1 00:00:00 --> 00:00:04 So, one question to ask ourselves is, 2 00:00:04 --> 00:00:08 what is engineering? How do we define, 3 00:00:08 --> 00:00:15 what is engineering? Well, the definition I like to 4 00:00:15 --> 00:00:22 use is one put forth by Steve Senturia, one of our professors 5 00:00:22 --> 00:00:28 who is now retired. He defined engineering to be 6 00:00:28 --> 00:00:35 the purposeful use of science. All right, so what is 6.002 7 00:00:35 --> 00:00:38 about? So, 6.002 is a first course in 8 00:00:38 --> 00:00:41 engineering. And I like to view 6.002 as the 9 00:00:41 --> 00:00:44 gainful employment of Maxwell's equations. 10 00:00:44 --> 00:00:48 Many of you have seen Maxwell's equations before. 11 00:00:48 --> 00:00:52 Most of you should have. And they are hard stuff. 12 00:00:52 --> 00:00:57 6.002 is all about teaching you how to simplify our lives, 13 00:00:57 --> 00:01:02 make things simple. So, if you can gainfully employ 14 00:01:02 --> 00:01:07 Maxwell's equations, gainfully employ the facts of 15 00:01:07 --> 00:01:11 nature to build very interesting systems. 16 00:01:11 --> 00:01:15 So let me show you how the transition is made. 17 00:01:15 --> 00:01:20 So, there's a world around us, nature, so we made some 18 00:01:20 --> 00:01:24 observations in nature. We make measurements, 19 00:01:24 --> 00:01:30 and we can write down large tables of measurements. 20 00:01:30 --> 00:01:33 So, for example, we can take objects and measure 21 00:01:33 --> 00:01:37 the voltage across them, and look at the resulting 22 00:01:37 --> 00:01:41 current through the elements. So, we may end up getting a 23 00:01:41 --> 00:01:44 bunch of values such as [CHALKBOARD]. 24 00:01:44 --> 00:01:48 So, we start out life with making measurements on what 25 00:01:48 --> 00:01:51 exists. And we build a bunch of tables. 26 00:01:51 --> 00:01:54 Now, we could directly take these tables, 27 00:01:54 --> 00:01:57 and based on observations of these tables, 28 00:01:57 --> 00:02:01 we could go ahead and build very interesting engineering 29 00:02:01 --> 00:02:06 systems that help us out in day-to-day lives. 30 00:02:06 --> 00:02:10 But that's incredibly hard. Imagine having to resort to a 31 00:02:10 --> 00:02:14 set of tables to do any kind of useful work. 32 00:02:14 --> 00:02:18 So what we do as engineers, we first layer a level of 33 00:02:18 --> 00:02:21 abstraction. We look at all the data, 34 00:02:21 --> 00:02:25 and somehow layer abstraction such that we can simplify or 35 00:02:25 --> 00:02:30 much more succinctly put in a simple equation or a simple 36 00:02:30 --> 00:02:35 statement what these numbers are telling us. 37 00:02:35 --> 00:02:37 OK, so for example, our physics laws, 38 00:02:37 --> 00:02:41 so laws of physics for example are simply abstractions, 39 00:02:41 --> 00:02:45 the laws of abstractions. So, these sets of numbers can 40 00:02:45 --> 00:02:48 be codified by Ohm's law, for example, 41 00:02:48 --> 00:02:51 V is equal to RI, the voltage current, 42 00:02:51 --> 00:02:54 relates to the resistance of the object. 43 00:02:54 --> 00:02:58 So, V is equal to RI is a law that succinctly describes a set 44 00:02:58 --> 00:03:02 of experiments, and replaces a large number of 45 00:03:02 --> 00:03:06 tables with a very simple statement. 46 00:03:06 --> 00:03:09 You could call this the law, or you could call it an 47 00:03:09 --> 00:03:13 abstraction. OK so you see laws of physics, 48 00:03:13 --> 00:03:16 call them abstractions of physics if you like. 49 00:03:16 --> 00:03:21 Similarly, there are Maxwell's equations and so on and so 50 00:03:21 --> 00:03:23 forth. So, this is what is. 51 00:03:23 --> 00:03:27 This is what's out there. OK, and a law as an abstraction 52 00:03:27 --> 00:03:31 describe the properties of nature, as we see it, 53 00:03:31 --> 00:03:35 in some succinct form. Now, if you want to go and 54 00:03:35 --> 00:03:38 build useful things, we could take these 55 00:03:38 --> 00:03:40 abstractions, take Maxwell's equations, 56 00:03:40 --> 00:03:43 and go and build things. But it's hard. 57 00:03:43 --> 00:03:44 It's really, really hard. 58 00:03:44 --> 00:03:48 And what you learn in, at MIT is this place is all 59 00:03:48 --> 00:03:51 about simplifying things. Take complicated things, 60 00:03:51 --> 00:03:55 build layers of abstraction, and simplify things so that we 61 00:03:55 --> 00:04:00 can build useful systems. Even in 6.002 we start life by 62 00:04:00 --> 00:04:04 making a huge leap from Maxwell's equations to a couple 63 00:04:04 --> 00:04:09 of very, very simple laws. OK, I'm going to show you that 64 00:04:09 --> 00:04:14 leap that we will make today. So, the first abstraction that 65 00:04:14 --> 00:04:18 we layer is called the lump circuit abstraction. 66 00:04:18 --> 00:04:22 OK, in the lump circuit abstraction, what we do is we 67 00:04:22 --> 00:04:27 make a set of simplifications that allows us to view a set of 68 00:04:27 --> 00:04:32 objects as discrete or lumped elements. 69 00:04:32 --> 00:04:35 So, we may, I will define voltage sources. 70 00:04:35 --> 00:04:38 We'll define resistors. We'll define capacitors, 71 00:04:38 --> 00:04:41 and so on. OK, and I'm going to make the 72 00:04:41 --> 00:04:46 jump, and show you how we make the jump in a few minutes. 73 00:04:46 --> 00:04:49 So, on that sort of abstraction, we then layer yet 74 00:04:49 --> 00:04:53 another abstract layer. And let me call that the 75 00:04:53 --> 00:04:56 amplifier abstraction. OK, remember, 76 00:04:56 --> 00:05:00 here we are absolutely down and dirty. 77 00:05:00 --> 00:05:02 We are setting the probes, measuring objects, 78 00:05:02 --> 00:05:05 and building huge tables. We abstracted things into 79 00:05:05 --> 00:05:07 simple laws, and life got a little better. 80 00:05:07 --> 00:05:11 OK, I'm going to show you can abstract things further out and 81 00:05:11 --> 00:05:14 build discrete objects, and, you could build even more 82 00:05:14 --> 00:05:17 interesting components called amplifiers and begin playing 83 00:05:17 --> 00:05:20 around with amplifiers. OK, so when you are using 84 00:05:20 --> 00:05:23 amplifiers, you don't really have to worry about the details 85 00:05:23 --> 00:05:26 of Maxwell's equations. OK, I'll give you some very 86 00:05:26 --> 00:05:29 simple abstract rules of behavior for an amplifier, 87 00:05:29 --> 00:05:32 and you can go build very interesting systems without 88 00:05:32 --> 00:05:35 really, really knowing how Maxwell's equations applies to 89 00:05:35 --> 00:05:40 that because you will be working at this abstract layer. 90 00:05:40 --> 00:05:43 However, since you're engineers, and you are good at 91 00:05:43 --> 00:05:47 building such systems, it's very important for you to 92 00:05:47 --> 00:05:51 understand how we make this leap from the laws of physics into 93 00:05:51 --> 00:05:54 some of our very primitive engineering abstractions. 94 00:05:54 --> 00:05:58 So, once we make the amplified abstraction in 6.002, 95 00:05:58 --> 00:06:02 by the way, 6.002 starts here. We start from the laws of 96 00:06:02 --> 00:06:06 physics and then proceed all the way out. 97 00:06:06 --> 00:06:10 So, once we talk about amplifiers we will take two 98 00:06:10 --> 00:06:12 pads. On the amplifier, 99 00:06:12 --> 00:06:18 you will build the next abstraction called the digital 100 00:06:18 --> 00:06:21 abstraction. OK, and with the digital 101 00:06:21 --> 00:06:27 abstraction, we will build new elements such as inverters and 102 00:06:27 --> 00:06:31 combinational gates, OK? 103 00:06:31 --> 00:06:35 So, notice we are building bigger, and bigger things, 104 00:06:35 --> 00:06:38 which have more and more complicated behavior inside 105 00:06:38 --> 00:06:42 them, but which are very simple to describe, right? 106 00:06:42 --> 00:06:47 So, following the digital abstraction, we will superimpose 107 00:06:47 --> 00:06:51 the combinational logic abstraction on top of that, 108 00:06:51 --> 00:06:54 and define functional blocks that look like this: 109 00:06:54 --> 00:06:56 some inputs, some function, 110 00:06:56 --> 00:07:01 some outputs. The next abstraction on top of 111 00:07:01 --> 00:07:06 that will be the clock digital abstraction, where we will have 112 00:07:06 --> 00:07:10 some notion of time introduced into the system. 113 00:07:10 --> 00:07:14 There will be a clock, and this will be some function. 114 00:07:14 --> 00:07:19 And there will be a clock that introduces time into the sort of 115 00:07:19 --> 00:07:23 logic values that functions operate upon. 116 00:07:23 --> 00:07:26 Following that, the next level of abstraction 117 00:07:26 --> 00:07:32 that we build is called instruction set abstraction. 118 00:07:32 --> 00:07:37 OK, now you begin to see things that consumers get to look at. 119 00:07:37 --> 00:07:42 Can someone give me an example of, or name an instruction set, 120 00:07:42 --> 00:07:45 or instruction set abstraction? Bingo. 121 00:07:45 --> 00:07:48 So, x86 is one set of abstractions. 122 00:07:48 --> 00:07:51 And in fact, in many universities, 123 00:07:51 --> 00:07:55 education could well start just by saying, OK, 124 00:07:55 --> 00:07:59 here's an abstraction. These are the x86 instructions, 125 00:07:59 --> 00:08:02 OK? Some MIT gurus have designed 126 00:08:02 --> 00:08:05 this awesome little microprocessor, 127 00:08:05 --> 00:08:07 OK? So you just worry about, 128 00:08:07 --> 00:08:11 you take this abstraction layer here, the assembly instructions, 129 00:08:11 --> 00:08:14 and you go and build systems on top of that. 130 00:08:14 --> 00:08:18 OK, so this is an abstraction layer called the x86 layer. 131 00:08:18 --> 00:08:20 There are other abstraction layers. 132 00:08:20 --> 00:08:24 In 6.004, you will learn about, I believe, the alpha or the 133 00:08:24 --> 00:08:29 beta, OK, and various other abstractions at this point. 134 00:08:29 --> 00:08:31 So, 6.002 kind of goes until here. 135 00:08:31 --> 00:08:36 6.002 takes me from the world of physics all the way to the 136 00:08:36 --> 00:08:40 world of interesting analog and digital systems. 137 00:08:40 --> 00:08:44 OK, 004, the course on computation structures, 138 00:08:44 --> 00:08:48 will show you how to build computers all the way from 139 00:08:48 --> 00:08:53 simple digital objects all the way to big systems. 140 00:08:53 --> 00:08:56 Following that, you learn about language 141 00:08:56 --> 00:08:59 abstractions, Java, C, and other languages, 142 00:08:59 --> 00:09:05 and that's in 6.002. And there are several other 143 00:09:05 --> 00:09:08 courses that will cover that. Following this, 144 00:09:08 --> 00:09:12 you learn about software system abstractions, 145 00:09:12 --> 00:09:16 and software systems, you will learn about operating 146 00:09:16 --> 00:09:18 systems. Any example of an operating 147 00:09:18 --> 00:09:22 system abstraction that people know out there? 148 00:09:22 --> 00:09:23 What's that? Linux. 149 00:09:23 --> 00:09:26 What else? I'm just wondering how long 150 00:09:26 --> 00:09:32 I'll have to go before I hear what I want to hear. 151 00:09:32 --> 00:09:35 [LAUGHTER] OK, so we have a bunch of software 152 00:09:35 --> 00:09:37 systems. So, if we have a bunch of 153 00:09:37 --> 00:09:39 software systems, these are nothing but 154 00:09:39 --> 00:09:42 abstractions. Linux simply implies a set of 155 00:09:42 --> 00:09:45 system calls that the programs must adhere to. 156 00:09:45 --> 00:09:48 Windows is another set of system calls. 157 00:09:48 --> 00:09:50 That's it. And see how much money they 158 00:09:50 --> 00:09:54 made out of it? OK, it's all about abstraction 159 00:09:54 --> 00:09:56 layers, that all start from nature. 160 00:09:56 --> 00:09:58 All right? Build abstraction upon 161 00:09:58 --> 00:10:01 abstraction upon abstraction upon abstraction, 162 00:10:01 --> 00:10:06 and someone out here are lots of dollars. 163 00:10:06 --> 00:10:09 OK, so based on these abstractions, 164 00:10:09 --> 00:10:14 we can then build useful things for human beings. 165 00:10:14 --> 00:10:18 We can build very useful things, video games, 166 00:10:18 --> 00:10:24 so we can send space shuttles up, and a whole bunch of other 167 00:10:24 --> 00:10:27 systems. But it's based on these 168 00:10:27 --> 00:10:32 abstraction layers. What's unique about education 169 00:10:32 --> 00:10:34 at MIT? What's unique about 6.002 and 170 00:10:34 --> 00:10:36 EECS? Is to my knowledge, 171 00:10:36 --> 00:10:41 there are not many other places in the world where you will get 172 00:10:41 --> 00:10:45 an education in everything going all the way from nature to how 173 00:10:45 --> 00:10:49 to build very complicated analog and digital systems. 174 00:10:49 --> 00:10:53 OK, we will show you layer upon layer upon layer upon layer, 175 00:10:53 --> 00:10:57 peel away the onion until you are down to raw nature, 176 00:10:57 --> 00:11:00 OK, through Maxwell's equations. 177 00:11:00 --> 00:11:02 So, 6.002, 004, this is 033, 178 00:11:02 --> 00:11:07 OK, 6.170, and so on. OK, the whole EECS is about 179 00:11:07 --> 00:11:11 building abstraction layers, one on top of the other. 180 00:11:11 --> 00:11:14 So that's one path. There's the analog path. 181 00:11:14 --> 00:11:18 The analog path would take an amplifier, and build an 182 00:11:18 --> 00:11:21 abstraction layer called the op-amp. 183 00:11:21 --> 00:11:25 See how similar they all look? You know the amplifier, 184 00:11:25 --> 00:11:29 the inverter of the digital world, and the operational 185 00:11:29 --> 00:11:34 amplifier in the analog world, just different ways of looking 186 00:11:34 --> 00:11:39 at the same devices. So, to build an analog system, 187 00:11:39 --> 00:11:43 to build an operational amplifier, and then, 188 00:11:43 --> 00:11:48 here we go end up building a whole bunch of different 189 00:11:48 --> 00:11:51 interesting analog system components. 190 00:11:51 --> 00:11:56 OK, and these components might look like oscillators. 191 00:11:56 --> 00:12:02 They might look like filters. OK, they look like power 192 00:12:02 --> 00:12:08 supplies, a whole bunch of very interesting abstract components, 193 00:12:08 --> 00:12:13 which pulled together can then give you the next set of 194 00:12:13 --> 00:12:17 systems. And these systems might be 195 00:12:17 --> 00:12:22 toasters, or say for example other analog systems like the 196 00:12:22 --> 00:12:28 various control systems for various power plants and so on 197 00:12:28 --> 00:12:31 and so forth, and ultimately, 198 00:12:31 --> 00:12:36 fun and dollars. OK, so 6.002 is about going 199 00:12:36 --> 00:12:39 from physics all the way to this point. 200 00:12:39 --> 00:12:43 We will build interesting analog systems, 201 00:12:43 --> 00:12:48 and take you up to interesting digital system components, 202 00:12:48 --> 00:12:54 from which 004 will take you all the way to building computer 203 00:12:54 --> 00:12:57 architectures. So that, in a nutshell, 204 00:12:57 --> 00:13:03 kind of gives you a feel for the space of EECS. 205 00:13:03 --> 00:13:08 OK, this chart here is almost a vignette of what EECS at MIT is 206 00:13:08 --> 00:13:11 all about. And this is the world according 207 00:13:11 --> 00:13:14 to Agarwal, because he's teaching 002. 208 00:13:14 --> 00:13:18 OK, so this is 6.002, and the rest of EECS is 209 00:13:18 --> 00:13:22 somewhere out there. OK, so I'm going to do now is 210 00:13:22 --> 00:13:26 throughout this course; I want you to think about which 211 00:13:26 --> 00:13:30 part in this vignette we are in. So, right now, 212 00:13:30 --> 00:13:33 I'm going to start here and take you here. 213 00:13:33 --> 00:13:37 OK, and as you get closer and closer, things get simpler, 214 00:13:37 --> 00:13:39 and simpler, and simpler. 215 00:13:39 --> 00:13:42 Still, the final abstractions are pedal, brake, 216 00:13:42 --> 00:13:45 steering wheel. I mean, that's the abstraction 217 00:13:45 --> 00:13:48 to play a game, right, four or five very simple 218 00:13:48 --> 00:13:51 interfaces, and that's all you need to know. 219 00:13:51 --> 00:13:54 And everybody in the world can play stuff. 220 00:13:54 --> 00:13:56 So remember, this stuff is complicated. 221 00:13:56 --> 00:14:00 This stuff is very, very simple. 222 00:14:00 --> 00:14:03 OK, and the more we build abstractions and come to this 223 00:14:03 --> 00:14:05 side, things get simpler and simpler. 224 00:14:05 --> 00:14:09 So, a large part of what I'll cover today is make the biggest 225 00:14:09 --> 00:14:11 simplification. The biggest simplification we 226 00:14:11 --> 00:14:15 will make his go from Maxwell's equation to some very, 227 00:14:15 --> 00:14:18 very simple algebraic rules. OK, I did Maxwell's equations 228 00:14:18 --> 00:14:19 myself. And I tell you, 229 00:14:19 --> 00:14:22 they were very interesting stuff but complicated. 230 00:14:22 --> 00:14:25 I can't imagine building efficient systems using 231 00:14:25 --> 00:14:30 Maxwell's equations. So, let's take an example, 232 00:14:30 --> 00:14:34 OK? So, let's say I have a battery. 233 00:14:34 --> 00:14:39 Just switch to page three of your course notes. 234 00:14:39 --> 00:14:43 And let's say I connect that to a bulb. 235 00:14:43 --> 00:14:49 OK, and this is a wire. And, the battery supplies some 236 00:14:49 --> 00:14:53 voltage, V, and I ask you a simple question. 237 00:14:53 --> 00:14:57 What is the current through the bulb? 238 00:14:57 --> 00:15:05 OK, so here is something that I can build using objects. 239 00:15:05 --> 00:15:07 I can pick a round from stores and so on. 240 00:15:07 --> 00:15:11 And I can collect them up in this way, and ask the question, 241 00:15:11 --> 00:15:12 what is the current, I? 242 00:15:12 --> 00:15:16 Now, if all you've done is learn about Maxwell's equations, 243 00:15:16 --> 00:15:19 you can roll up your sleeves and say, ah-ha! 244 00:15:19 --> 00:15:23 The first step is to write down all of Maxwell's equations, 245 00:15:23 --> 00:15:26 and you can say, del cross E is minus del and go 246 00:15:26 --> 00:15:28 on, and on, and on, OK, and write out all of 247 00:15:28 --> 00:15:32 Maxwell's equations and say, now how do I get from there to 248 00:15:32 --> 00:15:35 here? OK, it's very good. 249 00:15:35 --> 00:15:37 You can do it. OK, you can do it, 250 00:15:37 --> 00:15:39 but it's very complicated. OK, so instead, 251 00:15:39 --> 00:15:42 what you're going to do is take the easy way. 252 00:15:42 --> 00:15:46 So, what I want to remind you is that this course is actually 253 00:15:46 --> 00:15:47 very easy. OK remember, 254 00:15:47 --> 00:15:51 we're going to be building abstraction upon abstraction to 255 00:15:51 --> 00:15:54 make your lives easier. If you think your lives are 256 00:15:54 --> 00:15:57 getting more complicated, then you are not using 257 00:15:57 --> 00:16:02 intuition enough. OK, just remember the big I 258 00:16:02 --> 00:16:04 word. It's all about making things 259 00:16:04 --> 00:16:07 simple. OK, so let me give you an 260 00:16:07 --> 00:16:10 analogy. So, suppose you have an object. 261 00:16:10 --> 00:16:13 OK, and I apply a force to the object. 262 00:16:13 --> 00:16:16 It's an analogy, OK to get some insight into how 263 00:16:16 --> 00:16:19 to do this. So, I say here's an object. 264 00:16:19 --> 00:16:22 I apply a force, and I ask you the question. 265 00:16:22 --> 00:16:27 What is the acceleration of the object when I apply a force, 266 00:16:27 --> 00:16:31 F? So, how would you do it? 267 00:16:31 --> 00:16:33 OK, and eighth, or ninth, or tenth grader can 268 00:16:33 --> 00:16:36 do this. OK, they would ask me, 269 00:16:36 --> 00:16:39 what's the mass of the object? OK, I ask you what is the 270 00:16:39 --> 00:16:42 acceleration? You would turn around and ask 271 00:16:42 --> 00:16:44 me, what is the mass of the object? 272 00:16:44 --> 00:16:47 I tell you, the mass of the object is M. 273 00:16:47 --> 00:16:50 And then you say, oh sure, A is F divided by M, 274 00:16:50 --> 00:16:52 done. It's as simple as that. 275 00:16:52 --> 00:16:56 OK, I could have gone into all kinds of differential equations 276 00:16:56 --> 00:17:02 and so on to figure that out, but you asked me for the mass. 277 00:17:02 --> 00:17:05 And you gave me the answer, A is F divided by M. 278 00:17:05 --> 00:17:08 So, you ignored a bunch of things. 279 00:17:08 --> 00:17:10 You ignored the shape of the object. 280 00:17:10 --> 00:17:14 You ignored its color. You ignored its temperature. 281 00:17:14 --> 00:17:17 OK, and you ignored the soft or hard or whatever. 282 00:17:17 --> 00:17:20 OK, you ignored a whole bunch of things. 283 00:17:20 --> 00:17:25 You were focused on one thing. OK, you're focused on its mass. 284 00:17:25 --> 00:17:29 And, it turns out that the process really was developed 285 00:17:29 --> 00:17:34 from a set of simplifications. That is called, 286 00:17:34 --> 00:17:40 does anybody remember this? Point mass simplification. 287 00:17:40 --> 00:17:44 OK, so, in physics, you've done this before. 288 00:17:44 --> 00:17:49 OK, you've simplified your lives by viewing objects as 289 00:17:49 --> 00:17:55 having a mass at a point, and force is acting at that 290 00:17:55 --> 00:17:58 point. OK, M is that property of the 291 00:17:58 --> 00:18:02 object that is of interest to you. 292 00:18:02 --> 00:18:06 This process is called, in physics, point mass 293 00:18:06 --> 00:18:14 discretization. OK, now using an analogy, 294 00:18:14 --> 00:18:24 and I'm going to show you a similar simple process to do the 295 00:18:24 --> 00:18:31 problem with the light bulb. OK, so take my light bulb 296 00:18:31 --> 00:18:32 again, 297 00:18:32 --> 00:18:42 298 00:18:42 --> 00:18:44 And I focus on the filament of the light bulb. 299 00:18:44 --> 00:18:48 OK, all I care about is the current flowing through the 300 00:18:48 --> 00:18:50 light bulb. OK, I don't care about whether 301 00:18:50 --> 00:18:53 the filament is twisted, whether it's hot. 302 00:18:53 --> 00:18:57 I don't care about its shape. I don't care about its color. 303 00:18:57 --> 00:19:00 All I care about is the current. 304 00:19:00 --> 00:19:03 OK, so to do that, what we can do here at a very 305 00:19:03 --> 00:19:07 high level is since we just need the current and don't care about 306 00:19:07 --> 00:19:12 a bunch of other properties, we will simply replace the bulb 307 00:19:12 --> 00:19:15 with a discrete object called a resistor. 308 00:19:15 --> 00:19:19 So the discrete object is a resistor, much like the point 309 00:19:19 --> 00:19:23 mass simplification that we did earlier that replaced the bulb 310 00:19:23 --> 00:19:27 filament with a object called a resistor, a discrete object 311 00:19:27 --> 00:19:31 called a resistor. Or a lump object called 312 00:19:31 --> 00:19:37 resister, and put a value next to it just like the mass for the 313 00:19:37 --> 00:19:39 object, a resistance value, R. 314 00:19:39 --> 00:19:44 OK, now what I can do is in the same manner, replace the battery 315 00:19:44 --> 00:19:49 with an object called a battery object, and connect that here, 316 00:19:49 --> 00:19:52 the voltage, V, applied to it. 317 00:19:52 --> 00:19:56 V falls across the resistor, and I get my I simply from 318 00:19:56 --> 00:20:01 Ohm's law as we divide by R. So, notice here, 319 00:20:01 --> 00:20:04 to replace this complicated bulb, this really twisty, 320 00:20:04 --> 00:20:07 weird old thing with this discreet thing called a 321 00:20:07 --> 00:20:11 resistor, and its only property of interest was its resistance 322 00:20:11 --> 00:20:14 value, R, direct analogy to what we did there. 323 00:20:14 --> 00:20:18 So, since R represents the only property of interest, 324 00:20:18 --> 00:20:21 we can simply ignore all the other things. 325 00:20:21 --> 00:20:24 So, notice here, we've done things the simple 326 00:20:24 --> 00:20:25 way. And remember, 327 00:20:25 --> 00:20:28 in EE, in the electrical engineering, we do things the 328 00:20:28 --> 00:20:33 simple way. OK, we could go the hard route 329 00:20:33 --> 00:20:37 and do Maxwell's equations, and get PhD's in physics, 330 00:20:37 --> 00:20:38 and so on. But out here, 331 00:20:38 --> 00:20:42 we are looking to do useful, interesting systems in the 332 00:20:42 --> 00:20:46 simplest way that we can. OK, we do things a simple way. 333 00:20:46 --> 00:20:51 All right, so we just did this, and boom, I found out what the 334 00:20:51 --> 00:20:54 current was. Now, I cheated a little bit. 335 00:20:54 --> 00:20:58 I've cheated a little bit. R is a lumped abstraction for 336 00:20:58 --> 00:21:01 the bulb. So, you look at this resistor 337 00:21:01 --> 00:21:04 here. That is simply a placeholder. 338 00:21:04 --> 00:21:08 It's a stand-in for this complicated thing called a bulb. 339 00:21:08 --> 00:21:11 It's a discreet object. It's a lumped object, 340 00:21:11 --> 00:21:14 and represents the bulb. Now, so most of 6.002 will take 341 00:21:14 --> 00:21:17 off from here, OK, and that's it. 342 00:21:17 --> 00:21:20 To very simple stuff, like V is equal to IR, 343 00:21:20 --> 00:21:23 it's a simple high school algebra to take off in that 344 00:21:23 --> 00:21:25 direction. But before we go there, 345 00:21:25 --> 00:21:30 it's important to understand, why was it that we were able to 346 00:21:30 --> 00:21:34 make the simplification? OK, we did something else. 347 00:21:34 --> 00:21:37 Something's going on under the covers here. 348 00:21:37 --> 00:21:39 On the one hand, I say let's use Maxwell's, 349 00:21:39 --> 00:21:42 and then I jump out and say, hey, we can just use this 350 00:21:42 --> 00:21:45 simple thing. I did something that allowed me 351 00:21:45 --> 00:21:48 to go from here to here. And you need to understand why 352 00:21:48 --> 00:21:51 I did that and how I did that. Understand it once, 353 00:21:51 --> 00:21:54 and then you won't have to need that information again. 354 00:21:54 --> 00:21:58 You just need to understand it. So, let's take a closer look at 355 00:21:58 --> 00:22:02 the bulb filament, and look at what we really did. 356 00:22:02 --> 00:22:08 So, here's my filament, A, and let's say that the 357 00:22:08 --> 00:22:12 surface area here, I label that SA, 358 00:22:12 --> 00:22:17 and the one down here SB, my voltage, V, 359 00:22:17 --> 00:22:23 applied there, and this is what I call my 360 00:22:23 --> 00:22:28 black box that I've replaced with a resistor. 361 00:22:28 --> 00:22:33 Notice that, in order for this to work, 362 00:22:33 --> 00:22:40 V and I need to be defined. So I needs to be defined, 363 00:22:40 --> 00:22:45 and V needs to be defined. OK, if I give you a random 364 00:22:45 --> 00:22:49 object, and I don't tell you anything else about the object, 365 00:22:49 --> 00:22:54 it's not clear I can do that. OK, if it's a much more general 366 00:22:54 --> 00:22:58 situation, I have to write down Maxwell's equations, 367 00:22:58 --> 00:23:01 and this is what I would write down. 368 00:23:01 --> 00:23:05 Write down J dot dS as a function of the coordinate here 369 00:23:05 --> 00:23:10 integrated over the area minus, OK, I would have to start from 370 00:23:10 --> 00:23:15 there from one of Maxwell's equations. 371 00:23:15 --> 00:23:19 All right, notice that this becomes IA, and this becomes IB 372 00:23:19 --> 00:23:23 in our simplification. But, if I don't tell you 373 00:23:23 --> 00:23:26 anything else, you have to start from here. 374 00:23:26 --> 00:23:31 You will have some varying current here by point. 375 00:23:31 --> 00:23:34 You might have some other current coming out here because 376 00:23:34 --> 00:23:38 I may have some charge buildup happening inside. 377 00:23:38 --> 00:23:41 If charge is building up inside the filament; 378 00:23:41 --> 00:23:44 then I would have to put del q by del t out here, 379 00:23:44 --> 00:23:48 right, the current in minus the current out must equal charge 380 00:23:48 --> 00:23:51 buildup. Whoa, where is this and where 381 00:23:51 --> 00:23:53 is that? So this is reality. 382 00:23:53 --> 00:23:55 This is really, really what I have to do. 383 00:23:55 --> 00:24:00 But how did I get there? How did I get there? 384 00:24:00 --> 00:24:02 The key answer is, as engineers, 385 00:24:02 --> 00:24:05 when in doubt we simplify. Remember, we are engineers. 386 00:24:05 --> 00:24:09 Our goal in life is to build interesting systems. 387 00:24:09 --> 00:24:11 OK and some are motivated by money. 388 00:24:11 --> 00:24:15 OK, so our goal is to build interesting systems and do good 389 00:24:15 --> 00:24:18 to humanity. So, as long as we can build a 390 00:24:18 --> 00:24:20 good light bulb, we are happy. 391 00:24:20 --> 00:24:23 So what we can do is we can say, look, all I care about is 392 00:24:23 --> 00:24:26 building interesting systems. So I can say, 393 00:24:26 --> 00:24:32 hey, this stuff is too hard. Let's make the assumption that 394 00:24:32 --> 00:24:36 all the systems that we will consider will have this thing be 395 00:24:36 --> 00:24:37 zero. OK, in other words, 396 00:24:37 --> 00:24:41 if I take a complete object, if I take an element like a 397 00:24:41 --> 00:24:44 resistor or a capacitor, the box around the entire 398 00:24:44 --> 00:24:48 element, OK, and I want to just deal with those systems in which 399 00:24:48 --> 00:24:52 this thing is zero. You can come and beat me up and 400 00:24:52 --> 00:24:53 say, but why? Why not? 401 00:24:53 --> 00:24:57 Why am I doing this? And I am saying the world is 402 00:24:57 --> 00:24:58 arbitrary. I'm an engineer; 403 00:24:58 --> 00:25:04 I want to build good systems. By making this simplification, 404 00:25:04 --> 00:25:07 I eliminate this squiggle thing, and so on. 405 00:25:07 --> 00:25:11 I don't want to deal with it. I want to make my life simple. 406 00:25:11 --> 00:25:14 So this is gone to zero because, why? 407 00:25:14 --> 00:25:19 Because I have said that in the future I will only deal with 408 00:25:19 --> 00:25:21 those elements for which this is true. 409 00:25:21 --> 00:25:26 I'm going to discipline myself. I'm going to discipline myself 410 00:25:26 --> 00:25:32 to only deal with those systems. OK, Maxwell is turning around 411 00:25:32 --> 00:25:36 and, you know, mad at me and all that stuff, 412 00:25:36 --> 00:25:39 but tough. So this, what I've said about 413 00:25:39 --> 00:25:43 making a simplification here, and this is one of the 414 00:25:43 --> 00:25:48 simplifications I'm making. And I give a name to the 415 00:25:48 --> 00:25:51 simplification. And that's called the lumped 416 00:25:51 --> 00:25:55 matter discipline. OK, so I'm saying I will only 417 00:25:55 --> 00:26:00 deal with elements for which if I put a black box around it, 418 00:26:00 --> 00:26:06 this is going to be true. And if this is going to be 419 00:26:06 --> 00:26:10 true, then notice, there is no charge buildup. 420 00:26:10 --> 00:26:13 Current in must equal current out. 421 00:26:13 --> 00:26:15 Ah-ha! So this becomes IA. 422 00:26:15 --> 00:26:16 This becomes IB. Yes. 423 00:26:16 --> 00:26:20 OK, I can now deal with IA's and IB's. 424 00:26:20 --> 00:26:24 And IB and IA are equal because this is zero. 425 00:26:24 --> 00:26:29 Notice that there is a whole bunch of depth here in the jump 426 00:26:29 --> 00:26:33 from here to here. As MIT graduates, 427 00:26:33 --> 00:26:37 you really, really need to understand why it is that we 428 00:26:37 --> 00:26:40 made that jump, and then go and use that, 429 00:26:40 --> 00:26:43 and do cool things. All right, this allows us to 430 00:26:43 --> 00:26:46 define I. We have a unique I associated 431 00:26:46 --> 00:26:50 with an element for the current through the element. 432 00:26:50 --> 00:26:55 We still have to worry about B, and I won't go through that in 433 00:26:55 --> 00:26:57 detail. The course notes have some 434 00:26:57 --> 00:27:02 discussion of that and so does the textbook. 435 00:27:02 --> 00:27:07 So V, AB is defined when del phi B, the rate of change of 436 00:27:07 --> 00:27:11 magnetic flux is zero. So, if I take the element and I 437 00:27:11 --> 00:27:16 take any region outside the element, this must be true. 438 00:27:16 --> 00:27:20 And you say, why should that be true? 439 00:27:20 --> 00:27:23 That's not true in general. Absolutely. 440 00:27:23 --> 00:27:28 It's not true in general. But I, because I choose to, 441 00:27:28 --> 00:27:33 I going to deal with only those elements. 442 00:27:33 --> 00:27:36 I will discipline myself. But these are only those 443 00:27:36 --> 00:27:39 elements for which this is true, and this is true. 444 00:27:39 --> 00:27:42 I'm going to limit my world. I'm going to create a play 445 00:27:42 --> 00:27:44 field for myself. You want to play; 446 00:27:44 --> 00:27:47 follow my rules. OK, and that's called the 447 00:27:47 --> 00:27:50 lumped matter discipline. So once you say that I'm going 448 00:27:50 --> 00:27:54 to adhere to the lump matter discipline, and this is true 449 00:27:54 --> 00:27:56 inside your elements. This is true outside the 450 00:27:56 --> 00:27:59 elements. You can define VA and VB, 451 00:27:59 --> 00:28:03 and good things happen to you. OK, let me show you a few 452 00:28:03 --> 00:28:06 examples of lumped elements. But remember, 453 00:28:06 --> 00:28:10 a large part of what we're doing is based on these two 454 00:28:10 --> 00:28:13 assumptions. And to just go through the 455 00:28:13 --> 00:28:17 background on that, I would encourage you to go to 456 00:28:17 --> 00:28:21 chapter 1 of your course notes and read through just as how 457 00:28:21 --> 00:28:23 this came about, that comes about. 458 00:28:23 --> 00:28:28 So, by doing that by adhering to a lumped matter discipline, 459 00:28:28 --> 00:28:32 we can now lump objects. We could lump a bulb into a 460 00:28:32 --> 00:28:34 resistor. OK, so to be clear, 461 00:28:34 --> 00:28:36 a certain number of lumped objects, and now, 462 00:28:36 --> 00:28:40 the universe is going to be comprised into lumped objects. 463 00:28:40 --> 00:28:42 OK, so before this, when he went home, 464 00:28:42 --> 00:28:44 we talked about eggs, and omelets, 465 00:28:44 --> 00:28:46 and light bulbs, and switches, 466 00:28:46 --> 00:28:49 but once you come to MIT, and after you've taken 6.002, 467 00:28:49 --> 00:28:52 you begin talking about lumped elements, you know, 468 00:28:52 --> 00:28:55 resistors, voltage sources, capacitors, little inky-dinky 469 00:28:55 --> 00:29:00 objects that follow the lumped matter discipline. 470 00:29:00 --> 00:29:04 OK, they stick to very simple rules, and the math that you 471 00:29:04 --> 00:29:07 have to do to analyze them is incredibly simple. 472 00:29:07 --> 00:29:11 What could be simpler than V is equal to IR? 473 00:29:11 --> 00:29:15 So, let me give you an example of interesting lumped elements, 474 00:29:15 --> 00:29:20 and then show you a couple of really nasty lumped elements. 475 00:29:20 --> 00:29:21 OK. 476 00:29:21 --> 00:29:29 477 00:29:29 --> 00:29:33 OK, so what you see out here, so we characterize lumped 478 00:29:33 --> 00:29:35 elements by the VI characteristics. 479 00:29:35 --> 00:29:39 OK, you apply voltage, measure the current. 480 00:29:39 --> 00:29:43 OK, so what I can do is I can plot I here, and V here, 481 00:29:43 --> 00:29:48 and see what it looks like. OK, I can characterize elements 482 00:29:48 --> 00:29:51 by their VI relationship. And there are a bunch of 483 00:29:51 --> 00:29:56 elements that I can create based on the VI relationship. 484 00:29:56 --> 00:30:00 So let me show you a few examples. 485 00:30:00 --> 00:30:02 So for the resistor, since V is directly 486 00:30:02 --> 00:30:05 proportional to I, and R is a constant, 487 00:30:05 --> 00:30:08 I get a straight line. That's the I axis, 488 00:30:08 --> 00:30:11 the V axis, and this is the resistor. 489 00:30:11 --> 00:30:14 What I actually have is a variable resistor, 490 00:30:14 --> 00:30:17 so I'm going to change the resistance value, 491 00:30:17 --> 00:30:20 R, and the curve will also change slope. 492 00:30:20 --> 00:30:24 OK, I changed the value of R because it's a variable 493 00:30:24 --> 00:30:30 resistor, and the changes slope because my R is different. 494 00:30:30 --> 00:30:34 OK, next, let me go to a fixed resistor, and this guy here on 495 00:30:34 --> 00:30:37 the screen to your left is a fixed resistor. 496 00:30:37 --> 00:30:41 And you see that its IV characteristic is a line of a 497 00:30:41 --> 00:30:44 given slope, 1 by R, and that's it. 498 00:30:44 --> 00:30:46 I can't change it. Number three, 499 00:30:46 --> 00:30:51 I have another lumped element called a Zener diode that you 500 00:30:51 --> 00:30:54 will see in the fourth week of this class, and the 501 00:30:54 --> 00:30:58 characteristics for the Zener diode look like this: 502 00:30:58 --> 00:31:01 IV. If my voltage goes across the 503 00:31:01 --> 00:31:04 Zener diode goes up slightly, the current shoots up. 504 00:31:04 --> 00:31:07 But if the voltage becomes negative I don't have any 505 00:31:07 --> 00:31:11 current flowing into it until the voltage passes on the 506 00:31:11 --> 00:31:14 threshold, at which point my current begins to build up. 507 00:31:14 --> 00:31:17 OK, so I can increase the voltage a little bit, 508 00:31:17 --> 00:31:20 and it can show that the current starts building up 509 00:31:20 --> 00:31:22 again. So that's another interesting 510 00:31:22 --> 00:31:24 lumped element called a Zener diode. 511 00:31:24 --> 00:31:26 Let's switch to the next one called a diode. 512 00:31:26 --> 00:31:30 So a diode looks like this: IV. 513 00:31:30 --> 00:31:33 As the voltage across the diode becomes positive, 514 00:31:33 --> 00:31:35 around .6 volts, or thereabout, 515 00:31:35 --> 00:31:40 the current begins to shoot up. But when the voltage is below 516 00:31:40 --> 00:31:44 that threshold of .6, then my current is almost zero. 517 00:31:44 --> 00:31:47 It's another lumped element called a diode. 518 00:31:47 --> 00:31:51 And you will begin using these elements in your 002 lives to 519 00:31:51 --> 00:31:55 build interesting systems. The next example is a 520 00:31:55 --> 00:31:57 thermistor. A thermistor is a resistor 521 00:31:57 --> 00:32:02 whose resistance varies with temperature. 522 00:32:02 --> 00:32:08 OK, so this is a very expensive little hairdryer, 523 00:32:08 --> 00:32:14 and what I'm going to do is blow some hot air at my 524 00:32:14 --> 00:32:22 resistor, and you're going to see that its value is going to 525 00:32:22 --> 00:32:27 change depending on how much I heat it. 526 00:32:27 --> 00:32:32 So as it cools down, let me cool it down, 527 00:32:32 --> 00:32:38 so you can see it's coming down. 528 00:32:38 --> 00:32:41 I can zap it again. I could do this all day. 529 00:32:41 --> 00:32:45 This is so much fun. OK, so that's another 530 00:32:45 --> 00:32:49 interesting lumped element. As the temperature rises, 531 00:32:49 --> 00:32:53 its resistance changes. The next thing is called a 532 00:32:53 --> 00:32:56 photo resistor. It's a resistor. 533 00:32:56 --> 00:33:00 It used to be a resistor; Lorenzo? 534 00:33:00 --> 00:33:03 Oh OK, that's fine. So this is a photo resistor. 535 00:33:03 --> 00:33:08 And notice that it almost behaves like an open circuit. 536 00:33:08 --> 00:33:12 But what I'm going to do is shine some light on it. 537 00:33:12 --> 00:33:16 When I shine light on it, it begins to conduct and 538 00:33:16 --> 00:33:18 becomes a resistor of some value. 539 00:33:18 --> 00:33:22 There you go. OK, so that's a photo resistor. 540 00:33:22 --> 00:33:25 So now I'm going to show you a battery. 541 00:33:25 --> 00:33:30 Notice we did talk about batteries before. 542 00:33:30 --> 00:33:33 I'll show you a battery. So before you show a battery, 543 00:33:33 --> 00:33:36 just thinking your own minds, what should the IV 544 00:33:36 --> 00:33:39 characteristic of a battery look like? 545 00:33:39 --> 00:33:41 IV. A battery supplies a constant 546 00:33:41 --> 00:33:44 voltage. You know your little cell, 547 00:33:44 --> 00:33:45 the AA battery, 1.5 volts? 548 00:33:45 --> 00:33:49 So, think of what the IV characteristic of a battery 549 00:33:49 --> 00:33:53 should look like for three seconds before it shows you. 550 00:33:53 --> 00:33:55 This is the one I showed, Lorenzo?. 551 00:33:55 --> 00:34:00 It's a straight line. This is a good battery. 552 00:34:00 --> 00:34:01 It's a straight, vertical line, 553 00:34:01 --> 00:34:05 but says that the voltage is 1.5 volts, or thereabouts. 554 00:34:05 --> 00:34:08 No matter what current it supplies as an ideal voltage 555 00:34:08 --> 00:34:12 source, it has a fixed voltage, V, and no matter what the 556 00:34:12 --> 00:34:15 current going through is. Now, I'll show you a dud, 557 00:34:15 --> 00:34:18 a bad battery, and this is what the bad 558 00:34:18 --> 00:34:21 battery looks like. So, many of you have had your 559 00:34:21 --> 00:34:24 car batteries die on you. When you go to the store, 560 00:34:24 --> 00:34:27 they check your batteries. They use exactly this 561 00:34:27 --> 00:34:32 principle, that dead batteries have resistance. 562 00:34:32 --> 00:34:34 By the way, you see slopes here. 563 00:34:34 --> 00:34:38 You're thinking of resistance. OK, they can use this property 564 00:34:38 --> 00:34:41 to figure out that your battery is dead. 565 00:34:41 --> 00:34:44 So that's a dead battery. And finally, 566 00:34:44 --> 00:34:47 let me show you a bulb. We started with a bulb, 567 00:34:47 --> 00:34:51 and so I need to end, OK, we started with a bulb, 568 00:34:51 --> 00:34:55 so I need to end with a bulb. And what you will see is that a 569 00:34:55 --> 00:34:57 bulb simply behaves like a resistor. 570 00:34:57 --> 00:35:02 Its IV curve is going to look like this. 571 00:35:02 --> 00:35:04 OK, notice this is my bulb. And guess what, 572 00:35:04 --> 00:35:08 it behaves like a resistor. It's a very interesting kind of 573 00:35:08 --> 00:35:11 resistor, so I won't go into details for now. 574 00:35:11 --> 00:35:14 But notice its IV characteristic behaves like a 575 00:35:14 --> 00:35:17 resistor. OK, so those are some pretty 576 00:35:17 --> 00:35:20 standard lumped elements. You deal with a lot more sets 577 00:35:20 --> 00:35:23 of lumped elements, switches, MOSFETs, 578 00:35:23 --> 00:35:26 capacitors, inductors, a bunch of other fun stuff. 579 00:35:26 --> 00:35:29 But before we do that, what I wanted to tell you, 580 00:35:29 --> 00:35:34 don't go berserk on this abstraction binge. 581 00:35:34 --> 00:35:36 Too much of anything is bad for you. 582 00:35:36 --> 00:35:39 So what I'm going to show you is, abstractions or models are 583 00:35:39 --> 00:35:43 only valid provided you work within a set of constraints. 584 00:35:43 --> 00:35:46 Notice, we have already had this tacit handshake which said 585 00:35:46 --> 00:35:49 that we follow the discipline. Even after we follow the 586 00:35:49 --> 00:35:53 discipline, there are ranges to how well physical elements can 587 00:35:53 --> 00:35:55 behave like ideal lumped elements. 588 00:35:55 --> 00:35:58 OK, for example, what we will do is show you the 589 00:35:58 --> 00:36:02 resistor. And it's going to look like a 590 00:36:02 --> 00:36:04 resistor. And I'm going to keep 591 00:36:04 --> 00:36:07 increasing the voltage around it. 592 00:36:07 --> 00:36:10 OK, what's going to happen at some point? 593 00:36:10 --> 00:36:14 I just keep doing that. If it's an ideal element, 594 00:36:14 --> 00:36:17 if you're a theorist, you say, oh yeah, 595 00:36:17 --> 00:36:22 the curve will keep extending until I reach infinity. 596 00:36:22 --> 00:36:26 But this is a practical resistor, so people out here can 597 00:36:26 --> 00:36:31 cover your eyes or something. OK, so you're abstraction can't 598 00:36:31 --> 00:36:36 predict that. All it says is the current is 599 00:36:36 --> 00:36:38 an amp. It can't predict the heat, 600 00:36:38 --> 00:36:41 light, or the smell. In the laboratory, 601 00:36:41 --> 00:36:45 even, you get the smell. You know what somebody has just 602 00:36:45 --> 00:36:47 done. So that's one example of the 603 00:36:47 --> 00:36:50 lumped abstraction breaking down. 604 00:36:50 --> 00:36:54 So, if I really believe that my own BS, anything is a lumped 605 00:36:54 --> 00:36:56 element. So here's a pickle. 606 00:36:56 --> 00:37:02 A pickle is a lumped element. I can choose it as a lumped 607 00:37:02 --> 00:37:05 resistor. But this is a very interesting 608 00:37:05 --> 00:37:09 lumped resistor. Don't try this at home. 609 00:37:09 --> 00:37:14 This is a standard pickle into which you are pumping 110 V AC. 610 00:37:14 --> 00:37:18 I promise you, this is a standard pickle. 611 00:37:18 --> 00:37:23 So, it has a fixed resistance, but your lumped abstraction 612 00:37:23 --> 00:37:27 cannot predict the nice light and sound effect. 613 00:37:27 --> 00:37:32 OK, so the last two or three minutes what I want to do, 614 00:37:32 --> 00:37:35 so remember, don't get carried away by 615 00:37:35 --> 00:37:39 abstractions. There are limits. 616 00:37:39 --> 00:37:42 OK, you can't predict everything. 617 00:37:42 --> 00:37:45 OK, that's the smell of a pickle. 618 00:37:45 --> 00:37:49 OK, so let me give you a preview of some upcoming 619 00:37:49 --> 00:37:55 attractions, and show you one more quick simplification in the 620 00:37:55 --> 00:37:58 last few minutes. So what we can do, 621 00:37:58 --> 00:38:03 once we build these lumped elements, we can connect them in 622 00:38:03 --> 00:38:07 circuits. OK, so I can build a circuit, 623 00:38:07 --> 00:38:10 of the sort. So here's a voltage source with 624 00:38:10 --> 00:38:14 a bunch of resistors. I can connect them with wires 625 00:38:14 --> 00:38:18 and build a circuit of the sort. One interesting question we can 626 00:38:18 --> 00:38:21 ask ourselves is, under the lumped matter 627 00:38:21 --> 00:38:24 discipline, what can we say about the voltages? 628 00:38:24 --> 00:38:28 OK, if I go around the loop, provided my world adheres to 629 00:38:28 --> 00:38:32 the lumped matter discipline, what can I say about the 630 00:38:32 --> 00:38:36 voltages around this loop? Ah-ha, Maxwell again, 631 00:38:36 --> 00:38:39 right? So, I can write Maxwell's 632 00:38:39 --> 00:38:42 appropriate equation to solve that. 633 00:38:42 --> 00:38:47 OK, voltages have something to do with E and your integral of E 634 00:38:47 --> 00:38:50 dot dl and all of that stuff, right? 635 00:38:50 --> 00:38:54 So this is the appropriate Maxwell's equations to use. 636 00:38:54 --> 00:38:58 And I want to find out what happens here. 637 00:38:58 --> 00:39:00 Now remember, under LMD, I made the 638 00:39:00 --> 00:39:04 assumption. OK, my world, 639 00:39:04 --> 00:39:09 my playground, has del phi B by del t being 640 00:39:09 --> 00:39:13 zero. The rate of change of flux is 641 00:39:13 --> 00:39:16 zero. So, under these circumstances, 642 00:39:16 --> 00:39:21 I can write this. I can break up this line 643 00:39:21 --> 00:39:28 integral into three parts across the voltage source and across 644 00:39:28 --> 00:39:34 the two resistors and write that down. 645 00:39:34 --> 00:39:38 OK, and then when I can do, is now that the right-hand side 646 00:39:38 --> 00:39:42 is zero, I can simply take this. And I know that E dot dl across 647 00:39:42 --> 00:39:45 this element is simply VCA. This is VAB, 648 00:39:45 --> 00:39:49 and this is VBC equals zero. OK, so when I make the 649 00:39:49 --> 00:39:53 assumption that del phi B by del t is zero, and I go around this 650 00:39:53 --> 00:39:58 loop, apply Maxwell's equations, what do I find? 651 00:39:58 --> 00:40:03 I find that the sum of the voltages, VCA plus VAB plus VBC, 652 00:40:03 --> 00:40:06 is zero. That's fantastic. 653 00:40:06 --> 00:40:11 So now, I could say hasta la vista to this baby here. 654 00:40:11 --> 00:40:17 And I can focus on this guy and say, Maxwell's equations, 655 00:40:17 --> 00:40:22 this thing with squiggles and dels and all that stuff, 656 00:40:22 --> 00:40:28 can be simplified to the sum of the voltages across a set of 657 00:40:28 --> 00:40:34 elements in a loop in a circuit is zero. 658 00:40:34 --> 00:40:39 OK, and this is called Kirchhoff's first first law, 659 00:40:39 --> 00:40:40 KVL. OK, similarly, 660 00:40:40 --> 00:40:46 in recitation section, you'll see the application of 661 00:40:46 --> 00:40:51 Kirchhoff's current law, which comes from this be equal 662 00:40:51 --> 00:40:57 to zero, and all the currents coming into a node being zero. 663 00:40:57 --> 00:41:02 So, KVL and KCl directly come out of the lumped matter 664 00:41:02 --> 00:41:06 discipline. And you can use those to solve 665 00:41:06 --> 41:09 circuits like this.