canask ourselves is, under the lumped matterWatch at: 38:20 / 38:40discipline, what can we say about the voltages?OK, if I go around the loop, provided my world adheres tothe lumped matter discipline, what can I say about thevoltages around this loop? Ah-ha, Maxwell again,right? So, I can write Maxwell'sappropriate equation to solve that.Watch at: 38:40 / 39:00OK, voltages have something to do with E and your integral of Edot dl and all of that stuff, right?So this is the appropriate Maxwell's equations to use.And I want to find out what happens here.Now remember, under LMD, I made theWatch at: 39:00 / 39:20assumption. OK, my world,my playground, has del phi B by del t beingzero. The rate of change of flux iszero. So, under these circumstances,I can write this. I can break up this lineWatch at: 39:20 / 39:40integral into three parts across the voltage source and acrossthe two resistors and write that down.OK, and then when I can do, is now that the right-hand sideis zero, I can simply take this. And I know that E dot dl acrossWatch at: 39:40 / 40:00this element is simply VCA. This is VAB,and this is VBC equals zero. OK, so when I make theassumption that del phi B by del t is zero, and I go around thisloop, apply Maxwell's equations, what do I find?I find that the sum of the voltages, VCA plus VAB plus VBC,Watch at: 40:00 / 40:20is zero. That's fantastic.So now, I could say hasta la vista to this baby here.And I can focus on this guy and say, Maxwell's equations,this thing with squiggles and dels and all that stuff,Watch at: 40:20 / 40:40can be simplified to the sum of the voltages across a set ofelements in a loop in a circuit is zero.OK, and this is called Kirchhoff's first first law,KVL. OK, similarly,Watch at: 40:40 / 41:00in recitation section, you'll see the application ofKirchhoff's current law, which comes from this be equalto zero, and all the currents coming into a node being zero.So, KVL and KCl directly come out of the lumped matterWatch at: 41:00 / 41:20discipline. And you can use those to solvecircuits like this.