1
00:00:00,000 --> 00:00:01,080


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00:00:01,080 --> 00:00:03,360
Let's make our circle a little
bit more complicated now.

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00:00:03,360 --> 00:00:06,370
So let's say I have a battery
again, and let me do it in a

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00:00:06,370 --> 00:00:07,810
different color just
for variety.

5
00:00:07,810 --> 00:00:10,740


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00:00:10,740 --> 00:00:13,273
That's the positive terminal,
that's the negative terminal.

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00:00:13,273 --> 00:00:18,660
Let's say I have this perfect
conductor, and let's say I

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00:00:18,660 --> 00:00:25,450
have one resistor and I
have another resistor.

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00:00:25,450 --> 00:00:26,440
I don't know, just
for fun, let's

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00:00:26,440 --> 00:00:27,690
throw in a third resistor.

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00:00:27,690 --> 00:00:31,400


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00:00:31,400 --> 00:00:33,310
And we know, of course, that
the convention is that the

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00:00:33,310 --> 00:00:36,820
current flows from positive to
negative, that that's the flow

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00:00:36,820 --> 00:00:38,390
of the current.

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00:00:38,390 --> 00:00:42,810
And remember, current is just
the charge that flows per unit

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00:00:42,810 --> 00:00:45,800
of time or the speed
of the charge flow.

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00:00:45,800 --> 00:00:48,610
But we know, of course, that in
reality what is happening,

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00:00:48,610 --> 00:00:51,580
if there's any such thing as
reality, is that we have a

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00:00:51,580 --> 00:00:56,590
bunch of electrons here that,
because of this voltage across

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the battery terminals, these
electrons want to really badly

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get to the positive terminal.

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And the higher the voltage, the
more they really want to

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get to this positive terminal.

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So what's going to happen
in this circuit?

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00:01:10,770 --> 00:01:12,030
Actually, let me label
everything.

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So let's call this R1,
let's call this R2,

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let's call this R3.

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The first thing I want you to
realize is that between

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elements that the voltage
is always constant.

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And why is that?

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Well, we assume that this is a
perfect conductor-- let's say

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this little segment
right here, right?

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00:01:31,650 --> 00:01:33,100
And so it's a perfect
conductor.

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Well, let's look at
it at this end.

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00:01:34,620 --> 00:01:35,440
So you have all these
electrons.

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00:01:35,440 --> 00:01:38,060
This is a perfect conductor,
so there's nothing stopping

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these electrons from
just distributing

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themselves over this wire.

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00:01:45,220 --> 00:01:50,060
Before you encounter an element
in the circuit or

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00:01:50,060 --> 00:01:53,550
device or whatever you want to
call that, you can view this

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00:01:53,550 --> 00:01:56,070
ideal conducting wire just from
a schematic point of view

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00:01:56,070 --> 00:01:58,180
as an extension of the
negative terminal.

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00:01:58,180 --> 00:02:00,920
And similarly, you can view
this wire right here, this

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00:02:00,920 --> 00:02:02,380
part of the wire, as
an extension of

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00:02:02,380 --> 00:02:03,570
the positive terminal.

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00:02:03,570 --> 00:02:05,410
And the reason why I want to
say that is because it

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actually turns out that it
doesn't matter if you measure

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00:02:08,190 --> 00:02:09,520
the voltage here.

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00:02:09,520 --> 00:02:12,050
So let's say if I take a measure
of the voltage across

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00:02:12,050 --> 00:02:14,500
those two terminals using what
we call a voltmeter.

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00:02:14,500 --> 00:02:17,470
And I'll later do a whole video
on how voltmeters work,

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00:02:17,470 --> 00:02:20,550
but remember, when we measure
voltage, we have to measure it

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at two points.

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00:02:21,180 --> 00:02:21,880
And why is that?

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00:02:21,880 --> 00:02:24,430
Because voltage is a potential
difference.

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00:02:24,430 --> 00:02:25,790
It's not some kind of
absolute number.

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It's a difference between
essentially how bad do

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00:02:28,430 --> 00:02:30,510
electrons want to get
from here to here.

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00:02:30,510 --> 00:02:32,980
So if we measure the voltage
between those two points, it

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00:02:32,980 --> 00:02:35,680
would be the exact same thing as
if we measured the voltage

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between these two points.

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00:02:37,810 --> 00:02:39,530
Theoretically.

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00:02:39,530 --> 00:02:44,660
As we know, no wires really
have no resistivity.

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00:02:44,660 --> 00:02:46,360
All wires have a little bit,
but when we draw these

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00:02:46,360 --> 00:02:49,840
schematics, we assume that the
wires are perfect conductors

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00:02:49,840 --> 00:02:52,000
and all the resistance takes
place in the resistor.

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So that's the first thing I want
you to realize, and it

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00:02:53,840 --> 00:02:56,780
makes things very-- so, for
example, everywhere along this

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00:02:56,780 --> 00:03:00,460
wire, this part of the wire,
the voltage is constant.

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00:03:00,460 --> 00:03:03,040
Everywhere along this wire,
the voltage is constant.

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00:03:03,040 --> 00:03:06,010


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00:03:06,010 --> 00:03:09,965
Let me erase some of this,
because I don't want this to

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get too messy.

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00:03:11,215 --> 00:03:13,730


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00:03:13,730 --> 00:03:15,830
That's a big important
realization when you later

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become an electrical engineer
and have much

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00:03:18,190 --> 00:03:19,375
harder problems to solve.

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00:03:19,375 --> 00:03:20,625
Let me erase all of this.

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00:03:20,625 --> 00:03:23,120


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00:03:23,120 --> 00:03:25,730
Let me erase all of that.

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00:03:25,730 --> 00:03:28,110
Let me redraw that, because we
can't have that gap there,

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00:03:28,110 --> 00:03:31,040
because if there was that gap,
current wouldn't flow.

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00:03:31,040 --> 00:03:33,440
That's actually-- well, I'll
draw later how you can draw a

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00:03:33,440 --> 00:03:35,170
switch, but a switch is
essentially a gap.

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00:03:35,170 --> 00:03:37,330
It looks like a gap in the
circuit that you can open or

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00:03:37,330 --> 00:03:37,990
close, right?

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00:03:37,990 --> 00:03:39,640
Because if you open it,
no current will flow.

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00:03:39,640 --> 00:03:40,610
If you close it, current
will flow.

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00:03:40,610 --> 00:03:43,820
OK, so you now know
that the voltage

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00:03:43,820 --> 00:03:45,220
between devices is constant.

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00:03:45,220 --> 00:03:46,790
The other thing I want to
convince you is that the

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00:03:46,790 --> 00:03:49,920
current through this entire
circuit is constant, and that

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00:03:49,920 --> 00:03:52,910
applies to any circuit
in series.

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00:03:52,910 --> 00:03:53,990
Now, what do I mean by series?

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00:03:53,990 --> 00:03:56,340
Series just means that
everything in the circuit is

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00:03:56,340 --> 00:03:57,880
after one another, right?

97
00:03:57,880 --> 00:04:00,470
If we take the convention and
we say current flows in this

98
00:04:00,470 --> 00:04:02,710
direction, it'll hit this
resistor, then the next

99
00:04:02,710 --> 00:04:04,100
resistor, then the
next resistor.

100
00:04:04,100 --> 00:04:07,420
At no point does the circuit
branch off and have to choose

101
00:04:07,420 --> 00:04:09,590
whether I want to go down
path A or path B.

102
00:04:09,590 --> 00:04:14,000
So this circuit is completely
in series, and there's a

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00:04:14,000 --> 00:04:17,800
couple ways I can convince you
that the current-- let's call

104
00:04:17,800 --> 00:04:24,850
the current here I1.

105
00:04:24,850 --> 00:04:31,730
Let's call this current
here I2.

106
00:04:31,730 --> 00:04:33,150
Let's call this current
here I3.

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00:04:33,150 --> 00:04:35,215
I could draw another
one here, I3.

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00:04:35,215 --> 00:04:37,550
So there's a couple of ways
I can convince you that I1

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00:04:37,550 --> 00:04:38,780
equals I2, I3.

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00:04:38,780 --> 00:04:41,540
One is I could just say if you
experimentally tried it out

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00:04:41,540 --> 00:04:43,910
using an ammeter, which measures
current, you would

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00:04:43,910 --> 00:04:45,230
see that they are identical.

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00:04:45,230 --> 00:04:47,460
But the other way to think about
it, and this time I'm

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00:04:47,460 --> 00:04:49,230
going to actually talk about the
electrons, so let's talk

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00:04:49,230 --> 00:04:52,790
about things going in this
direction, is-- so these

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00:04:52,790 --> 00:04:55,070
electrons, through this wire,
they can go as fast as they

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00:04:55,070 --> 00:04:56,400
want to go, right?

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00:04:56,400 --> 00:04:58,570
The speed of light or close to
the speed of light since they

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00:04:58,570 --> 00:05:01,430
have very, very,
very low mass.

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00:05:01,430 --> 00:05:03,980
And we'll go into relativity
one day.

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00:05:03,980 --> 00:05:06,220
But once they get to this
resistor, they start bumping

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00:05:06,220 --> 00:05:07,560
into things, and
they slow down.

123
00:05:07,560 --> 00:05:09,840
This resistor is a bit of
a bottleneck, right?

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00:05:09,840 --> 00:05:12,620
So as fast as they're traveling
here, they have to

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00:05:12,620 --> 00:05:13,720
slow down here.

126
00:05:13,720 --> 00:05:16,510
And if they slow down here, they
have to slow down here,

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00:05:16,510 --> 00:05:19,280
because if they kept going
superfast here and then they

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00:05:19,280 --> 00:05:21,660
slowed down here, then they
would start building up here,

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00:05:21,660 --> 00:05:23,650
and that just doesn't make
sense, because we know that

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00:05:23,650 --> 00:05:25,260
they're evenly spread
out, et cetera.

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00:05:25,260 --> 00:05:29,330
And similarly, they might exit
this resistor at a certain

132
00:05:29,330 --> 00:05:31,650
speed and then slow down even
further as they bump into

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00:05:31,650 --> 00:05:36,070
resistors here, but if they're
going even slower at this

134
00:05:36,070 --> 00:05:39,540
point, then there would be
a bottleneck here, so

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00:05:39,540 --> 00:05:43,330
essentially, they would have to
go at that rate throughout

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00:05:43,330 --> 00:05:44,020
the whole thing.

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00:05:44,020 --> 00:05:47,890
And another way to think about
it is the resistance is kind

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00:05:47,890 --> 00:05:49,090
of a probabilistic thing.

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00:05:49,090 --> 00:05:50,752
I know when you think on a macro
level, you say, oh, it

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00:05:50,752 --> 00:05:51,260
has this resistance.

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00:05:51,260 --> 00:05:52,490
It just slows it down.

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00:05:52,490 --> 00:05:54,980
But the longer there's a
resistor, it increases the

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00:05:54,980 --> 00:05:58,350
probability that some of the
electrons are going to bump

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00:05:58,350 --> 00:06:00,810
into something and create
a little bit of heat,

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00:06:00,810 --> 00:06:02,240
et cetera, et cetera.

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00:06:02,240 --> 00:06:05,850
So when you put resistors in
series, what you're actually

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00:06:05,850 --> 00:06:08,540
doing is increasing the
probability that more

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00:06:08,540 --> 00:06:11,700
electrons will bump into
more things, right?

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00:06:11,700 --> 00:06:14,910
Say there's an electron that
travels-- say, somehow through

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00:06:14,910 --> 00:06:17,455
freak luck, it doesn't bump
into anything as it goes

151
00:06:17,455 --> 00:06:18,790
through here's because it's
going really fast, but then it

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00:06:18,790 --> 00:06:19,900
bumps into something
here, right?

153
00:06:19,900 --> 00:06:21,160
It only increases the
probability that something

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00:06:21,160 --> 00:06:22,240
bumps into it.

155
00:06:22,240 --> 00:06:24,200
So there's a bunch of ways you
can think about it, and I

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00:06:24,200 --> 00:06:25,880
encourage you to let me
know if there's other

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00:06:25,880 --> 00:06:27,840
ways that help you.

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00:06:27,840 --> 00:06:31,510
But the current through
this entire

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00:06:31,510 --> 00:06:33,130
series circuit is constant.

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00:06:33,130 --> 00:06:36,750
Now if we say that, what
else can we say?

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00:06:36,750 --> 00:06:39,240
Well, if the current here--
let's say the current through

162
00:06:39,240 --> 00:06:40,490
here is I1.

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00:06:40,490 --> 00:06:43,020


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00:06:43,020 --> 00:06:45,620
If the current through here is
I1, what is going to be the

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00:06:45,620 --> 00:06:50,470
voltage if I measured it
from here to here?

166
00:06:50,470 --> 00:06:54,060
What is this voltage here?

167
00:06:54,060 --> 00:06:55,570
I measured it with
a voltmeter.

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00:06:55,570 --> 00:07:01,465
Well, V1 is going to be
equal to I1 times R1.

169
00:07:01,465 --> 00:07:03,310
I don't know why I put an R.

170
00:07:03,310 --> 00:07:04,380
That's a 1, not an I.

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00:07:04,380 --> 00:07:06,790
I1 times R1, right?

172
00:07:06,790 --> 00:07:12,720
And similarly, if I measured the
voltage from here to here,

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00:07:12,720 --> 00:07:17,570
that voltage is going to be
equal to I2 times R2.

174
00:07:17,570 --> 00:07:20,080
Let's say this is where I3 is.

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00:07:20,080 --> 00:07:31,320
So the voltage, if I were to
measure it from here to here--

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00:07:31,320 --> 00:07:35,560
But anyway, if we look at the
voltage from here to here,

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00:07:35,560 --> 00:07:41,850
it's going to be I3 times R3.

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00:07:41,850 --> 00:07:45,930
So what we see is that the
voltage across the entire

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00:07:45,930 --> 00:07:51,490
circuit, which I can write as
V-total, is going to be equal

180
00:07:51,490 --> 00:07:54,790
to the potential drops, the
total potential drop across

181
00:07:54,790 --> 00:07:55,420
each of these devices.

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00:07:55,420 --> 00:07:58,980
So the way to think about it
is that-- well, let's think

183
00:07:58,980 --> 00:07:59,450
about the electrons.

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00:07:59,450 --> 00:08:03,950
The electrons here, they really
want to get here.

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00:08:03,950 --> 00:08:06,270
But after they've bumped around
a little bit and they

186
00:08:06,270 --> 00:08:10,600
get here, they've experienced
some potential drop.

187
00:08:10,600 --> 00:08:15,390
So the electrons here actually
are a little bit less

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00:08:15,390 --> 00:08:16,710
eager to get here.

189
00:08:16,710 --> 00:08:18,460
And then once they've gone
through here, maybe they're

190
00:08:18,460 --> 00:08:19,960
just tired of bumping
around so much.

191
00:08:19,960 --> 00:08:21,480
And once they're here, they're
a little bit less

192
00:08:21,480 --> 00:08:23,060
eager to get here.

193
00:08:23,060 --> 00:08:26,200
So there's a voltage drop across
each device, right?

194
00:08:26,200 --> 00:08:29,220
So the total voltage is equal
to the voltage drop across

195
00:08:29,220 --> 00:08:30,100
each of the devices.

196
00:08:30,100 --> 00:08:31,822
And now let's go back to the
convention, and we'll say that

197
00:08:31,822 --> 00:08:33,570
the current is going
in that direction.

198
00:08:33,570 --> 00:08:41,970
The total voltage drop is equal
to V1 plus V2 plus V3,

199
00:08:41,970 --> 00:08:49,110
so the total voltage drop
is equal to I1 R1 plus

200
00:08:49,110 --> 00:08:55,080
I2 R2 plus I3 R3.

201
00:08:55,080 --> 00:08:56,420
And what's the total
voltage drop?

202
00:08:56,420 --> 00:08:59,310
Well, that's equal to the total
current through the

203
00:08:59,310 --> 00:09:00,330
whole system.

204
00:09:00,330 --> 00:09:06,660
I-total, or we just call it I,
times the total resistance is

205
00:09:06,660 --> 00:09:15,540
equal to I1 R1, plus
I2 R2 plus I3 R3.

206
00:09:15,540 --> 00:09:17,140
Well, we know that all
the I's are the same.

207
00:09:17,140 --> 00:09:21,120
Hopefully, you can take it as,
just conceptually it makes

208
00:09:21,120 --> 00:09:23,120
sense to you that the current
through the entire circuit

209
00:09:23,120 --> 00:09:24,170
will be the same.

210
00:09:24,170 --> 00:09:25,970
So all these I's are
the same, so we can

211
00:09:25,970 --> 00:09:27,520
just cancel them out.

212
00:09:27,520 --> 00:09:28,680
Divide both sides by that I.

213
00:09:28,680 --> 00:09:34,230
We assume it's non-zero, so I,
I, I, I, and then we have that

214
00:09:34,230 --> 00:09:38,200
the total resistance of the
circuit is equal to R1

215
00:09:38,200 --> 00:09:41,600
plus R2 plus R3.

216
00:09:41,600 --> 00:09:44,590
So when you have resistors in
series like this, the total

217
00:09:44,590 --> 00:09:47,420
resistance, their combined
resistance, is just

218
00:09:47,420 --> 00:09:48,840
equal to their sum.

219
00:09:48,840 --> 00:09:51,030
And that was just a very
long-winded way of explaining

220
00:09:51,030 --> 00:09:53,600
something very simple, and
I'll do an example.

221
00:09:53,600 --> 00:09:56,580
Let's say that this voltage
is-- I don't know.

222
00:09:56,580 --> 00:10:00,650
Let's say it's 20 volts.

223
00:10:00,650 --> 00:10:07,760
Let's say resistor 1 is 2 ohms.
Let's say resistor 2 is

224
00:10:07,760 --> 00:10:16,930
3 ohms, and let's say resistor
3 is 5 ohms. So what is the

225
00:10:16,930 --> 00:10:18,670
total resistance through
this circuit?

226
00:10:18,670 --> 00:10:22,130
Well, the total resistance is
2 ohms plus 3 ohms plus 5

227
00:10:22,130 --> 00:10:25,580
ohms, so it's equal to 10 ohms.
So total resistance is

228
00:10:25,580 --> 00:10:27,370
equal to 10 ohms.

229
00:10:27,370 --> 00:10:29,440
So if I were to ask you what is
the current going through

230
00:10:29,440 --> 00:10:30,550
this circuit?

231
00:10:30,550 --> 00:10:33,980
Well, the total resistance is
10 ohms. We know Ohm's law:

232
00:10:33,980 --> 00:10:37,180
voltage is equal to current
times resistance.

233
00:10:37,180 --> 00:10:39,740
The voltage is just
equal to 20.

234
00:10:39,740 --> 00:10:42,700
20 is equal to the current
times 10 ohms, right?

235
00:10:42,700 --> 00:10:45,380
We just added the resistances.

236
00:10:45,380 --> 00:10:46,730
Divide both sides by 10.

237
00:10:46,730 --> 00:10:53,410
You get the current is
equal to 2 amps or 2

238
00:10:53,410 --> 00:10:55,510
coulombs per second.

239
00:10:55,510 --> 00:10:58,710
So what seemed like a very
long-winded explanation

240
00:10:58,710 --> 00:11:00,510
actually results in something
that's very, very,

241
00:11:00,510 --> 00:11:02,070
very easy to apply.

242
00:11:02,070 --> 00:11:05,100
When resistors are in series,
we just add them up.

243
00:11:05,100 --> 00:11:06,350
I will see you in
the next video.

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00:11:06,350 --> 00:00:00,000