1
00:00:00,000 --> 00:00:00,760
 

2
00:00:00,760 --> 00:00:06,010
Well, we've spent many videos
talking about electrostatic

3
00:00:06,010 --> 00:00:10,160
fields and the potential on a
charge or the potential energy

4
00:00:10,160 --> 00:00:11,930
of a charge when it's
in one place.

5
00:00:11,930 --> 00:00:15,330
But let's see what happens
where, given a potential, what

6
00:00:15,330 --> 00:00:18,060
happens when we actually allow
the charge to move?

7
00:00:18,060 --> 00:00:20,490
And this will probably be a lot
more interesting to you,

8
00:00:20,490 --> 00:00:26,070
because you'll learn how much
of the modern world works.

9
00:00:26,070 --> 00:00:30,120
So let's say that I have
a source of voltage.

10
00:00:30,120 --> 00:00:32,220
Let me see how I want
to draw that.

11
00:00:32,220 --> 00:00:34,430
I'm going to draw
that like that.

12
00:00:34,430 --> 00:00:36,930
I'll draw it in yellow.

13
00:00:36,930 --> 00:00:39,580
So this is my source
of voltage,

14
00:00:39,580 --> 00:00:41,990
often known as a battery.

15
00:00:41,990 --> 00:00:43,310
This is the positive terminal.

16
00:00:43,310 --> 00:00:44,830
This is the negative terminal.

17
00:00:44,830 --> 00:00:48,230
It's a whole other subject, a
whole other video, and I'll

18
00:00:48,230 --> 00:00:51,080
make one eventually, of
how a battery works.

19
00:00:51,080 --> 00:00:54,590
But let's just say that no
matter how much current--

20
00:00:54,590 --> 00:00:58,260
well, actually, let me explain
in a second, but no matter how

21
00:00:58,260 --> 00:01:01,860
much charge flows out of one
side of a battery to the other

22
00:01:01,860 --> 00:01:04,010
side of the battery,
that somehow the

23
00:01:04,010 --> 00:01:06,040
voltages remain constant.

24
00:01:06,040 --> 00:01:08,090
So that's kind of a
non-intuitive thing, because

25
00:01:08,090 --> 00:01:10,290
we learned about capacitors, and
we will learn more about

26
00:01:10,290 --> 00:01:13,180
capacitors in the context of
circuits, but what we learned

27
00:01:13,180 --> 00:01:17,200
about a capacitor is that if we
got rid of some charge on

28
00:01:17,200 --> 00:01:19,540
one end, the total voltage
across the

29
00:01:19,540 --> 00:01:20,130
capacitor will decrease.

30
00:01:20,130 --> 00:01:22,930
But a battery is this
magical thing.

31
00:01:22,930 --> 00:01:25,920
I think it was invented by
Volta, and that's why we call

32
00:01:25,920 --> 00:01:28,040
everything volts and voltage
and all of that.

33
00:01:28,040 --> 00:01:33,810
But it's this magical thing
that, even as one side loses

34
00:01:33,810 --> 00:01:36,900
charge to the other side, that
the actual voltage, or the

35
00:01:36,900 --> 00:01:39,070
potential between
the two sides,

36
00:01:39,070 --> 00:01:40,420
actually remains constant.

37
00:01:40,420 --> 00:01:41,500
That's the magic of a battery.

38
00:01:41,500 --> 00:01:43,320
So let's just assume that we
have one of these magic

39
00:01:43,320 --> 00:01:44,060
instruments.

40
00:01:44,060 --> 00:01:47,520
You probably have one in your
calculator or your cellphone.

41
00:01:47,520 --> 00:01:51,460
And let's see what happens when
we allow the charge to

42
00:01:51,460 --> 00:01:53,990
actually travel from one
side to the other.

43
00:01:53,990 --> 00:01:58,200
So let's say that I have an
ultra-good conductor.

44
00:01:58,200 --> 00:02:01,328
Let's say it's a perfect
conductor.

45
00:02:01,328 --> 00:02:03,180
It's normally drawn straighter
than what

46
00:02:03,180 --> 00:02:04,180
I'm capable of doing.

47
00:02:04,180 --> 00:02:05,680
And no, I haven't had
anything to drink

48
00:02:05,680 --> 00:02:06,930
before making this video.

49
00:02:06,930 --> 00:02:12,350
 

50
00:02:12,350 --> 00:02:14,270
So what did I do here?

51
00:02:14,270 --> 00:02:19,170
So in the process of kind of
connecting this positive

52
00:02:19,170 --> 00:02:21,400
terminal to the negative
terminal of the battery, I'm

53
00:02:21,400 --> 00:02:26,630
also exposing you to common
schematic notation for

54
00:02:26,630 --> 00:02:29,250
electrical engineers
and electricians,

55
00:02:29,250 --> 00:02:30,560
et cetera, et cetera.

56
00:02:30,560 --> 00:02:34,700
So what this is, these lines
here essentially are wires.

57
00:02:34,700 --> 00:02:37,180
There's no reason why I drew
it at a right angle here.

58
00:02:37,180 --> 00:02:39,970
I just did that to be neat,
those right angles.

59
00:02:39,970 --> 00:02:42,910
And it's assumed that this wire
is an ideal conductor,

60
00:02:42,910 --> 00:02:47,310
that charge can flow freely
without being impeded.

61
00:02:47,310 --> 00:02:50,540
This thing right here, this
scratchy line, this is a

62
00:02:50,540 --> 00:02:53,540
resistor, and this is something
that will actually

63
00:02:53,540 --> 00:02:54,970
impede the charge.

64
00:02:54,970 --> 00:02:58,630
It'll keep the charge from going
as fast as possible.

65
00:02:58,630 --> 00:03:01,680
And then, of course,
out here, this is a

66
00:03:01,680 --> 00:03:03,770
perfect conductor again.

67
00:03:03,770 --> 00:03:07,240
Now, which way will
the charge flow?

68
00:03:07,240 --> 00:03:10,190
Well, I think I've mentioned
this before, but in electric

69
00:03:10,190 --> 00:03:13,400
circuits, it's actually the
electrons that are flowing.

70
00:03:13,400 --> 00:03:16,130
The electrons are those small
particles that are going

71
00:03:16,130 --> 00:03:18,880
really, really fast around
the nucleus of an atom.

72
00:03:18,880 --> 00:03:21,240
And it's actually the electrons
that have this

73
00:03:21,240 --> 00:03:24,390
fluidity that allow it to flow
through a conductor.

74
00:03:24,390 --> 00:03:27,490
So the actual movement of
objects, if you call an

75
00:03:27,490 --> 00:03:30,090
electron an object, some would
argue that they're almost just

76
00:03:30,090 --> 00:03:33,540
notional objects, but the actual
flow is the electrons

77
00:03:33,540 --> 00:03:37,160
from the negative terminal
to the positive terminal.

78
00:03:37,160 --> 00:03:42,640
But the people and all who
originally created circuit

79
00:03:42,640 --> 00:03:45,410
schematics and were the
pioneers of electrical

80
00:03:45,410 --> 00:03:48,390
engineering and electricians and
whoever, I don't know who

81
00:03:48,390 --> 00:03:52,500
came up with it, they decided to
say-- and I think the point

82
00:03:52,500 --> 00:03:55,450
here was to confuse people--
that the current flows from

83
00:03:55,450 --> 00:03:56,700
the positive to the negative.

84
00:03:56,700 --> 00:04:00,620
So the direction of the current
is normally given in

85
00:04:00,620 --> 00:04:05,970
this direction, and current
is specified by I.

86
00:04:05,970 --> 00:04:07,340
And what is current?

87
00:04:07,340 --> 00:04:08,770
Well, current-- so wait.

88
00:04:08,770 --> 00:04:10,690
Actually, before I tell you
what is current, just

89
00:04:10,690 --> 00:04:13,250
remember, even though people
say that the current-- and

90
00:04:13,250 --> 00:04:15,260
most textbooks do this, and if
you become an electrical

91
00:04:15,260 --> 00:04:17,740
engineer, people will often
say that the current is

92
00:04:17,740 --> 00:04:19,560
flowing from the positive
terminal to the negative

93
00:04:19,560 --> 00:04:23,770
terminal, the actual flowing of
things actually occurs from

94
00:04:23,770 --> 00:04:25,810
the negative terminal to
the positive terminal.

95
00:04:25,810 --> 00:04:28,610
It's not like somehow these big
heavy protons and nuclei

96
00:04:28,610 --> 00:04:32,170
are somehow traveling
this way.

97
00:04:32,170 --> 00:04:34,540
Once you compare the size of an
electron to a proton, you

98
00:04:34,540 --> 00:04:36,140
would realize how
crazy that is.

99
00:04:36,140 --> 00:04:40,110
It's the electrons, these little
super-fast particles

100
00:04:40,110 --> 00:04:42,730
that are moving through the
conductor from the negative

101
00:04:42,730 --> 00:04:43,970
terminal this way.

102
00:04:43,970 --> 00:04:46,870
So you could almost view this
current as, the lack of

103
00:04:46,870 --> 00:04:48,430
electrons are flowing
this way.

104
00:04:48,430 --> 00:04:49,310
I don't want to confuse you.

105
00:04:49,310 --> 00:04:52,330
But anyway, just remember that
this is the convention, but

106
00:04:52,330 --> 00:04:55,130
the reality is to some degree
the opposite of the

107
00:04:55,130 --> 00:04:56,430
convention.

108
00:04:56,430 --> 00:05:00,040
So what is this resistor?

109
00:05:00,040 --> 00:05:03,740
Well, as the current is
flowing-- and I want to stay

110
00:05:03,740 --> 00:05:05,680
as close as possible to reality
so you have a good

111
00:05:05,680 --> 00:05:07,170
visualization of what's
going on.

112
00:05:07,170 --> 00:05:10,740
As the electrons are flowing,
you have these little

113
00:05:10,740 --> 00:05:13,600
electrons, and they're
flowing in this wire.

114
00:05:13,600 --> 00:05:16,620
And we assume for some reason
this wire is just so amazing

115
00:05:16,620 --> 00:05:18,850
that they don't in any way bump
into any of the atoms of

116
00:05:18,850 --> 00:05:19,580
the wire or anything.

117
00:05:19,580 --> 00:05:22,370
But when they get to this
resistor, that's when these

118
00:05:22,370 --> 00:05:24,300
electrons start bumping
into things.

119
00:05:24,300 --> 00:05:26,020
They start bumping
into the other

120
00:05:26,020 --> 00:05:27,840
electrons in this material.

121
00:05:27,840 --> 00:05:29,210
So this is the resistor
right here.

122
00:05:29,210 --> 00:05:30,430
They start bumping
into the other

123
00:05:30,430 --> 00:05:31,610
electrons in this material.

124
00:05:31,610 --> 00:05:34,750
They bump into the atoms and
molecules in this material.

125
00:05:34,750 --> 00:05:37,760
And in the process, the
electrons essentially slow

126
00:05:37,760 --> 00:05:38,360
down, right?

127
00:05:38,360 --> 00:05:39,790
They're bumping into things.

128
00:05:39,790 --> 00:05:42,040
So essentially, the more things
that there are to bump

129
00:05:42,040 --> 00:05:44,990
into, or the less space there
are for the electrons to flow

130
00:05:44,990 --> 00:05:50,450
through, the more that this
material is going to slow down

131
00:05:50,450 --> 00:05:50,890
the electrons.

132
00:05:50,890 --> 00:05:53,350
And as we'll see later, the
longer it is, that only

133
00:05:53,350 --> 00:05:56,480
increases the chance that
electrons bump into things.

134
00:05:56,480 --> 00:06:05,850
And this is called a resistor
and it provides resistance,

135
00:06:05,850 --> 00:06:09,870
and it dictates how fast
the current flows.

136
00:06:09,870 --> 00:06:13,120
So current, even though the
convention is it flows from

137
00:06:13,120 --> 00:06:16,860
positive to negative, current
is actually just the flow of

138
00:06:16,860 --> 00:06:18,210
charge per second.

139
00:06:18,210 --> 00:06:19,340
So we could write that down.

140
00:06:19,340 --> 00:06:21,720
I know I'm saying this in kind
of a disjointed way, but I

141
00:06:21,720 --> 00:06:22,540
think you get what I say.

142
00:06:22,540 --> 00:06:28,630
Current is flow of charge, so
change in charge per second,

143
00:06:28,630 --> 00:06:32,360
or per change in time, right?

144
00:06:32,360 --> 00:06:35,550
So the way you could think about
it is, what is voltage?

145
00:06:35,550 --> 00:06:38,760
Voltage is how badly does
current want to flow?

146
00:06:38,760 --> 00:06:43,490
So if there's a high voltage
difference between these two

147
00:06:43,490 --> 00:06:47,670
terminals, then the electrons
that are sitting here, these

148
00:06:47,670 --> 00:06:51,430
electrons want to really
badly get here, right?

149
00:06:51,430 --> 00:06:52,870
And if the voltage is even
higher, these electrons want

150
00:06:52,870 --> 00:06:55,510
to get there even more badly.

151
00:06:55,510 --> 00:06:59,110
So before people understood
that voltage was just a

152
00:06:59,110 --> 00:07:01,810
potential difference, they
would actually call this

153
00:07:01,810 --> 00:07:04,630
desire of the electrons to
get from here to here the

154
00:07:04,630 --> 00:07:06,260
electromotive force.

155
00:07:06,260 --> 00:07:08,390
But what we've learned now,
it's not actually a force.

156
00:07:08,390 --> 00:07:11,040
It's just this potential
difference that makes the-- we

157
00:07:11,040 --> 00:07:13,000
could almost view it as an
electrical pressure, and

158
00:07:13,000 --> 00:07:15,280
that's what people used to
actually call voltage,

159
00:07:15,280 --> 00:07:16,480
electrical pressure.

160
00:07:16,480 --> 00:07:19,340
How badly do the electrons want
to get from here to here?

161
00:07:19,340 --> 00:07:21,750
As soon as we give the electrons
a path through this

162
00:07:21,750 --> 00:07:24,610
circuit, the electrons
will start traveling.

163
00:07:24,610 --> 00:07:28,190
They'll start traveling, and
we assume that this wire

164
00:07:28,190 --> 00:07:30,190
provides no resistance, that
they can travel as

165
00:07:30,190 --> 00:07:31,060
fast as they want.

166
00:07:31,060 --> 00:07:33,480
But when they get to this
resistor, they start bumping

167
00:07:33,480 --> 00:07:36,190
into things, and this
limits how fast the

168
00:07:36,190 --> 00:07:37,900
electrons can travel.

169
00:07:37,900 --> 00:07:41,440
So you can imagine that if
this object right here is

170
00:07:41,440 --> 00:07:44,290
somehow the rate-determining
factor in how fast the

171
00:07:44,290 --> 00:07:47,180
electrons travel, no matter
how fast the electrons can

172
00:07:47,180 --> 00:07:50,450
travel after that, this
was the bottleneck.

173
00:07:50,450 --> 00:07:53,535
So even though electrons can
travel really fast here, they

174
00:07:53,535 --> 00:07:55,540
have to slow down here, then
they could travel really fast

175
00:07:55,540 --> 00:07:59,580
here, the electrons here can't
travel any faster than the

176
00:07:59,580 --> 00:08:00,750
electrons through this.

177
00:08:00,750 --> 00:08:01,940
Well, why is that?

178
00:08:01,940 --> 00:08:05,970
Because if these electrons are
traveling slower, so the

179
00:08:05,970 --> 00:08:08,590
current here is lower-- current
is really just the

180
00:08:08,590 --> 00:08:12,440
rate at which the charge
is traveling, right?

181
00:08:12,440 --> 00:08:14,600
So if the current is lower
here and the current was

182
00:08:14,600 --> 00:08:17,280
higher here, we would
essentially end up having a

183
00:08:17,280 --> 00:08:20,120
buildup of charge someplace here
while all of the current

184
00:08:20,120 --> 00:08:21,700
were waiting to travel
through this.

185
00:08:21,700 --> 00:08:25,740
And we know that that's not
the case, that all of the

186
00:08:25,740 --> 00:08:28,170
electrons actually travel at
the exact same rate through

187
00:08:28,170 --> 00:08:30,570
the entire circuit.

188
00:08:30,570 --> 00:08:33,380
I'm going in the opposite of
the convention right now,

189
00:08:33,380 --> 00:08:36,960
because the convention is that
somehow we have the positive

190
00:08:36,960 --> 00:08:38,120
things traveling this way.

191
00:08:38,120 --> 00:08:40,630
But I want to give you a really
intuitive sense of

192
00:08:40,630 --> 00:08:42,340
what's going on in a circuit,
because I think once you

193
00:08:42,340 --> 00:08:46,880
understand that, once problems
get a lot more complicated,

194
00:08:46,880 --> 00:08:48,380
they won't be so daunting.

195
00:08:48,380 --> 00:08:54,100
So what we know, and this is
called Ohm's law, we know that

196
00:08:54,100 --> 00:08:59,350
the current is actually
proportional to the voltage

197
00:08:59,350 --> 00:09:02,360
across the circuit.

198
00:09:02,360 --> 00:09:06,040
So we know that voltage-- or
we could view it the other

199
00:09:06,040 --> 00:09:08,760
way, that the voltage is
proportional to the current

200
00:09:08,760 --> 00:09:10,700
through a circuit.

201
00:09:10,700 --> 00:09:14,610
So the voltage is equal to the
current times the resistance,

202
00:09:14,610 --> 00:09:17,330
or you could say that the
voltage divided by the

203
00:09:17,330 --> 00:09:20,140
resistance is equal
to the current.

204
00:09:20,140 --> 00:09:26,860
This is called Ohm's law, and
this is true whenever we're at

205
00:09:26,860 --> 00:09:28,170
a constant temperature.

206
00:09:28,170 --> 00:09:30,390
We'll go into more depth later,
and we'll learn that if

207
00:09:30,390 --> 00:09:33,360
a resistor actually has
temperature increases, then

208
00:09:33,360 --> 00:09:35,850
its particles and its molecules
are moving around

209
00:09:35,850 --> 00:09:38,530
more, they have higher
kinetic energy.

210
00:09:38,530 --> 00:09:41,520
And then it's even more likely
that electrons will bump into

211
00:09:41,520 --> 00:09:43,160
them, so actually, the
resistance increases with

212
00:09:43,160 --> 00:09:43,580
temperature.

213
00:09:43,580 --> 00:09:47,310
But if we assume at a constant
temperature for a given

214
00:09:47,310 --> 00:09:49,840
material-- and we'll also learn
later that different

215
00:09:49,840 --> 00:09:52,180
materials have different
resistivities.

216
00:09:52,180 --> 00:09:54,960
But for a given material at a
constant temperature in a

217
00:09:54,960 --> 00:10:00,040
given configuration, the voltage
across a resistor

218
00:10:00,040 --> 00:10:02,870
divided by the resistor is
equal to the current that

219
00:10:02,870 --> 00:10:03,990
flows through it.

220
00:10:03,990 --> 00:10:07,145
An object's resistance is
actually measured as ohms, and

221
00:10:07,145 --> 00:10:10,510
it's given by the Greek
letter Omega.

222
00:10:10,510 --> 00:10:12,430
So let's do a simple example.

223
00:10:12,430 --> 00:10:17,140
Let's say that this is a
16-volt battery, so the

224
00:10:17,140 --> 00:10:20,550
potential difference here is 16
volts between the positive

225
00:10:20,550 --> 00:10:21,860
and the negative terminal.

226
00:10:21,860 --> 00:10:24,690
So it's a 16-volt battery.

227
00:10:24,690 --> 00:10:31,130
Let's say that this resistor is
8 ohms. What is the current

228
00:10:31,130 --> 00:10:34,120
flowing through-- and I keep
doing it in the opposite of

229
00:10:34,120 --> 00:10:36,530
the convention, but let's go
back to the convention.

230
00:10:36,530 --> 00:10:40,380
What is the current flowing
through this circuit?

231
00:10:40,380 --> 00:10:41,990
Well, it's fairly
straightforward.

232
00:10:41,990 --> 00:10:46,860
It's just Ohm's law,
V equals IR.

233
00:10:46,860 --> 00:10:51,720
The voltage is 16 volts, and
it equals the current times

234
00:10:51,720 --> 00:11:00,250
the resistance, times 8 ohms. So
the current is equal to 16

235
00:11:00,250 --> 00:11:05,750
volts divided by 8 ohms,
which is equal to 2,

236
00:11:05,750 --> 00:11:09,880
and this is 2 amperes.

237
00:11:09,880 --> 00:11:11,520
Or sometimes they're called
amps, and that's

238
00:11:11,520 --> 00:11:15,150
the units for current.

239
00:11:15,150 --> 00:11:19,910
But as we know, all current is,
is the amount of charge

240
00:11:19,910 --> 00:11:24,670
per amount of time, so an ampere
is just 2 coulombs per

241
00:11:24,670 --> 00:11:28,280
second, right?

242
00:11:28,280 --> 00:11:30,190
Oh, I'm already at
11 1/2 minutes.

243
00:11:30,190 --> 00:11:31,250
So I will leave you there.

244
00:11:31,250 --> 00:11:33,640
You now know the basics of Ohm's
law and maybe a little

245
00:11:33,640 --> 00:11:36,240
bit of intuition on actually
what's going on in a circuit,

246
00:11:36,240 --> 00:11:38,730
and I will see you in
the next video.

247
00:11:38,730 --> 00:00:00,000