1
00:00:00,000 --> 00:00:04,000
So, one question to ask
ourselves is,

2
00:00:04,000 --> 00:00:08,000
what is engineering?
How do we define,

3
00:00:08,000 --> 00:00:15,000
what is engineering?
Well, the definition I like to

4
00:00:15,000 --> 00:00:22,000
use is one put forth by Steve
Senturia, one of our professors

5
00:00:22,000 --> 00:00:28,000
who is now retired.
He defined engineering to be

6
00:00:28,000 --> 00:00:35,000
the purposeful use of science.
All right, so what is 6.002

7
00:00:35,000 --> 00:00:38,000
about?
So, 6.002 is a first course in

8
00:00:38,000 --> 00:00:41,000
engineering.
And I like to view 6.002 as the

9
00:00:41,000 --> 00:00:44,000
gainful employment of Maxwell's
equations.

10
00:00:44,000 --> 00:00:48,000
Many of you have seen Maxwell's
equations before.

11
00:00:48,000 --> 00:00:52,000
Most of you should have.
And they are hard stuff.

12
00:00:52,000 --> 00:00:57,000
6.002 is all about teaching you
how to simplify our lives,

13
00:00:57,000 --> 00:01:02,000
make things simple.
So, if you can gainfully employ

14
00:01:02,000 --> 00:01:07,000
Maxwell's equations,
gainfully employ the facts of

15
00:01:07,000 --> 00:01:11,000
nature to build very interesting
systems.

16
00:01:11,000 --> 00:01:15,000
So let me show you how the
transition is made.

17
00:01:15,000 --> 00:01:20,000
So, there's a world around us,
nature, so we made some

18
00:01:20,000 --> 00:01:24,000
observations in nature.
We make measurements,

19
00:01:24,000 --> 00:01:30,000
and we can write down large
tables of measurements.

20
00:01:30,000 --> 00:01:33,000
So, for example,
we can take objects and measure

21
00:01:33,000 --> 00:01:37,000
the voltage across them,
and look at the resulting

22
00:01:37,000 --> 00:01:41,000
current through the elements.
So, we may end up getting a

23
00:01:41,000 --> 00:01:44,000
bunch of values such as
[CHALKBOARD].

24
00:01:44,000 --> 00:01:48,000
So, we start out life with
making measurements on what

25
00:01:48,000 --> 00:01:51,000
exists.
And we build a bunch of tables.

26
00:01:51,000 --> 00:01:54,000
Now, we could directly take
these tables,

27
00:01:54,000 --> 00:01:57,000
and based on observations of
these tables,

28
00:01:57,000 --> 00:02:01,000
we could go ahead and build
very interesting engineering

29
00:02:01,000 --> 00:02:06,000
systems that help us out in
day-to-day lives.

30
00:02:06,000 --> 00:02:10,000
But that's incredibly hard.
Imagine having to resort to a

31
00:02:10,000 --> 00:02:14,000
set of tables to do any kind of
useful work.

32
00:02:14,000 --> 00:02:18,000
So what we do as engineers,
we first layer a level of

33
00:02:18,000 --> 00:02:21,000
abstraction.
We look at all the data,

34
00:02:21,000 --> 00:02:25,000
and somehow layer abstraction
such that we can simplify or

35
00:02:25,000 --> 00:02:30,000
much more succinctly put in a
simple equation or a simple

36
00:02:30,000 --> 00:02:35,000
statement what these numbers are
telling us.

37
00:02:35,000 --> 00:02:37,000
OK, so for example,
our physics laws,

38
00:02:37,000 --> 00:02:41,000
so laws of physics for example
are simply abstractions,

39
00:02:41,000 --> 00:02:45,000
the laws of abstractions.
So, these sets of numbers can

40
00:02:45,000 --> 00:02:48,000
be codified by Ohm's law,
for example,

41
00:02:48,000 --> 00:02:51,000
V is equal to RI,
the voltage current,

42
00:02:51,000 --> 00:02:54,000
relates to the resistance of
the object.

43
00:02:54,000 --> 00:02:58,000
So, V is equal to RI is a law
that succinctly describes a set

44
00:02:58,000 --> 00:03:02,000
of experiments,
and replaces a large number of

45
00:03:02,000 --> 00:03:06,000
tables with a very simple
statement.

46
00:03:06,000 --> 00:03:09,000
You could call this the law,
or you could call it an

47
00:03:09,000 --> 00:03:13,000
abstraction.
OK so you see laws of physics,

48
00:03:13,000 --> 00:03:16,000
call them abstractions of
physics if you like.

49
00:03:16,000 --> 00:03:21,000
Similarly, there are Maxwell's
equations and so on and so

50
00:03:21,000 --> 00:03:23,000
forth.
So, this is what is.

51
00:03:23,000 --> 00:03:27,000
This is what's out there.
OK, and a law as an abstraction

52
00:03:27,000 --> 00:03:31,000
describe the properties of
nature, as we see it,

53
00:03:31,000 --> 00:03:35,000
in some succinct form.
Now, if you want to go and

54
00:03:35,000 --> 00:03:38,000
build useful things,
we could take these

55
00:03:38,000 --> 00:03:40,000
abstractions,
take Maxwell's equations,

56
00:03:40,000 --> 00:03:43,000
and go and build things.
But it's hard.

57
00:03:43,000 --> 00:03:44,000
It's really,
really hard.

58
00:03:44,000 --> 00:03:48,000
And what you learn in,
at MIT is this place is all

59
00:03:48,000 --> 00:03:51,000
about simplifying things.
Take complicated things,

60
00:03:51,000 --> 00:03:55,000
build layers of abstraction,
and simplify things so that we

61
00:03:55,000 --> 00:04:00,000
can build useful systems.
Even in 6.002 we start life by

62
00:04:00,000 --> 00:04:04,000
making a huge leap from
Maxwell's equations to a couple

63
00:04:04,000 --> 00:04:09,000
of very, very simple laws.
OK, I'm going to show you that

64
00:04:09,000 --> 00:04:14,000
leap that we will make today.
So, the first abstraction that

65
00:04:14,000 --> 00:04:18,000
we layer is called the lump
circuit abstraction.

66
00:04:18,000 --> 00:04:22,000
OK, in the lump circuit
abstraction, what we do is we

67
00:04:22,000 --> 00:04:27,000
make a set of simplifications
that allows us to view a set of

68
00:04:27,000 --> 00:04:32,000
objects as discrete or lumped
elements.

69
00:04:32,000 --> 00:04:35,000
So, we may, I will define
voltage sources.

70
00:04:35,000 --> 00:04:38,000
We'll define resistors.
We'll define capacitors,

71
00:04:38,000 --> 00:04:41,000
and so on.
OK, and I'm going to make the

72
00:04:41,000 --> 00:04:46,000
jump, and show you how we make
the jump in a few minutes.

73
00:04:46,000 --> 00:04:49,000
So, on that sort of
abstraction, we then layer yet

74
00:04:49,000 --> 00:04:53,000
another abstract layer.
And let me call that the

75
00:04:53,000 --> 00:04:56,000
amplifier abstraction.
OK, remember,

76
00:04:56,000 --> 00:05:00,000
here we are absolutely down and
dirty.

77
00:05:00,000 --> 00:05:02,000
We are setting the probes,
measuring objects,

78
00:05:02,000 --> 00:05:05,000
and building huge tables.
We abstracted things into

79
00:05:05,000 --> 00:05:07,000
simple laws, and life got a
little better.

80
00:05:07,000 --> 00:05:11,000
OK, I'm going to show you can
abstract things further out and

81
00:05:11,000 --> 00:05:14,000
build discrete objects,
and, you could build even more

82
00:05:14,000 --> 00:05:17,000
interesting components called
amplifiers and begin playing

83
00:05:17,000 --> 00:05:20,000
around with amplifiers.
OK, so when you are using

84
00:05:20,000 --> 00:05:23,000
amplifiers, you don't really
have to worry about the details

85
00:05:23,000 --> 00:05:26,000
of Maxwell's equations.
OK, I'll give you some very

86
00:05:26,000 --> 00:05:29,000
simple abstract rules of
behavior for an amplifier,

87
00:05:29,000 --> 00:05:32,000
and you can go build very
interesting systems without

88
00:05:32,000 --> 00:05:35,000
really, really knowing how
Maxwell's equations applies to

89
00:05:35,000 --> 00:05:40,000
that because you will be working
at this abstract layer.

90
00:05:40,000 --> 00:05:43,000
However, since you're
engineers, and you are good at

91
00:05:43,000 --> 00:05:47,000
building such systems,
it's very important for you to

92
00:05:47,000 --> 00:05:51,000
understand how we make this leap
from the laws of physics into

93
00:05:51,000 --> 00:05:54,000
some of our very primitive
engineering abstractions.

94
00:05:54,000 --> 00:05:58,000
So, once we make the amplified
abstraction in 6.002,

95
00:05:58,000 --> 00:06:02,000
by the way, 6.002 starts here.
We start from the laws of

96
00:06:02,000 --> 00:06:06,000
physics and then proceed all the
way out.

97
00:06:06,000 --> 00:06:10,000
So, once we talk about
amplifiers we will take two

98
00:06:10,000 --> 00:06:12,000
pads.
On the amplifier,

99
00:06:12,000 --> 00:06:18,000
you will build the next
abstraction called the digital

100
00:06:18,000 --> 00:06:21,000
abstraction.
OK, and with the digital

101
00:06:21,000 --> 00:06:27,000
abstraction, we will build new
elements such as inverters and

102
00:06:27,000 --> 00:06:31,000
combinational gates,
OK?

103
00:06:31,000 --> 00:06:35,000
So, notice we are building
bigger, and bigger things,

104
00:06:35,000 --> 00:06:38,000
which have more and more
complicated behavior inside

105
00:06:38,000 --> 00:06:42,000
them, but which are very simple
to describe, right?

106
00:06:42,000 --> 00:06:47,000
So, following the digital
abstraction, we will superimpose

107
00:06:47,000 --> 00:06:51,000
the combinational logic
abstraction on top of that,

108
00:06:51,000 --> 00:06:54,000
and define functional blocks
that look like this:

109
00:06:54,000 --> 00:06:56,000
some inputs,
some function,

110
00:06:56,000 --> 00:07:01,000
some outputs.
The next abstraction on top of

111
00:07:01,000 --> 00:07:06,000
that will be the clock digital
abstraction, where we will have

112
00:07:06,000 --> 00:07:10,000
some notion of time introduced
into the system.

113
00:07:10,000 --> 00:07:14,000
There will be a clock,
and this will be some function.

114
00:07:14,000 --> 00:07:19,000
And there will be a clock that
introduces time into the sort of

115
00:07:19,000 --> 00:07:23,000
logic values that functions
operate upon.

116
00:07:23,000 --> 00:07:26,000
Following that,
the next level of abstraction

117
00:07:26,000 --> 00:07:32,000
that we build is called
instruction set abstraction.

118
00:07:32,000 --> 00:07:37,000
OK, now you begin to see things
that consumers get to look at.

119
00:07:37,000 --> 00:07:42,000
Can someone give me an example
of, or name an instruction set,

120
00:07:42,000 --> 00:07:45,000
or instruction set abstraction?
Bingo.

121
00:07:45,000 --> 00:07:48,000
So, x86 is one set of
abstractions.

122
00:07:48,000 --> 00:07:51,000
And in fact,
in many universities,

123
00:07:51,000 --> 00:07:55,000
education could well start just
by saying, OK,

124
00:07:55,000 --> 00:07:59,000
here's an abstraction.
These are the x86 instructions,

125
00:07:59,000 --> 00:08:02,000
OK?
Some MIT gurus have designed

126
00:08:02,000 --> 00:08:05,000
this awesome little
microprocessor,

127
00:08:05,000 --> 00:08:07,000
OK?
So you just worry about,

128
00:08:07,000 --> 00:08:11,000
you take this abstraction layer
here, the assembly instructions,

129
00:08:11,000 --> 00:08:14,000
and you go and build systems on
top of that.

130
00:08:14,000 --> 00:08:18,000
OK, so this is an abstraction
layer called the x86 layer.

131
00:08:18,000 --> 00:08:20,000
There are other abstraction
layers.

132
00:08:20,000 --> 00:08:24,000
In 6.004, you will learn about,
I believe, the alpha or the

133
00:08:24,000 --> 00:08:29,000
beta, OK, and various other
abstractions at this point.

134
00:08:29,000 --> 00:08:31,000
So, 6.002 kind of goes until
here.

135
00:08:31,000 --> 00:08:36,000
6.002 takes me from the world
of physics all the way to the

136
00:08:36,000 --> 00:08:40,000
world of interesting analog and
digital systems.

137
00:08:40,000 --> 00:08:44,000
OK, 004, the course on
computation structures,

138
00:08:44,000 --> 00:08:48,000
will show you how to build
computers all the way from

139
00:08:48,000 --> 00:08:53,000
simple digital objects all the
way to big systems.

140
00:08:53,000 --> 00:08:56,000
Following that,
you learn about language

141
00:08:56,000 --> 00:08:59,000
abstractions,
Java, C, and other languages,

142
00:08:59,000 --> 00:09:05,000
and that's in 6.002.
And there are several other

143
00:09:05,000 --> 00:09:08,000
courses that will cover that.
Following this,

144
00:09:08,000 --> 00:09:12,000
you learn about software system
abstractions,

145
00:09:12,000 --> 00:09:16,000
and software systems,
you will learn about operating

146
00:09:16,000 --> 00:09:18,000
systems.
Any example of an operating

147
00:09:18,000 --> 00:09:22,000
system abstraction that people
know out there?

148
00:09:22,000 --> 00:09:23,000
What's that?
Linux.

149
00:09:23,000 --> 00:09:26,000
What else?
I'm just wondering how long

150
00:09:26,000 --> 00:09:32,000
I'll have to go before I hear
what I want to hear.

151
00:09:32,000 --> 00:09:35,000
[LAUGHTER] OK,
so we have a bunch of software

152
00:09:35,000 --> 00:09:37,000
systems.
So, if we have a bunch of

153
00:09:37,000 --> 00:09:39,000
software systems,
these are nothing but

154
00:09:39,000 --> 00:09:42,000
abstractions.
Linux simply implies a set of

155
00:09:42,000 --> 00:09:45,000
system calls that the programs
must adhere to.

156
00:09:45,000 --> 00:09:48,000
Windows is another set of
system calls.

157
00:09:48,000 --> 00:09:50,000
That's it.
And see how much money they

158
00:09:50,000 --> 00:09:54,000
made out of it?
OK, it's all about abstraction

159
00:09:54,000 --> 00:09:56,000
layers, that all start from
nature.

160
00:09:56,000 --> 00:09:58,000
All right?
Build abstraction upon

161
00:09:58,000 --> 00:10:01,000
abstraction upon abstraction
upon abstraction,

162
00:10:01,000 --> 00:10:06,000
and someone out here are lots
of dollars.

163
00:10:06,000 --> 00:10:09,000
OK, so based on these
abstractions,

164
00:10:09,000 --> 00:10:14,000
we can then build useful things
for human beings.

165
00:10:14,000 --> 00:10:18,000
We can build very useful
things, video games,

166
00:10:18,000 --> 00:10:24,000
so we can send space shuttles
up, and a whole bunch of other

167
00:10:24,000 --> 00:10:27,000
systems.
But it's based on these

168
00:10:27,000 --> 00:10:32,000
abstraction layers.
What's unique about education

169
00:10:32,000 --> 00:10:34,000
at MIT?
What's unique about 6.002 and

170
00:10:34,000 --> 00:10:36,000
EECS?
Is to my knowledge,

171
00:10:36,000 --> 00:10:41,000
there are not many other places
in the world where you will get

172
00:10:41,000 --> 00:10:45,000
an education in everything going
all the way from nature to how

173
00:10:45,000 --> 00:10:49,000
to build very complicated analog
and digital systems.

174
00:10:49,000 --> 00:10:53,000
OK, we will show you layer upon
layer upon layer upon layer,

175
00:10:53,000 --> 00:10:57,000
peel away the onion until you
are down to raw nature,

176
00:10:57,000 --> 00:11:00,000
OK, through Maxwell's
equations.

177
00:11:00,000 --> 00:11:02,000
So, 6.002, 004,
this is 033,

178
00:11:02,000 --> 00:11:07,000
OK, 6.170, and so on.
OK, the whole EECS is about

179
00:11:07,000 --> 00:11:11,000
building abstraction layers,
one on top of the other.

180
00:11:11,000 --> 00:11:14,000
So that's one path.
There's the analog path.

181
00:11:14,000 --> 00:11:18,000
The analog path would take an
amplifier, and build an

182
00:11:18,000 --> 00:11:21,000
abstraction layer called the
op-amp.

183
00:11:21,000 --> 00:11:25,000
See how similar they all look?
You know the amplifier,

184
00:11:25,000 --> 00:11:29,000
the inverter of the digital
world, and the operational

185
00:11:29,000 --> 00:11:34,000
amplifier in the analog world,
just different ways of looking

186
00:11:34,000 --> 00:11:39,000
at the same devices.
So, to build an analog system,

187
00:11:39,000 --> 00:11:43,000
to build an operational
amplifier, and then,

188
00:11:43,000 --> 00:11:48,000
here we go end up building a
whole bunch of different

189
00:11:48,000 --> 00:11:51,000
interesting analog system
components.

190
00:11:51,000 --> 00:11:56,000
OK, and these components might
look like oscillators.

191
00:11:56,000 --> 00:12:02,000
They might look like filters.
OK, they look like power

192
00:12:02,000 --> 00:12:08,000
supplies, a whole bunch of very
interesting abstract components,

193
00:12:08,000 --> 00:12:13,000
which pulled together can then
give you the next set of

194
00:12:13,000 --> 00:12:17,000
systems.
And these systems might be

195
00:12:17,000 --> 00:12:22,000
toasters, or say for example
other analog systems like the

196
00:12:22,000 --> 00:12:28,000
various control systems for
various power plants and so on

197
00:12:28,000 --> 00:12:31,000
and so forth,
and ultimately,

198
00:12:31,000 --> 00:12:36,000
fun and dollars.
OK, so 6.002 is about going

199
00:12:36,000 --> 00:12:39,000
from physics all the way to this
point.

200
00:12:39,000 --> 00:12:43,000
We will build interesting
analog systems,

201
00:12:43,000 --> 00:12:48,000
and take you up to interesting
digital system components,

202
00:12:48,000 --> 00:12:54,000
from which 004 will take you
all the way to building computer

203
00:12:54,000 --> 00:12:57,000
architectures.
So that, in a nutshell,

204
00:12:57,000 --> 00:13:03,000
kind of gives you a feel for
the space of EECS.

205
00:13:03,000 --> 00:13:08,000
OK, this chart here is almost a
vignette of what EECS at MIT is

206
00:13:08,000 --> 00:13:11,000
all about.
And this is the world according

207
00:13:11,000 --> 00:13:14,000
to Agarwal, because he's
teaching 002.

208
00:13:14,000 --> 00:13:18,000
OK, so this is 6.002,
and the rest of EECS is

209
00:13:18,000 --> 00:13:22,000
somewhere out there.
OK, so I'm going to do now is

210
00:13:22,000 --> 00:13:26,000
throughout this course;
I want you to think about which

211
00:13:26,000 --> 00:13:30,000
part in this vignette we are in.
So, right now,

212
00:13:30,000 --> 00:13:33,000
I'm going to start here and
take you here.

213
00:13:33,000 --> 00:13:37,000
OK, and as you get closer and
closer, things get simpler,

214
00:13:37,000 --> 00:13:39,000
and simpler,
and simpler.

215
00:13:39,000 --> 00:13:42,000
Still, the final abstractions
are pedal, brake,

216
00:13:42,000 --> 00:13:45,000
steering wheel.
I mean, that's the abstraction

217
00:13:45,000 --> 00:13:48,000
to play a game,
right, four or five very simple

218
00:13:48,000 --> 00:13:51,000
interfaces, and that's all you
need to know.

219
00:13:51,000 --> 00:13:54,000
And everybody in the world can
play stuff.

220
00:13:54,000 --> 00:13:56,000
So remember,
this stuff is complicated.

221
00:13:56,000 --> 00:14:00,000
This stuff is very,
very simple.

222
00:14:00,000 --> 00:14:03,000
OK, and the more we build
abstractions and come to this

223
00:14:03,000 --> 00:14:05,000
side, things get simpler and
simpler.

224
00:14:05,000 --> 00:14:09,000
So, a large part of what I'll
cover today is make the biggest

225
00:14:09,000 --> 00:14:11,000
simplification.
The biggest simplification we

226
00:14:11,000 --> 00:14:15,000
will make his go from Maxwell's
equation to some very,

227
00:14:15,000 --> 00:14:18,000
very simple algebraic rules.
OK, I did Maxwell's equations

228
00:14:18,000 --> 00:14:19,000
myself.
And I tell you,

229
00:14:19,000 --> 00:14:22,000
they were very interesting
stuff but complicated.

230
00:14:22,000 --> 00:14:25,000
I can't imagine building
efficient systems using

231
00:14:25,000 --> 00:14:30,000
Maxwell's equations.
So, let's take an example,

232
00:14:30,000 --> 00:14:34,000
OK?
So, let's say I have a battery.

233
00:14:34,000 --> 00:14:39,000
Just switch to page three of
your course notes.

234
00:14:39,000 --> 00:14:43,000
And let's say I connect that to
a bulb.

235
00:14:43,000 --> 00:14:49,000
OK, and this is a wire.
And, the battery supplies some

236
00:14:49,000 --> 00:14:53,000
voltage, V, and I ask you a
simple question.

237
00:14:53,000 --> 00:14:57,000
What is the current through the
bulb?

238
00:14:57,000 --> 00:15:05,000
OK, so here is something that I
can build using objects.

239
00:15:05,000 --> 00:15:07,000
I can pick a round from stores
and so on.

240
00:15:07,000 --> 00:15:11,000
And I can collect them up in
this way, and ask the question,

241
00:15:11,000 --> 00:15:12,000
what is the current,
I?

242
00:15:12,000 --> 00:15:16,000
Now, if all you've done is
learn about Maxwell's equations,

243
00:15:16,000 --> 00:15:19,000
you can roll up your sleeves
and say, ah-ha!

244
00:15:19,000 --> 00:15:23,000
The first step is to write down
all of Maxwell's equations,

245
00:15:23,000 --> 00:15:26,000
and you can say,
del cross E is minus del and go

246
00:15:26,000 --> 00:15:28,000
on, and on, and on,
OK, and write out all of

247
00:15:28,000 --> 00:15:32,000
Maxwell's equations and say,
now how do I get from there to

248
00:15:32,000 --> 00:15:35,000
here?
OK, it's very good.

249
00:15:35,000 --> 00:15:37,000
You can do it.
OK, you can do it,

250
00:15:37,000 --> 00:15:39,000
but it's very complicated.
OK, so instead,

251
00:15:39,000 --> 00:15:42,000
what you're going to do is take
the easy way.

252
00:15:42,000 --> 00:15:46,000
So, what I want to remind you
is that this course is actually

253
00:15:46,000 --> 00:15:47,000
very easy.
OK remember,

254
00:15:47,000 --> 00:15:51,000
we're going to be building
abstraction upon abstraction to

255
00:15:51,000 --> 00:15:54,000
make your lives easier.
If you think your lives are

256
00:15:54,000 --> 00:15:57,000
getting more complicated,
then you are not using

257
00:15:57,000 --> 00:16:02,000
intuition enough.
OK, just remember the big I

258
00:16:02,000 --> 00:16:04,000
word.
It's all about making things

259
00:16:04,000 --> 00:16:07,000
simple.
OK, so let me give you an

260
00:16:07,000 --> 00:16:10,000
analogy.
So, suppose you have an object.

261
00:16:10,000 --> 00:16:13,000
OK, and I apply a force to the
object.

262
00:16:13,000 --> 00:16:16,000
It's an analogy,
OK to get some insight into how

263
00:16:16,000 --> 00:16:19,000
to do this.
So, I say here's an object.

264
00:16:19,000 --> 00:16:22,000
I apply a force,
and I ask you the question.

265
00:16:22,000 --> 00:16:27,000
What is the acceleration of the
object when I apply a force,

266
00:16:27,000 --> 00:16:31,000
F?
So, how would you do it?

267
00:16:31,000 --> 00:16:33,000
OK, and eighth,
or ninth, or tenth grader can

268
00:16:33,000 --> 00:16:36,000
do this.
OK, they would ask me,

269
00:16:36,000 --> 00:16:39,000
what's the mass of the object?
OK, I ask you what is the

270
00:16:39,000 --> 00:16:42,000
acceleration?
You would turn around and ask

271
00:16:42,000 --> 00:16:44,000
me, what is the mass of the
object?

272
00:16:44,000 --> 00:16:47,000
I tell you, the mass of the
object is M.

273
00:16:47,000 --> 00:16:50,000
And then you say,
oh sure, A is F divided by M,

274
00:16:50,000 --> 00:16:52,000
done.
It's as simple as that.

275
00:16:52,000 --> 00:16:56,000
OK, I could have gone into all
kinds of differential equations

276
00:16:56,000 --> 00:17:02,000
and so on to figure that out,
but you asked me for the mass.

277
00:17:02,000 --> 00:17:05,000
And you gave me the answer,
A is F divided by M.

278
00:17:05,000 --> 00:17:08,000
So, you ignored a bunch of
things.

279
00:17:08,000 --> 00:17:10,000
You ignored the shape of the
object.

280
00:17:10,000 --> 00:17:14,000
You ignored its color.
You ignored its temperature.

281
00:17:14,000 --> 00:17:17,000
OK, and you ignored the soft or
hard or whatever.

282
00:17:17,000 --> 00:17:20,000
OK, you ignored a whole bunch
of things.

283
00:17:20,000 --> 00:17:25,000
You were focused on one thing.
OK, you're focused on its mass.

284
00:17:25,000 --> 00:17:29,000
And, it turns out that the
process really was developed

285
00:17:29,000 --> 00:17:34,000
from a set of simplifications.
That is called,

286
00:17:34,000 --> 00:17:40,000
does anybody remember this?
Point mass simplification.

287
00:17:40,000 --> 00:17:44,000
OK, so, in physics,
you've done this before.

288
00:17:44,000 --> 00:17:49,000
OK, you've simplified your
lives by viewing objects as

289
00:17:49,000 --> 00:17:55,000
having a mass at a point,
and force is acting at that

290
00:17:55,000 --> 00:17:58,000
point.
OK, M is that property of the

291
00:17:58,000 --> 00:18:02,000
object that is of interest to
you.

292
00:18:02,000 --> 00:18:06,000
This process is called,
in physics, point mass

293
00:18:06,000 --> 00:18:14,000
discretization.
OK, now using an analogy,

294
00:18:14,000 --> 00:18:24,000
and I'm going to show you a
similar simple process to do the

295
00:18:24,000 --> 00:18:31,000
problem with the light bulb.
OK, so take my light bulb

296
00:18:31,000 --> 00:18:32,000
again,

297
00:18:42,000 --> 00:18:44,000
And I focus on the filament of
the light bulb.

298
00:18:44,000 --> 00:18:48,000
OK, all I care about is the
current flowing through the

299
00:18:48,000 --> 00:18:50,000
light bulb.
OK, I don't care about whether

300
00:18:50,000 --> 00:18:53,000
the filament is twisted,
whether it's hot.

301
00:18:53,000 --> 00:18:57,000
I don't care about its shape.
I don't care about its color.

302
00:18:57,000 --> 00:19:00,000
All I care about is the
current.

303
00:19:00,000 --> 00:19:03,000
OK, so to do that,
what we can do here at a very

304
00:19:03,000 --> 00:19:07,000
high level is since we just need
the current and don't care about

305
00:19:07,000 --> 00:19:12,000
a bunch of other properties,
we will simply replace the bulb

306
00:19:12,000 --> 00:19:15,000
with a discrete object called a
resistor.

307
00:19:15,000 --> 00:19:19,000
So the discrete object is a
resistor, much like the point

308
00:19:19,000 --> 00:19:23,000
mass simplification that we did
earlier that replaced the bulb

309
00:19:23,000 --> 00:19:27,000
filament with a object called a
resistor, a discrete object

310
00:19:27,000 --> 00:19:31,000
called a resistor.
Or a lump object called

311
00:19:31,000 --> 00:19:37,000
resister, and put a value next
to it just like the mass for the

312
00:19:37,000 --> 00:19:39,000
object, a resistance value,
R.

313
00:19:39,000 --> 00:19:44,000
OK, now what I can do is in the
same manner, replace the battery

314
00:19:44,000 --> 00:19:49,000
with an object called a battery
object, and connect that here,

315
00:19:49,000 --> 00:19:52,000
the voltage,
V, applied to it.

316
00:19:52,000 --> 00:19:56,000
V falls across the resistor,
and I get my I simply from

317
00:19:56,000 --> 00:20:01,000
Ohm's law as we divide by R.
So, notice here,

318
00:20:01,000 --> 00:20:04,000
to replace this complicated
bulb, this really twisty,

319
00:20:04,000 --> 00:20:07,000
weird old thing with this
discreet thing called a

320
00:20:07,000 --> 00:20:11,000
resistor, and its only property
of interest was its resistance

321
00:20:11,000 --> 00:20:14,000
value, R, direct analogy to what
we did there.

322
00:20:14,000 --> 00:20:18,000
So, since R represents the only
property of interest,

323
00:20:18,000 --> 00:20:21,000
we can simply ignore all the
other things.

324
00:20:21,000 --> 00:20:24,000
So, notice here,
we've done things the simple

325
00:20:24,000 --> 00:20:25,000
way.
And remember,

326
00:20:25,000 --> 00:20:28,000
in EE, in the electrical
engineering, we do things the

327
00:20:28,000 --> 00:20:33,000
simple way.
OK, we could go the hard route

328
00:20:33,000 --> 00:20:37,000
and do Maxwell's equations,
and get PhD's in physics,

329
00:20:37,000 --> 00:20:38,000
and so on.
But out here,

330
00:20:38,000 --> 00:20:42,000
we are looking to do useful,
interesting systems in the

331
00:20:42,000 --> 00:20:46,000
simplest way that we can.
OK, we do things a simple way.

332
00:20:46,000 --> 00:20:51,000
All right, so we just did this,
and boom, I found out what the

333
00:20:51,000 --> 00:20:54,000
current was.
Now, I cheated a little bit.

334
00:20:54,000 --> 00:20:58,000
I've cheated a little bit.
R is a lumped abstraction for

335
00:20:58,000 --> 00:21:01,000
the bulb.
So, you look at this resistor

336
00:21:01,000 --> 00:21:04,000
here.
That is simply a placeholder.

337
00:21:04,000 --> 00:21:08,000
It's a stand-in for this
complicated thing called a bulb.

338
00:21:08,000 --> 00:21:11,000
It's a discreet object.
It's a lumped object,

339
00:21:11,000 --> 00:21:14,000
and represents the bulb.
Now, so most of 6.002 will take

340
00:21:14,000 --> 00:21:17,000
off from here,
OK, and that's it.

341
00:21:17,000 --> 00:21:20,000
To very simple stuff,
like V is equal to IR,

342
00:21:20,000 --> 00:21:23,000
it's a simple high school
algebra to take off in that

343
00:21:23,000 --> 00:21:25,000
direction.
But before we go there,

344
00:21:25,000 --> 00:21:30,000
it's important to understand,
why was it that we were able to

345
00:21:30,000 --> 00:21:34,000
make the simplification?
OK, we did something else.

346
00:21:34,000 --> 00:21:37,000
Something's going on under the
covers here.

347
00:21:37,000 --> 00:21:39,000
On the one hand,
I say let's use Maxwell's,

348
00:21:39,000 --> 00:21:42,000
and then I jump out and say,
hey, we can just use this

349
00:21:42,000 --> 00:21:45,000
simple thing.
I did something that allowed me

350
00:21:45,000 --> 00:21:48,000
to go from here to here.
And you need to understand why

351
00:21:48,000 --> 00:21:51,000
I did that and how I did that.
Understand it once,

352
00:21:51,000 --> 00:21:54,000
and then you won't have to need
that information again.

353
00:21:54,000 --> 00:21:58,000
You just need to understand it.
So, let's take a closer look at

354
00:21:58,000 --> 00:22:02,000
the bulb filament,
and look at what we really did.

355
00:22:02,000 --> 00:22:08,000
So, here's my filament,
A, and let's say that the

356
00:22:08,000 --> 00:22:12,000
surface area here,
I label that SA,

357
00:22:12,000 --> 00:22:17,000
and the one down here SB,
my voltage, V,

358
00:22:17,000 --> 00:22:23,000
applied there,
and this is what I call my

359
00:22:23,000 --> 00:22:28,000
black box that I've replaced
with a resistor.

360
00:22:28,000 --> 00:22:33,000
Notice that,
in order for this to work,

361
00:22:33,000 --> 00:22:40,000
V and I need to be defined.
So I needs to be defined,

362
00:22:40,000 --> 00:22:45,000
and V needs to be defined.
OK, if I give you a random

363
00:22:45,000 --> 00:22:49,000
object, and I don't tell you
anything else about the object,

364
00:22:49,000 --> 00:22:54,000
it's not clear I can do that.
OK, if it's a much more general

365
00:22:54,000 --> 00:22:58,000
situation, I have to write down
Maxwell's equations,

366
00:22:58,000 --> 00:23:01,000
and this is what I would write
down.

367
00:23:01,000 --> 00:23:05,000
Write down J dot dS as a
function of the coordinate here

368
00:23:05,000 --> 00:23:10,000
integrated over the area minus,
OK, I would have to start from

369
00:23:10,000 --> 00:23:15,000
there from one of Maxwell's
equations.

370
00:23:15,000 --> 00:23:19,000
All right, notice that this
becomes IA, and this becomes IB

371
00:23:19,000 --> 00:23:23,000
in our simplification.
But, if I don't tell you

372
00:23:23,000 --> 00:23:26,000
anything else,
you have to start from here.

373
00:23:26,000 --> 00:23:31,000
You will have some varying
current here by point.

374
00:23:31,000 --> 00:23:34,000
You might have some other
current coming out here because

375
00:23:34,000 --> 00:23:38,000
I may have some charge buildup
happening inside.

376
00:23:38,000 --> 00:23:41,000
If charge is building up inside
the filament;

377
00:23:41,000 --> 00:23:44,000
then I would have to put del q
by del t out here,

378
00:23:44,000 --> 00:23:48,000
right, the current in minus the
current out must equal charge

379
00:23:48,000 --> 00:23:51,000
buildup.
Whoa, where is this and where

380
00:23:51,000 --> 00:23:53,000
is that?
So this is reality.

381
00:23:53,000 --> 00:23:55,000
This is really,
really what I have to do.

382
00:23:55,000 --> 00:24:00,000
But how did I get there?
How did I get there?

383
00:24:00,000 --> 00:24:02,000
The key answer is,
as engineers,

384
00:24:02,000 --> 00:24:05,000
when in doubt we simplify.
Remember, we are engineers.

385
00:24:05,000 --> 00:24:09,000
Our goal in life is to build
interesting systems.

386
00:24:09,000 --> 00:24:11,000
OK and some are motivated by
money.

387
00:24:11,000 --> 00:24:15,000
OK, so our goal is to build
interesting systems and do good

388
00:24:15,000 --> 00:24:18,000
to humanity.
So, as long as we can build a

389
00:24:18,000 --> 00:24:20,000
good light bulb,
we are happy.

390
00:24:20,000 --> 00:24:23,000
So what we can do is we can
say, look, all I care about is

391
00:24:23,000 --> 00:24:26,000
building interesting systems.
So I can say,

392
00:24:26,000 --> 00:24:32,000
hey, this stuff is too hard.
Let's make the assumption that

393
00:24:32,000 --> 00:24:36,000
all the systems that we will
consider will have this thing be

394
00:24:36,000 --> 00:24:37,000
zero.
OK, in other words,

395
00:24:37,000 --> 00:24:41,000
if I take a complete object,
if I take an element like a

396
00:24:41,000 --> 00:24:44,000
resistor or a capacitor,
the box around the entire

397
00:24:44,000 --> 00:24:48,000
element, OK, and I want to just
deal with those systems in which

398
00:24:48,000 --> 00:24:52,000
this thing is zero.
You can come and beat me up and

399
00:24:52,000 --> 00:24:53,000
say, but why?
Why not?

400
00:24:53,000 --> 00:24:57,000
Why am I doing this?
And I am saying the world is

401
00:24:57,000 --> 00:24:58,000
arbitrary.
I'm an engineer;

402
00:24:58,000 --> 00:25:04,000
I want to build good systems.
By making this simplification,

403
00:25:04,000 --> 00:25:07,000
I eliminate this squiggle
thing, and so on.

404
00:25:07,000 --> 00:25:11,000
I don't want to deal with it.
I want to make my life simple.

405
00:25:11,000 --> 00:25:14,000
So this is gone to zero
because, why?

406
00:25:14,000 --> 00:25:19,000
Because I have said that in the
future I will only deal with

407
00:25:19,000 --> 00:25:21,000
those elements for which this is
true.

408
00:25:21,000 --> 00:25:26,000
I'm going to discipline myself.
I'm going to discipline myself

409
00:25:26,000 --> 00:25:32,000
to only deal with those systems.
OK, Maxwell is turning around

410
00:25:32,000 --> 00:25:36,000
and, you know,
mad at me and all that stuff,

411
00:25:36,000 --> 00:25:39,000
but tough.
So this, what I've said about

412
00:25:39,000 --> 00:25:43,000
making a simplification here,
and this is one of the

413
00:25:43,000 --> 00:25:48,000
simplifications I'm making.
And I give a name to the

414
00:25:48,000 --> 00:25:51,000
simplification.
And that's called the lumped

415
00:25:51,000 --> 00:25:55,000
matter discipline.
OK, so I'm saying I will only

416
00:25:55,000 --> 00:26:00,000
deal with elements for which if
I put a black box around it,

417
00:26:00,000 --> 00:26:06,000
this is going to be true.
And if this is going to be

418
00:26:06,000 --> 00:26:10,000
true, then notice,
there is no charge buildup.

419
00:26:10,000 --> 00:26:13,000
Current in must equal current
out.

420
00:26:13,000 --> 00:26:15,000
Ah-ha!
So this becomes IA.

421
00:26:15,000 --> 00:26:16,000
This becomes IB.
Yes.

422
00:26:16,000 --> 00:26:20,000
OK, I can now deal with IA's
and IB's.

423
00:26:20,000 --> 00:26:24,000
And IB and IA are equal because
this is zero.

424
00:26:24,000 --> 00:26:29,000
Notice that there is a whole
bunch of depth here in the jump

425
00:26:29,000 --> 00:26:33,000
from here to here.
As MIT graduates,

426
00:26:33,000 --> 00:26:37,000
you really, really need to
understand why it is that we

427
00:26:37,000 --> 00:26:40,000
made that jump,
and then go and use that,

428
00:26:40,000 --> 00:26:43,000
and do cool things.
All right, this allows us to

429
00:26:43,000 --> 00:26:46,000
define I.
We have a unique I associated

430
00:26:46,000 --> 00:26:50,000
with an element for the current
through the element.

431
00:26:50,000 --> 00:26:55,000
We still have to worry about B,
and I won't go through that in

432
00:26:55,000 --> 00:26:57,000
detail.
The course notes have some

433
00:26:57,000 --> 00:27:02,000
discussion of that and so does
the textbook.

434
00:27:02,000 --> 00:27:07,000
So V, AB is defined when del
phi B, the rate of change of

435
00:27:07,000 --> 00:27:11,000
magnetic flux is zero.
So, if I take the element and I

436
00:27:11,000 --> 00:27:16,000
take any region outside the
element, this must be true.

437
00:27:16,000 --> 00:27:20,000
And you say,
why should that be true?

438
00:27:20,000 --> 00:27:23,000
That's not true in general.
Absolutely.

439
00:27:23,000 --> 00:27:28,000
It's not true in general.
But I, because I choose to,

440
00:27:28,000 --> 00:27:33,000
I going to deal with only those
elements.

441
00:27:33,000 --> 00:27:36,000
I will discipline myself.
But these are only those

442
00:27:36,000 --> 00:27:39,000
elements for which this is true,
and this is true.

443
00:27:39,000 --> 00:27:42,000
I'm going to limit my world.
I'm going to create a play

444
00:27:42,000 --> 00:27:44,000
field for myself.
You want to play;

445
00:27:44,000 --> 00:27:47,000
follow my rules.
OK, and that's called the

446
00:27:47,000 --> 00:27:50,000
lumped matter discipline.
So once you say that I'm going

447
00:27:50,000 --> 00:27:54,000
to adhere to the lump matter
discipline, and this is true

448
00:27:54,000 --> 00:27:56,000
inside your elements.
This is true outside the

449
00:27:56,000 --> 00:27:59,000
elements.
You can define VA and VB,

450
00:27:59,000 --> 00:28:03,000
and good things happen to you.
OK, let me show you a few

451
00:28:03,000 --> 00:28:06,000
examples of lumped elements.
But remember,

452
00:28:06,000 --> 00:28:10,000
a large part of what we're
doing is based on these two

453
00:28:10,000 --> 00:28:13,000
assumptions.
And to just go through the

454
00:28:13,000 --> 00:28:17,000
background on that,
I would encourage you to go to

455
00:28:17,000 --> 00:28:21,000
chapter 1 of your course notes
and read through just as how

456
00:28:21,000 --> 00:28:23,000
this came about,
that comes about.

457
00:28:23,000 --> 00:28:28,000
So, by doing that by adhering
to a lumped matter discipline,

458
00:28:28,000 --> 00:28:32,000
we can now lump objects.
We could lump a bulb into a

459
00:28:32,000 --> 00:28:34,000
resistor.
OK, so to be clear,

460
00:28:34,000 --> 00:28:36,000
a certain number of lumped
objects, and now,

461
00:28:36,000 --> 00:28:40,000
the universe is going to be
comprised into lumped objects.

462
00:28:40,000 --> 00:28:42,000
OK, so before this,
when he went home,

463
00:28:42,000 --> 00:28:44,000
we talked about eggs,
and omelets,

464
00:28:44,000 --> 00:28:46,000
and light bulbs,
and switches,

465
00:28:46,000 --> 00:28:49,000
but once you come to MIT,
and after you've taken 6.002,

466
00:28:49,000 --> 00:28:52,000
you begin talking about lumped
elements, you know,

467
00:28:52,000 --> 00:28:55,000
resistors, voltage sources,
capacitors, little inky-dinky

468
00:28:55,000 --> 00:29:00,000
objects that follow the lumped
matter discipline.

469
00:29:00,000 --> 00:29:04,000
OK, they stick to very simple
rules, and the math that you

470
00:29:04,000 --> 00:29:07,000
have to do to analyze them is
incredibly simple.

471
00:29:07,000 --> 00:29:11,000
What could be simpler than V is
equal to IR?

472
00:29:11,000 --> 00:29:15,000
So, let me give you an example
of interesting lumped elements,

473
00:29:15,000 --> 00:29:20,000
and then show you a couple of
really nasty lumped elements.

474
00:29:20,000 --> 00:29:21,000
OK.

475
00:29:29,000 --> 00:29:33,000
OK, so what you see out here,
so we characterize lumped

476
00:29:33,000 --> 00:29:35,000
elements by the VI
characteristics.

477
00:29:35,000 --> 00:29:39,000
OK, you apply voltage,
measure the current.

478
00:29:39,000 --> 00:29:43,000
OK, so what I can do is I can
plot I here, and V here,

479
00:29:43,000 --> 00:29:48,000
and see what it looks like.
OK, I can characterize elements

480
00:29:48,000 --> 00:29:51,000
by their VI relationship.
And there are a bunch of

481
00:29:51,000 --> 00:29:56,000
elements that I can create based
on the VI relationship.

482
00:29:56,000 --> 00:30:00,000
So let me show you a few
examples.

483
00:30:00,000 --> 00:30:02,000
So for the resistor,
since V is directly

484
00:30:02,000 --> 00:30:05,000
proportional to I,
and R is a constant,

485
00:30:05,000 --> 00:30:08,000
I get a straight line.
That's the I axis,

486
00:30:08,000 --> 00:30:11,000
the V axis, and this is the
resistor.

487
00:30:11,000 --> 00:30:14,000
What I actually have is a
variable resistor,

488
00:30:14,000 --> 00:30:17,000
so I'm going to change the
resistance value,

489
00:30:17,000 --> 00:30:20,000
R, and the curve will also
change slope.

490
00:30:20,000 --> 00:30:24,000
OK, I changed the value of R
because it's a variable

491
00:30:24,000 --> 00:30:30,000
resistor, and the changes slope
because my R is different.

492
00:30:30,000 --> 00:30:34,000
OK, next, let me go to a fixed
resistor, and this guy here on

493
00:30:34,000 --> 00:30:37,000
the screen to your left is a
fixed resistor.

494
00:30:37,000 --> 00:30:41,000
And you see that its IV
characteristic is a line of a

495
00:30:41,000 --> 00:30:44,000
given slope, 1 by R,
and that's it.

496
00:30:44,000 --> 00:30:46,000
I can't change it.
Number three,

497
00:30:46,000 --> 00:30:51,000
I have another lumped element
called a Zener diode that you

498
00:30:51,000 --> 00:30:54,000
will see in the fourth week of
this class, and the

499
00:30:54,000 --> 00:30:58,000
characteristics for the Zener
diode look like this:

500
00:30:58,000 --> 00:31:01,000
IV.
If my voltage goes across the

501
00:31:01,000 --> 00:31:04,000
Zener diode goes up slightly,
the current shoots up.

502
00:31:04,000 --> 00:31:07,000
But if the voltage becomes
negative I don't have any

503
00:31:07,000 --> 00:31:11,000
current flowing into it until
the voltage passes on the

504
00:31:11,000 --> 00:31:14,000
threshold, at which point my
current begins to build up.

505
00:31:14,000 --> 00:31:17,000
OK, so I can increase the
voltage a little bit,

506
00:31:17,000 --> 00:31:20,000
and it can show that the
current starts building up

507
00:31:20,000 --> 00:31:22,000
again.
So that's another interesting

508
00:31:22,000 --> 00:31:24,000
lumped element called a Zener
diode.

509
00:31:24,000 --> 00:31:26,000
Let's switch to the next one
called a diode.

510
00:31:26,000 --> 00:31:30,000
So a diode looks like this:
IV.

511
00:31:30,000 --> 00:31:33,000
As the voltage across the diode
becomes positive,

512
00:31:33,000 --> 00:31:35,000
around .6 volts,
or thereabout,

513
00:31:35,000 --> 00:31:40,000
the current begins to shoot up.
But when the voltage is below

514
00:31:40,000 --> 00:31:44,000
that threshold of .6,
then my current is almost zero.

515
00:31:44,000 --> 00:31:47,000
It's another lumped element
called a diode.

516
00:31:47,000 --> 00:31:51,000
And you will begin using these
elements in your 002 lives to

517
00:31:51,000 --> 00:31:55,000
build interesting systems.
The next example is a

518
00:31:55,000 --> 00:31:57,000
thermistor.
A thermistor is a resistor

519
00:31:57,000 --> 00:32:02,000
whose resistance varies with
temperature.

520
00:32:02,000 --> 00:32:08,000
OK, so this is a very expensive
little hairdryer,

521
00:32:08,000 --> 00:32:14,000
and what I'm going to do is
blow some hot air at my

522
00:32:14,000 --> 00:32:22,000
resistor, and you're going to
see that its value is going to

523
00:32:22,000 --> 00:32:27,000
change depending on how much I
heat it.

524
00:32:27,000 --> 00:32:32,000
So as it cools down,
let me cool it down,

525
00:32:32,000 --> 00:32:38,000
so you can see it's coming
down.

526
00:32:38,000 --> 00:32:41,000
I can zap it again.
I could do this all day.

527
00:32:41,000 --> 00:32:45,000
This is so much fun.
OK, so that's another

528
00:32:45,000 --> 00:32:49,000
interesting lumped element.
As the temperature rises,

529
00:32:49,000 --> 00:32:53,000
its resistance changes.
The next thing is called a

530
00:32:53,000 --> 00:32:56,000
photo resistor.
It's a resistor.

531
00:32:56,000 --> 00:33:00,000
It used to be a resistor;
Lorenzo?

532
00:33:00,000 --> 00:33:03,000
Oh OK, that's fine.
So this is a photo resistor.

533
00:33:03,000 --> 00:33:08,000
And notice that it almost
behaves like an open circuit.

534
00:33:08,000 --> 00:33:12,000
But what I'm going to do is
shine some light on it.

535
00:33:12,000 --> 00:33:16,000
When I shine light on it,
it begins to conduct and

536
00:33:16,000 --> 00:33:18,000
becomes a resistor of some
value.

537
00:33:18,000 --> 00:33:22,000
There you go.
OK, so that's a photo resistor.

538
00:33:22,000 --> 00:33:25,000
So now I'm going to show you a
battery.

539
00:33:25,000 --> 00:33:30,000
Notice we did talk about
batteries before.

540
00:33:30,000 --> 00:33:33,000
I'll show you a battery.
So before you show a battery,

541
00:33:33,000 --> 00:33:36,000
just thinking your own minds,
what should the IV

542
00:33:36,000 --> 00:33:39,000
characteristic of a battery look
like?

543
00:33:39,000 --> 00:33:41,000
IV.
A battery supplies a constant

544
00:33:41,000 --> 00:33:44,000
voltage.
You know your little cell,

545
00:33:44,000 --> 00:33:45,000
the AA battery,
1.5 volts?

546
00:33:45,000 --> 00:33:49,000
So, think of what the IV
characteristic of a battery

547
00:33:49,000 --> 00:33:53,000
should look like for three
seconds before it shows you.

548
00:33:53,000 --> 00:33:55,000
This is the one I showed,
Lorenzo?.

549
00:33:55,000 --> 00:34:00,000
It's a straight line.
This is a good battery.

550
00:34:00,000 --> 00:34:01,000
It's a straight,
vertical line,

551
00:34:01,000 --> 00:34:05,000
but says that the voltage is
1.5 volts, or thereabouts.

552
00:34:05,000 --> 00:34:08,000
No matter what current it
supplies as an ideal voltage

553
00:34:08,000 --> 00:34:12,000
source, it has a fixed voltage,
V, and no matter what the

554
00:34:12,000 --> 00:34:15,000
current going through is.
Now, I'll show you a dud,

555
00:34:15,000 --> 00:34:18,000
a bad battery,
and this is what the bad

556
00:34:18,000 --> 00:34:21,000
battery looks like.
So, many of you have had your

557
00:34:21,000 --> 00:34:24,000
car batteries die on you.
When you go to the store,

558
00:34:24,000 --> 00:34:27,000
they check your batteries.
They use exactly this

559
00:34:27,000 --> 00:34:32,000
principle, that dead batteries
have resistance.

560
00:34:32,000 --> 00:34:34,000
By the way, you see slopes
here.

561
00:34:34,000 --> 00:34:38,000
You're thinking of resistance.
OK, they can use this property

562
00:34:38,000 --> 00:34:41,000
to figure out that your battery
is dead.

563
00:34:41,000 --> 00:34:44,000
So that's a dead battery.
And finally,

564
00:34:44,000 --> 00:34:47,000
let me show you a bulb.
We started with a bulb,

565
00:34:47,000 --> 00:34:51,000
and so I need to end,
OK, we started with a bulb,

566
00:34:51,000 --> 00:34:55,000
so I need to end with a bulb.
And what you will see is that a

567
00:34:55,000 --> 00:34:57,000
bulb simply behaves like a
resistor.

568
00:34:57,000 --> 00:35:02,000
Its IV curve is going to look
like this.

569
00:35:02,000 --> 00:35:04,000
OK, notice this is my bulb.
And guess what,

570
00:35:04,000 --> 00:35:08,000
it behaves like a resistor.
It's a very interesting kind of

571
00:35:08,000 --> 00:35:11,000
resistor, so I won't go into
details for now.

572
00:35:11,000 --> 00:35:14,000
But notice its IV
characteristic behaves like a

573
00:35:14,000 --> 00:35:17,000
resistor.
OK, so those are some pretty

574
00:35:17,000 --> 00:35:20,000
standard lumped elements.
You deal with a lot more sets

575
00:35:20,000 --> 00:35:23,000
of lumped elements,
switches, MOSFETs,

576
00:35:23,000 --> 00:35:26,000
capacitors, inductors,
a bunch of other fun stuff.

577
00:35:26,000 --> 00:35:29,000
But before we do that,
what I wanted to tell you,

578
00:35:29,000 --> 00:35:34,000
don't go berserk on this
abstraction binge.

579
00:35:34,000 --> 00:35:36,000
Too much of anything is bad for
you.

580
00:35:36,000 --> 00:35:39,000
So what I'm going to show you
is, abstractions or models are

581
00:35:39,000 --> 00:35:43,000
only valid provided you work
within a set of constraints.

582
00:35:43,000 --> 00:35:46,000
Notice, we have already had
this tacit handshake which said

583
00:35:46,000 --> 00:35:49,000
that we follow the discipline.
Even after we follow the

584
00:35:49,000 --> 00:35:53,000
discipline, there are ranges to
how well physical elements can

585
00:35:53,000 --> 00:35:55,000
behave like ideal lumped
elements.

586
00:35:55,000 --> 00:35:58,000
OK, for example,
what we will do is show you the

587
00:35:58,000 --> 00:36:02,000
resistor.
And it's going to look like a

588
00:36:02,000 --> 00:36:04,000
resistor.
And I'm going to keep

589
00:36:04,000 --> 00:36:07,000
increasing the voltage around
it.

590
00:36:07,000 --> 00:36:10,000
OK, what's going to happen at
some point?

591
00:36:10,000 --> 00:36:14,000
I just keep doing that.
If it's an ideal element,

592
00:36:14,000 --> 00:36:17,000
if you're a theorist,
you say, oh yeah,

593
00:36:17,000 --> 00:36:22,000
the curve will keep extending
until I reach infinity.

594
00:36:22,000 --> 00:36:26,000
But this is a practical
resistor, so people out here can

595
00:36:26,000 --> 00:36:31,000
cover your eyes or something.
OK, so you're abstraction can't

596
00:36:31,000 --> 00:36:36,000
predict that.
All it says is the current is

597
00:36:36,000 --> 00:36:38,000
an amp.
It can't predict the heat,

598
00:36:38,000 --> 00:36:41,000
light, or the smell.
In the laboratory,

599
00:36:41,000 --> 00:36:45,000
even, you get the smell.
You know what somebody has just

600
00:36:45,000 --> 00:36:47,000
done.
So that's one example of the

601
00:36:47,000 --> 00:36:50,000
lumped abstraction breaking
down.

602
00:36:50,000 --> 00:36:54,000
So, if I really believe that my
own BS, anything is a lumped

603
00:36:54,000 --> 00:36:56,000
element.
So here's a pickle.

604
00:36:56,000 --> 00:37:02,000
A pickle is a lumped element.
I can choose it as a lumped

605
00:37:02,000 --> 00:37:05,000
resistor.
But this is a very interesting

606
00:37:05,000 --> 00:37:09,000
lumped resistor.
Don't try this at home.

607
00:37:09,000 --> 00:37:14,000
This is a standard pickle into
which you are pumping 110 V AC.

608
00:37:14,000 --> 00:37:18,000
I promise you,
this is a standard pickle.

609
00:37:18,000 --> 00:37:23,000
So, it has a fixed resistance,
but your lumped abstraction

610
00:37:23,000 --> 00:37:27,000
cannot predict the nice light
and sound effect.

611
00:37:27,000 --> 00:37:32,000
OK, so the last two or three
minutes what I want to do,

612
00:37:32,000 --> 00:37:35,000
so remember,
don't get carried away by

613
00:37:35,000 --> 00:37:39,000
abstractions.
There are limits.

614
00:37:39,000 --> 00:37:42,000
OK, you can't predict
everything.

615
00:37:42,000 --> 00:37:45,000
OK, that's the smell of a
pickle.

616
00:37:45,000 --> 00:37:49,000
OK, so let me give you a
preview of some upcoming

617
00:37:49,000 --> 00:37:55,000
attractions, and show you one
more quick simplification in the

618
00:37:55,000 --> 00:37:58,000
last few minutes.
So what we can do,

619
00:37:58,000 --> 00:38:03,000
once we build these lumped
elements, we can connect them in

620
00:38:03,000 --> 00:38:07,000
circuits.
OK, so I can build a circuit,

621
00:38:07,000 --> 00:38:10,000
of the sort.
So here's a voltage source with

622
00:38:10,000 --> 00:38:14,000
a bunch of resistors.
I can connect them with wires

623
00:38:14,000 --> 00:38:18,000
and build a circuit of the sort.
One interesting question we can

624
00:38:18,000 --> 00:38:21,000
ask ourselves is,
under the lumped matter

625
00:38:21,000 --> 00:38:24,000
discipline, what can we say
about the voltages?

626
00:38:24,000 --> 00:38:28,000
OK, if I go around the loop,
provided my world adheres to

627
00:38:28,000 --> 00:38:32,000
the lumped matter discipline,
what can I say about the

628
00:38:32,000 --> 00:38:36,000
voltages around this loop?
Ah-ha, Maxwell again,

629
00:38:36,000 --> 00:38:39,000
right?
So, I can write Maxwell's

630
00:38:39,000 --> 00:38:42,000
appropriate equation to solve
that.

631
00:38:42,000 --> 00:38:47,000
OK, voltages have something to
do with E and your integral of E

632
00:38:47,000 --> 00:38:50,000
dot dl and all of that stuff,
right?

633
00:38:50,000 --> 00:38:54,000
So this is the appropriate
Maxwell's equations to use.

634
00:38:54,000 --> 00:38:58,000
And I want to find out what
happens here.

635
00:38:58,000 --> 00:39:00,000
Now remember,
under LMD, I made the

636
00:39:00,000 --> 00:39:04,000
assumption.
OK, my world,

637
00:39:04,000 --> 00:39:09,000
my playground,
has del phi B by del t being

638
00:39:09,000 --> 00:39:13,000
zero.
The rate of change of flux is

639
00:39:13,000 --> 00:39:16,000
zero.
So, under these circumstances,

640
00:39:16,000 --> 00:39:21,000
I can write this.
I can break up this line

641
00:39:21,000 --> 00:39:28,000
integral into three parts across
the voltage source and across

642
00:39:28,000 --> 00:39:34,000
the two resistors and write that
down.

643
00:39:34,000 --> 00:39:38,000
OK, and then when I can do,
is now that the right-hand side

644
00:39:38,000 --> 00:39:42,000
is zero, I can simply take this.
And I know that E dot dl across

645
00:39:42,000 --> 00:39:45,000
this element is simply VCA.
This is VAB,

646
00:39:45,000 --> 00:39:49,000
and this is VBC equals zero.
OK, so when I make the

647
00:39:49,000 --> 00:39:53,000
assumption that del phi B by del
t is zero, and I go around this

648
00:39:53,000 --> 00:39:58,000
loop, apply Maxwell's equations,
what do I find?

649
00:39:58,000 --> 00:40:03,000
I find that the sum of the
voltages, VCA plus VAB plus VBC,

650
00:40:03,000 --> 00:40:06,000
is zero.
That's fantastic.

651
00:40:06,000 --> 00:40:11,000
So now, I could say hasta la
vista to this baby here.

652
00:40:11,000 --> 00:40:17,000
And I can focus on this guy and
say, Maxwell's equations,

653
00:40:17,000 --> 00:40:22,000
this thing with squiggles and
dels and all that stuff,

654
00:40:22,000 --> 00:40:28,000
can be simplified to the sum of
the voltages across a set of

655
00:40:28,000 --> 00:40:34,000
elements in a loop in a circuit
is zero.

656
00:40:34,000 --> 00:40:39,000
OK, and this is called
Kirchhoff's first first law,

657
00:40:39,000 --> 00:40:40,000
KVL.
OK, similarly,

658
00:40:40,000 --> 00:40:46,000
in recitation section,
you'll see the application of

659
00:40:46,000 --> 00:40:51,000
Kirchhoff's current law,
which comes from this be equal

660
00:40:51,000 --> 00:40:57,000
to zero, and all the currents
coming into a node being zero.

661
00:40:57,000 --> 00:41:02,000
So, KVL and KCl directly come
out of the lumped matter

662
00:41:02,000 --> 00:41:06,000
discipline.
And you can use those to solve

663
00:41:06,000 --> 00:41:09,000
circuits like this.