Resistors in series

WEBVTT
Kind: captions
Language: en

00:00:01.080 --> 00:00:03.360
Let's make our circle a little
bit more complicated now.

00:00:03.360 --> 00:00:06.370
So let's say I have a battery
again, and let me do it in a

00:00:06.370 --> 00:00:07.810
different color just
for variety.

00:00:10.740 --> 00:00:13.273
That's the positive terminal,
that's the negative terminal.

00:00:13.273 --> 00:00:18.660
Let's say I have this perfect
conductor, and let's say I

00:00:18.660 --> 00:00:25.450
have one resistor and I
have another resistor.

00:00:25.450 --> 00:00:26.440
I don't know, just
for fun, let's

00:00:26.440 --> 00:00:27.690
throw in a third resistor.

00:00:31.400 --> 00:00:33.310
And we know, of course, that
the convention is that the

00:00:33.310 --> 00:00:36.820
current flows from positive to
negative, that that's the flow

00:00:36.820 --> 00:00:38.390
of the current.

00:00:38.390 --> 00:00:42.810
And remember, current is just
the charge that flows per unit

00:00:42.810 --> 00:00:45.800
of time or the speed
of the charge flow.

00:00:45.800 --> 00:00:48.610
But we know, of course, that in
reality what is happening,

00:00:48.610 --> 00:00:51.580
if there's any such thing as
reality, is that we have a

00:00:51.580 --> 00:00:56.590
bunch of electrons here that,
because of this voltage across

00:00:56.590 --> 00:01:01.020
the battery terminals, these
electrons want to really badly

00:01:01.020 --> 00:01:02.410
get to the positive terminal.

00:01:02.410 --> 00:01:05.560
And the higher the voltage, the
more they really want to

00:01:05.560 --> 00:01:08.250
get to this positive terminal.

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So what's going to happen
in this circuit?

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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

00:01:28.440 --> 00:01:31.650
this little segment
right here, right?

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And so it's a perfect
conductor.

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

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So you have all these
electrons.

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This is a perfect conductor,
so there's nothing stopping

00:01:38.060 --> 00:01:40.050
these electrons from
just distributing

00:01:40.050 --> 00:01:45.220
themselves over this wire.

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Before you encounter an element
in the circuit or

00:01:50.060 --> 00:01:53.550
device or whatever you want to
call that, you can view this

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ideal conducting wire just from
a schematic point of view

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as an extension of the
negative terminal.

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And similarly, you can view
this wire right here, this

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part of the wire, as
an extension of

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the positive terminal.

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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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the voltage here.

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So let's say if I take a measure
of the voltage across

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those two terminals using what
we call a voltmeter.

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And I'll later do a whole video
on how voltmeters work,

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but remember, when we measure
voltage, we have to measure it

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at two points.

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And why is that?

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Because voltage is a potential
difference.

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It's not some kind of
absolute number.

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It's a difference between
essentially how bad do

00:02:28.430 --> 00:02:30.510
electrons want to get
from here to here.

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So if we measure the voltage
between those two points, it

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would be the exact same thing as
if we measured the voltage

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between these two points.

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Theoretically.

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As we know, no wires really
have no resistivity.

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All wires have a little bit,
but when we draw these

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schematics, we assume that the
wires are perfect conductors

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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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makes things very-- so, for
example, everywhere along this

00:02:56.780 --> 00:03:00.460
wire, this part of the wire,
the voltage is constant.

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Everywhere along this wire,
the voltage is constant.

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Let me erase some of this,
because I don't want this to

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get too messy.

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That's a big important
realization when you later

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become an electrical engineer
and have much

00:03:18.190 --> 00:03:19.375
harder problems to solve.

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Let me erase all of this.

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Let me erase all of that.

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Let me redraw that, because we
can't have that gap there,

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because if there was that gap,
current wouldn't flow.

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That's actually-- well, I'll
draw later how you can draw a

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switch, but a switch is
essentially a gap.

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It looks like a gap in the
circuit that you can open or

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close, right?

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Because if you open it,
no current will flow.

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If you close it, current
will flow.

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OK, so you now know
that the voltage

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between devices is constant.

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The other thing I want to
convince you is that the

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current through this entire
circuit is constant, and that

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applies to any circuit
in series.

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Now, what do I mean by series?

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Series just means that
everything in the circuit is

00:03:56.340 --> 00:03:57.880
after one another, right?

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If we take the convention and
we say current flows in this

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direction, it'll hit this
resistor, then the next

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resistor, then the
next resistor.

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At no point does the circuit
branch off and have to choose

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whether I want to go down
path A or path B.

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So this circuit is completely
in series, and there's a

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couple ways I can convince you
that the current-- let's call

00:04:17.800 --> 00:04:24.850
the current here I1.

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Let's call this current
here I2.

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Let's call this current
here I3.

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I could draw another
one here, I3.

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So there's a couple of ways
I can convince you that I1

00:04:37.550 --> 00:04:38.780
equals I2, I3.

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One is I could just say if you
experimentally tried it out

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using an ammeter, which measures
current, you would

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see that they are identical.

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But the other way to think about
it, and this time I'm

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going to actually talk about the
electrons, so let's talk

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about things going in this
direction, is-- so these

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electrons, through this wire,
they can go as fast as they

00:04:55.070 --> 00:04:56.400
want to go, right?

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The speed of light or close to
the speed of light since they

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have very, very,
very low mass.

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And we'll go into relativity
one day.

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But once they get to this
resistor, they start bumping

00:05:06.220 --> 00:05:07.560
into things, and
they slow down.

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This resistor is a bit of
a bottleneck, right?

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So as fast as they're traveling
here, they have to

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slow down here.

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And if they slow down here, they
have to slow down here,

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because if they kept going
superfast here and then they

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slowed down here, then they
would start building up here,

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and that just doesn't make
sense, because we know that

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they're evenly spread
out, et cetera.

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And similarly, they might exit
this resistor at a certain

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speed and then slow down even
further as they bump into

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resistors here, but if they're
going even slower at this

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point, then there would be
a bottleneck here, so

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essentially, they would have to
go at that rate throughout

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the whole thing.

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And another way to think about
it is the resistance is kind

00:05:47.890 --> 00:05:49.090
of a probabilistic thing.

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I know when you think on a macro
level, you say, oh, it

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has this resistance.

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It just slows it down.

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But the longer there's a
resistor, it increases the

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probability that some of the
electrons are going to bump

00:05:58.350 --> 00:06:00.810
into something and create
a little bit of heat,

00:06:00.810 --> 00:06:02.240
et cetera, et cetera.

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So when you put resistors in
series, what you're actually

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doing is increasing the
probability that more

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electrons will bump into
more things, right?

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Say there's an electron that
travels-- say, somehow through

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freak luck, it doesn't bump
into anything as it goes

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through here's because it's
going really fast, but then it

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bumps into something
here, right?

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It only increases the
probability that something

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bumps into it.

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So there's a bunch of ways you
can think about it, and I

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encourage you to let me
know if there's other

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ways that help you.

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But the current through
this entire

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series circuit is constant.

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Now if we say that, what
else can we say?

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Well, if the current here--
let's say the current through

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here is I1.

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If the current through here is
I1, what is going to be the

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voltage if I measured it
from here to here?

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What is this voltage here?

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I measured it with
a voltmeter.

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Well, V1 is going to be
equal to I1 times R1.

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I don't know why I put an R.

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That's a 1, not an I.

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I1 times R1, right?

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And similarly, if I measured the
voltage from here to here,

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that voltage is going to be
equal to I2 times R2.

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Let's say this is where I3 is.

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So the voltage, if I were to
measure it from here to here--

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But anyway, if we look at the
voltage from here to here,

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it's going to be I3 times R3.

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So what we see is that the
voltage across the entire

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circuit, which I can write as
V-total, is going to be equal

00:07:51.490 --> 00:07:54.790
to the potential drops, the
total potential drop across

00:07:54.790 --> 00:07:55.420
each of these devices.

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So the way to think about it
is that-- well, let's think

00:07:58.980 --> 00:07:59.450
about the electrons.

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The electrons here, they really
want to get here.

00:08:03.950 --> 00:08:06.270
But after they've bumped around
a little bit and they

00:08:06.270 --> 00:08:10.600
get here, they've experienced
some potential drop.

00:08:10.600 --> 00:08:15.390
So the electrons here actually
are a little bit less

00:08:15.390 --> 00:08:16.710
eager to get here.

00:08:16.710 --> 00:08:18.460
And then once they've gone
through here, maybe they're

00:08:18.460 --> 00:08:19.960
just tired of bumping
around so much.

00:08:19.960 --> 00:08:21.480
And once they're here, they're
a little bit less

00:08:21.480 --> 00:08:23.060
eager to get here.

00:08:23.060 --> 00:08:26.200
So there's a voltage drop across
each device, right?

00:08:26.200 --> 00:08:29.220
So the total voltage is equal
to the voltage drop across

00:08:29.220 --> 00:08:30.100
each of the devices.

00:08:30.100 --> 00:08:31.822
And now let's go back to the
convention, and we'll say that

00:08:31.822 --> 00:08:33.570
the current is going
in that direction.

00:08:33.570 --> 00:08:41.970
The total voltage drop is equal
to V1 plus V2 plus V3,

00:08:41.970 --> 00:08:49.110
so the total voltage drop
is equal to I1 R1 plus

00:08:49.110 --> 00:08:55.080
I2 R2 plus I3 R3.

00:08:55.080 --> 00:08:56.420
And what's the total
voltage drop?

00:08:56.420 --> 00:08:59.310
Well, that's equal to the total
current through the

00:08:59.310 --> 00:09:00.330
whole system.

00:09:00.330 --> 00:09:06.660
I-total, or we just call it I,
times the total resistance is

00:09:06.660 --> 00:09:15.540
equal to I1 R1, plus
I2 R2 plus I3 R3.

00:09:15.540 --> 00:09:17.140
Well, we know that all
the I's are the same.

00:09:17.140 --> 00:09:21.120
Hopefully, you can take it as,
just conceptually it makes

00:09:21.120 --> 00:09:23.120
sense to you that the current
through the entire circuit

00:09:23.120 --> 00:09:24.170
will be the same.

00:09:24.170 --> 00:09:25.970
So all these I's are
the same, so we can

00:09:25.970 --> 00:09:27.520
just cancel them out.

00:09:27.520 --> 00:09:28.680
Divide both sides by that I.

00:09:28.680 --> 00:09:34.230
We assume it's non-zero, so I,
I, I, I, and then we have that

00:09:34.230 --> 00:09:38.200
the total resistance of the
circuit is equal to R1

00:09:38.200 --> 00:09:41.600
plus R2 plus R3.

00:09:41.600 --> 00:09:44.590
So when you have resistors in
series like this, the total

00:09:44.590 --> 00:09:47.420
resistance, their combined
resistance, is just

00:09:47.420 --> 00:09:48.840
equal to their sum.

00:09:48.840 --> 00:09:51.030
And that was just a very
long-winded way of explaining

00:09:51.030 --> 00:09:53.600
something very simple, and
I'll do an example.

00:09:53.600 --> 00:09:56.580
Let's say that this voltage
is-- I don't know.

00:09:56.580 --> 00:10:00.650
Let's say it's 20 volts.

00:10:00.650 --> 00:10:07.760
Let's say resistor 1 is 2 ohms.
Let's say resistor 2 is

00:10:07.760 --> 00:10:16.930
3 ohms, and let's say resistor
3 is 5 ohms. So what is the

00:10:16.930 --> 00:10:18.670
total resistance through
this circuit?

00:10:18.670 --> 00:10:22.130
Well, the total resistance is
2 ohms plus 3 ohms plus 5

00:10:22.130 --> 00:10:25.580
ohms, so it's equal to 10 ohms.
So total resistance is

00:10:25.580 --> 00:10:27.370
equal to 10 ohms.

00:10:27.370 --> 00:10:29.440
So if I were to ask you what is
the current going through

00:10:29.440 --> 00:10:30.550
this circuit?

00:10:30.550 --> 00:10:33.980
Well, the total resistance is
10 ohms. We know Ohm's law:

00:10:33.980 --> 00:10:37.180
voltage is equal to current
times resistance.

00:10:37.180 --> 00:10:39.740
The voltage is just
equal to 20.

00:10:39.740 --> 00:10:42.700
20 is equal to the current
times 10 ohms, right?

00:10:42.700 --> 00:10:45.380
We just added the resistances.

00:10:45.380 --> 00:10:46.730
Divide both sides by 10.

00:10:46.730 --> 00:10:53.410
You get the current is
equal to 2 amps or 2

00:10:53.410 --> 00:10:55.510
coulombs per second.

00:10:55.510 --> 00:10:58.710
So what seemed like a very
long-winded explanation

00:10:58.710 --> 00:11:00.510
actually results in something
that's very, very,

00:11:00.510 --> 00:11:02.070
very easy to apply.

00:11:02.070 --> 00:11:05.100
When resistors are in series,
we just add them up.

00:11:05.100 --> 00:11:06.350
I will see you in
the next video.


Moments (part 2)

WEBVTT
Kind: captions
Language: en

00:00:00.980 --> 00:00:04.140
I'm going to do a couple more
moment and force problems,

00:00:04.140 --> 00:00:06.320
especially because I think
I might have bungled the

00:00:06.320 --> 00:00:08.680
terminology in the previous
video because I kept confusing

00:00:08.680 --> 00:00:11.120
clockwise with counterclockwise.

00:00:11.120 --> 00:00:14.370
This time I'll try to
be more consistent.

00:00:14.370 --> 00:00:18.080
Let me draw my lever again.

00:00:18.080 --> 00:00:20.590
My seesaw.

00:00:20.590 --> 00:00:27.680
So that's my seesaw, and that is
my axis of rotation, or my

00:00:27.680 --> 00:00:30.270
fulcrum, or my pivot point,
whatever you want to call it.

00:00:30.270 --> 00:00:34.490
And let me throw a bunch
of forces on there.

00:00:34.490 --> 00:00:40.760
So let's say that I have a
10-Newton force and it is at a

00:00:40.760 --> 00:00:46.830
distance of 10, so distance
is equal to 10.

00:00:46.830 --> 00:00:49.310
The moment arm distance is 10.

00:00:49.310 --> 00:00:58.140
Let's say that I have a
50-Newton force and its moment

00:00:58.140 --> 00:01:03.180
arm distance is equal to 8.

00:01:03.180 --> 00:01:08.710
Let's say that I have a 5-Newton
force, and its moment

00:01:08.710 --> 00:01:13.292
arm distance is 4.

00:01:13.292 --> 00:01:15.360
The distance is equal to 4.

00:01:15.360 --> 00:01:17.600
That's enough for that side.

00:01:17.600 --> 00:01:31.210
And let's say I have a I'm
going to switch colors.

00:01:31.210 --> 00:01:32.580
Actually, no, I'm going to keep
it all the same color and

00:01:32.580 --> 00:01:35.280
then we'll use colors to
differentiate between

00:01:35.280 --> 00:01:37.960
clockwise and counterclockwise
so I don't bungle

00:01:37.960 --> 00:01:39.300
everything up again.

00:01:39.300 --> 00:01:43.520
So let's say I have a 10-Newton
force here.

00:01:43.520 --> 00:01:46.055
And, of course, these vectors
aren't proportional to

00:01:46.055 --> 00:01:46.750
actually what I drew.

00:01:46.750 --> 00:01:50.230
50 Newtons would be huge if
these were the actual vectors.

00:01:50.230 --> 00:01:53.810
And let's say that that moment
arm distance is 3.

00:01:53.810 --> 00:01:54.670
Let me do a couple more.

00:01:54.670 --> 00:01:58.220
And let's say I have a moment
arm distance of 8.

00:01:58.220 --> 00:02:13.130
I have a clockwise force of 20
Newtons, And let's say at a

00:02:13.130 --> 00:02:17.330
distance of 10 again, so
distance is equal to 10, I

00:02:17.330 --> 00:02:18.680
have my mystery force.

00:02:18.680 --> 00:02:21.010
It's going to act in a
counterclockwise direction and

00:02:21.010 --> 00:02:23.500
I want to know what
it needs to be.

00:02:23.500 --> 00:02:26.670
So whenever you do any of
these moment of force

00:02:26.670 --> 00:02:29.680
problems, and you say, well,
what does the force need to be

00:02:29.680 --> 00:02:33.340
in order for this see
saw to not rotate?

00:02:33.340 --> 00:02:35.490
You just say, well, all the
clockwise moments have to

00:02:35.490 --> 00:02:37.800
equal all of the
counterclockwise moments, So

00:02:37.800 --> 00:02:45.500
clockwise moments equal
counterclockwise.

00:02:45.500 --> 00:02:46.750
I'll do them in different
colors.

00:02:51.450 --> 00:02:54.560
So what are all the
clockwise moments?

00:02:54.560 --> 00:02:57.140
Well, clockwise is this
direction, right?

00:02:57.140 --> 00:02:58.940
That's the way a clock goes.

00:02:58.940 --> 00:03:04.052
So this is clockwise,
that is clockwise.

00:03:04.052 --> 00:03:06.290
I want to go in this
direction.

00:03:06.290 --> 00:03:07.710
And so this is clockwise.

00:03:07.710 --> 00:03:08.950
What are all the clockwise
moments?

00:03:08.950 --> 00:03:12.450
It's 10 Newtons times its
moment arm distance 10.

00:03:12.450 --> 00:03:17.650
So 10 times 10 plus 5 Newtons
times this moment arm distance

00:03:17.650 --> 00:03:24.310
4, plus 5 times 4, plus 20
Newtons times its moment arm

00:03:24.310 --> 00:03:29.200
distance of 8, plus 20 times 8,
and that's going to equal

00:03:29.200 --> 00:03:32.400
the counterclockwise moments,
and so the leftover ones are

00:03:32.400 --> 00:03:34.280
counterclockwise.

00:03:34.280 --> 00:03:36.590
So we have 50 Newtons acting
downward here, and that's

00:03:36.590 --> 00:03:40.240
counterclockwise, and it's at
a distance of 8 from the

00:03:40.240 --> 00:03:44.240
moment arm, so 50 times 8.

00:03:44.240 --> 00:03:45.120
Let's see, we don't
have any other

00:03:45.120 --> 00:03:46.890
counterclockwise on that side.

00:03:46.890 --> 00:03:48.600
This is counterclockwise,
right?

00:03:48.600 --> 00:03:51.290
We have 10 Newtons acting
in the counterclockwise

00:03:51.290 --> 00:03:55.860
direction, and its moment arm
distance is 3, plus 10 times

00:03:55.860 --> 00:03:58.680
3, and we're assuming our
mystery force, which is at a

00:03:58.680 --> 00:04:01.390
distance of 10, is also
counterclockwise,

00:04:01.390 --> 00:04:04.000
plus force times 10.

00:04:04.000 --> 00:04:06.120
And now we simplify.

00:04:06.120 --> 00:04:08.630
And I'll just go to a neutral
color because this

00:04:08.630 --> 00:04:10.290
is just math now.

00:04:10.290 --> 00:04:16.610
100 plus 20 plus 160 is equal
to-- what's 50 times 8?

00:04:16.610 --> 00:04:23.220
That's 400 plus 30 plus 10F.

00:04:23.220 --> 00:04:23.770
What is this?

00:04:23.770 --> 00:04:25.500
2, 50 times 8.

00:04:25.500 --> 00:04:26.470
Right, that's 400.

00:04:26.470 --> 00:04:33.480
OK, this is 120 plus
a 160 is 280.

00:04:33.480 --> 00:04:41.860
280 is equal to 430-- this is
a good example-- plus 10F, I

00:04:41.860 --> 00:04:42.550
just realized.

00:04:42.550 --> 00:04:45.390
Subtract 430 from both sides.

00:04:45.390 --> 00:04:49.610
So what's 430 minus 280?

00:04:49.610 --> 00:04:56.050
It's 150.

00:04:56.050 --> 00:05:00.540
So it's minus 150
is equal to 10F.

00:05:00.540 --> 00:05:04.260
So F is equal to minus
15 Newtons in the

00:05:04.260 --> 00:05:06.290
counterclockwise direction.

00:05:06.290 --> 00:05:09.240
So F is minus 15 Newtons
in the counterclockwise

00:05:09.240 --> 00:05:15.830
direction, or it means that
it is 15 Newtons.

00:05:15.830 --> 00:05:17.620
We assumed that it was in the
counterclockwise direction,

00:05:17.620 --> 00:05:19.790
but when we did the math,
we got a minus number.

00:05:19.790 --> 00:05:21.490
[SNEEZE]

00:05:21.490 --> 00:05:23.060
Excuse me.

00:05:23.060 --> 00:05:26.860
I apologize if I blew out your
speakers with that sneeze.

00:05:26.860 --> 00:05:29.740
But anyway, we assume it was
going in the counterclockwise

00:05:29.740 --> 00:05:31.330
direction, but when we did the
math, we got a negative

00:05:31.330 --> 00:05:33.340
number, so that means it's
actually operating in the

00:05:33.340 --> 00:05:37.770
clockwise direction at 15
Newtons at a distance of 10

00:05:37.770 --> 00:05:40.630
from the moment arm.

00:05:40.630 --> 00:05:44.160
Hopefully, that one was less
confusing than the last one.

00:05:44.160 --> 00:05:46.000
So let me do another problem,
and these actually used to

00:05:46.000 --> 00:05:49.320
confuse me when I first learned
about moments, but in

00:05:49.320 --> 00:05:52.260
some ways, they're the
most useful ones.

00:05:52.260 --> 00:05:58.030
So let's say that I have
some type of table.

00:05:58.030 --> 00:05:58.940
I'll draw it in wood.

00:05:58.940 --> 00:06:00.190
It's a wood table.

00:06:03.080 --> 00:06:06.090
That's my table.

00:06:06.090 --> 00:06:12.920
And I have a leg here,
I have a leg here.

00:06:18.720 --> 00:06:26.020
Let's say that the center
of mass of the top of

00:06:26.020 --> 00:06:27.390
the table is here.

00:06:27.390 --> 00:06:28.350
It's at the center.

00:06:28.350 --> 00:06:32.010
And let's say that
it has a weight.

00:06:32.010 --> 00:06:35.410
It has a weight going down.

00:06:35.410 --> 00:06:37.370
What's a reasonable weight?

00:06:37.370 --> 00:06:40.540
Let's say 20 Newtons.

00:06:40.540 --> 00:06:43.480
It has a weight of 20 Newtons.

00:06:43.480 --> 00:06:47.510
Let's say that I place some
textbooks on top of this

00:06:47.510 --> 00:06:51.310
table, or box, just to make
the drawing simpler.

00:06:56.470 --> 00:06:58.010
Let's say I place a box there.

00:07:00.710 --> 00:07:06.140
Let's say the box weighs 10
kilograms, which would be

00:07:06.140 --> 00:07:07.350
about 100 Newtons.

00:07:07.350 --> 00:07:16.050
So let's say it weighs
about 100 Newtons.

00:07:16.050 --> 00:07:20.050
So what I want to figure out,
what I need to figure out, is

00:07:20.050 --> 00:07:25.090
how much weight is being
put onto each of

00:07:25.090 --> 00:07:26.540
the legs of the table?

00:07:26.540 --> 00:07:28.460
And this might not have even
been obviously a moment

00:07:28.460 --> 00:07:30.820
problem, but you'll see in
a second it really is.

00:07:30.820 --> 00:07:31.740
So how do we know that?

00:07:31.740 --> 00:07:35.100
Well, both of these legs are
supporting the table, right?

00:07:35.100 --> 00:07:40.020
Whatever the table is exerting
downwards, the leg is exerting

00:07:40.020 --> 00:07:45.220
upwards, so that's the amount of
force that each of the legs

00:07:45.220 --> 00:07:46.120
are holding.

00:07:46.120 --> 00:07:49.930
So what we do is we pick-- so
let's just pick this leg, just

00:07:49.930 --> 00:07:52.780
because I'm picking
it arbitrarily.

00:07:52.780 --> 00:07:54.040
Let's pick this leg,
and let's pick an

00:07:54.040 --> 00:07:55.340
arbitrary axis of rotation.

00:07:55.340 --> 00:07:58.920
Well, let's pick this is as
our axis of rotation.

00:07:58.920 --> 00:08:01.080
Why do I pick that as the
axis of rotation?

00:08:01.080 --> 00:08:02.690
Because think of it this way.

00:08:02.690 --> 00:08:07.950
If this leg started pushing more
than it needed to, the

00:08:07.950 --> 00:08:09.320
whole table would rotate in the

00:08:09.320 --> 00:08:10.390
counterclockwise direction.

00:08:10.390 --> 00:08:13.210
Or the other way, if this leg
started to weaken and started

00:08:13.210 --> 00:08:15.900
to buckle and couldn't hold
its force, the table would

00:08:15.900 --> 00:08:19.130
rotate down this way, and it
would rotate around the other

00:08:19.130 --> 00:08:20.760
leg, assuming that the other
leg doesn't fail.

00:08:20.760 --> 00:08:24.740
We're assuming that this leg
is just going to do its job

00:08:24.740 --> 00:08:26.280
and it's not going to move
one way or the other.

00:08:26.280 --> 00:08:29.110
But this leg, that's why we're
thinking about it that way.

00:08:29.110 --> 00:08:31.330
If it was too weak, the whole
table would rotate in the

00:08:31.330 --> 00:08:35.110
clockwise direction, and if it
was somehow exerting extra

00:08:35.110 --> 00:08:36.960
force, which we know a leg
can't, but let's say if it was

00:08:36.960 --> 00:08:39.380
a spring or something like that,
then the whole table

00:08:39.380 --> 00:08:42.409
would rotate in the
counterclockwise direction.

00:08:42.409 --> 00:08:48.560
So once we set that up, we can
actually set this up as a

00:08:48.560 --> 00:08:49.120
moment problem.

00:08:49.120 --> 00:08:50.450
So what is the force
of the leg?

00:08:50.450 --> 00:08:55.470
So the whole table is exerting
some type of-- if this leg

00:08:55.470 --> 00:08:58.960
wasn't here, the whole table
would have a net clockwise

00:08:58.960 --> 00:08:59.550
moment, right?

00:08:59.550 --> 00:09:02.690
The whole table would tilt down
and fall down like that.

00:09:02.690 --> 00:09:07.750
So the leg must be exerting a
counterclockwise moment in

00:09:07.750 --> 00:09:08.790
order to keep it stationary.

00:09:08.790 --> 00:09:12.640
So the leg must be exerting
a force upward right here.

00:09:12.640 --> 00:09:13.850
The force of the leg, right?

00:09:13.850 --> 00:09:14.400
We know that.

00:09:14.400 --> 00:09:16.190
We know that from
basic physics.

00:09:16.190 --> 00:09:19.690
There's some force coming down
here and the leg is doing an

00:09:19.690 --> 00:09:21.650
equal opposite force upwards.

00:09:21.650 --> 00:09:24.260
So what is that force
of that leg?

00:09:24.260 --> 00:09:25.740
And one thing I should
have told you

00:09:25.740 --> 00:09:26.720
is all of the distances.

00:09:26.720 --> 00:09:34.310
Let's say that this distance
between this leg and the book

00:09:34.310 --> 00:09:37.610
is 1 meter-- or the box.

00:09:37.610 --> 00:09:42.550
Let's say that this distance
between the leg and the center

00:09:42.550 --> 00:09:46.980
of mass is 2 meters, and so
this is also 2 meters.

00:09:46.980 --> 00:09:50.390
OK, so we can now set this
up as a moment problem.

00:09:50.390 --> 00:09:53.430
So remember, all of the
clockwise moments have to

00:09:53.430 --> 00:09:56.090
equal all of the
counterclockwise moments.

00:09:56.090 --> 00:09:57.930
So what are all of the
clockwise moments?

00:09:57.930 --> 00:10:01.060
What are all of the things that
want to make the table

00:10:01.060 --> 00:10:06.790
rotate this way or this way?

00:10:06.790 --> 00:10:08.920
Well, the leg is the
only thing keeping

00:10:08.920 --> 00:10:09.400
it from doing that.

00:10:09.400 --> 00:10:10.290
So everything else is

00:10:10.290 --> 00:10:11.840
essentially a clockwise moment.

00:10:11.840 --> 00:10:15.780
So we have this 100 Newtons,
and it is 1 meter away.

00:10:15.780 --> 00:10:17.270
Its moment arm distance is 1.

00:10:17.270 --> 00:10:22.500
So these are all the clockwise
moments, 100 times 1, right?

00:10:22.500 --> 00:10:25.320
It's 100 Newtons acting
downwards in the clockwise

00:10:25.320 --> 00:10:31.710
direction, clockwise moment, and
it's 1 meter away, plus we

00:10:31.710 --> 00:10:34.230
have the center of mass at the
top of the table, which is 20

00:10:34.230 --> 00:10:38.670
Newtons, plus 20 Newtons, and
that is 2 meters away from our

00:10:38.670 --> 00:10:44.250
designated axis,
so 20 times 2.

00:10:44.250 --> 00:10:46.950
And you might say, well, isn't
this leg exerting some force?

00:10:46.950 --> 00:10:49.780
Well, sure it is, but its
distance from our designated

00:10:49.780 --> 00:10:53.780
axis is zero, so its moment
of force is zero.

00:10:53.780 --> 00:10:56.420
Even if it is exerting a million
pounds or a million

00:10:56.420 --> 00:11:00.510
Newtons, its moment of force,
or its torque, would be zero

00:11:00.510 --> 00:11:03.470
because its moment arm distance
is zero, so we can

00:11:03.470 --> 00:11:05.330
ignore it, which makes
things simple.

00:11:05.330 --> 00:11:08.610
So those were the only
clockwise moments.

00:11:08.610 --> 00:11:10.490
And what's the counterclockwise
moment?

00:11:10.490 --> 00:11:13.350
Well, that's going to be the
force exerted by this leg.

00:11:13.350 --> 00:11:15.680
That's what's keeping the whole
thing from rotating.

00:11:15.680 --> 00:11:19.480
So it's the force of
the leg times its

00:11:19.480 --> 00:11:21.370
distance from our axis.

00:11:21.370 --> 00:11:23.770
Well, this is a total of 4
meters, which we've said here,

00:11:23.770 --> 00:11:25.020
times 4 meters.

00:11:28.330 --> 00:11:30.180
And so we can just solve.

00:11:30.180 --> 00:11:34.870
We get 100 plus 40, so we get
140 is equal to the force of

00:11:34.870 --> 00:11:37.110
the leg times 4.

00:11:37.110 --> 00:11:48.040
So what's 140-- 4 goes
into 140 35 times?

00:11:48.040 --> 00:11:50.430
My math is not so good.

00:11:50.430 --> 00:11:50.940
Is that right?

00:11:50.940 --> 00:11:53.730
4 times 30 is 120.

00:11:53.730 --> 00:11:55.690
120 plus 20.

00:11:55.690 --> 00:11:59.370
So the force of the leg
is 35 Newtons upwards.

00:11:59.370 --> 00:12:02.040
And since this isn't moving,
we know that the downward

00:12:02.040 --> 00:12:05.130
force right here must
be 35 Newtons.

00:12:05.130 --> 00:12:07.630
And so there's a couple of ways
we can think about it.

00:12:07.630 --> 00:12:14.950
If this leg is supporting 35
Newtons and we have a total

00:12:14.950 --> 00:12:18.850
weight here of 120 Newtons, our
total weight, the weight

00:12:18.850 --> 00:12:20.180
at the top of the
table plus the

00:12:20.180 --> 00:12:22.270
bookshelf, that's 120 Newtons.

00:12:22.270 --> 00:12:25.120
So the balance of this
must be supported by

00:12:25.120 --> 00:12:26.820
something or someone.

00:12:26.820 --> 00:12:28.060
So the balance of this
is going to be

00:12:28.060 --> 00:12:29.830
supported by this leg.

00:12:29.830 --> 00:12:33.810
So it's 120 minus 35 is what?

00:12:33.810 --> 00:12:34.120
[PHONE RINGS]

00:12:34.120 --> 00:12:36.640
Oh, my phone is ringing.

00:12:36.640 --> 00:12:39.010
120 minus 35 is what?

00:12:39.010 --> 00:12:41.710
120 minus 30 is 90.

00:12:41.710 --> 00:12:46.720
And then 90 minus
5 is 85 Newtons.

00:12:46.720 --> 00:12:49.540
It's so disconcerting
when my phone rings.

00:12:49.540 --> 00:12:51.340
I have trouble focusing.

00:12:51.340 --> 00:12:54.000
Anyway, it's probably because
my phone sounds

00:12:54.000 --> 00:12:56.160
like a freight train.

00:12:56.160 --> 00:12:58.940
Anyway, so there you go.

00:12:58.940 --> 00:13:01.800
This type of problem is actually
key to, as you can

00:13:01.800 --> 00:13:06.660
imagine, bridge builders, or
furniture manufacturers, or

00:13:06.660 --> 00:13:09.730
civil engineers who are bridge
builders, or architects,

00:13:09.730 --> 00:13:12.160
because you actually have to
figure out, well, if I design

00:13:12.160 --> 00:13:14.650
something a certain way, I have
to figure out how much

00:13:14.650 --> 00:13:18.160
weight each of the supporting
structures

00:13:18.160 --> 00:13:19.650
will have to support.

00:13:19.650 --> 00:13:22.920
And as you can imagine,
why is this one

00:13:22.920 --> 00:13:23.670
supporting more weight?

00:13:23.670 --> 00:13:25.990
Why is this leg supporting more
weight than that leg?

00:13:25.990 --> 00:13:29.340
Well, because this book, which
is 100 Newtons, which is a

00:13:29.340 --> 00:13:32.680
significant amount of the total
weight, is much closer

00:13:32.680 --> 00:13:35.670
to this leg than it
is to this leg.

00:13:35.670 --> 00:13:38.290
If we put it to the center, they
would balance, and then

00:13:38.290 --> 00:13:40.730
if we push it further to the
right, then this leg would

00:13:40.730 --> 00:13:43.310
start bearing more
of the weight.

00:13:43.310 --> 00:13:45.310
Anyway, hopefully you found
that interesting, and

00:13:45.310 --> 00:13:46.640
hopefully, I didn't
confuse you.

00:13:46.640 --> 00:13:49.160
And I will see you
in future videos.


Moments

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:04.390
Welcome to the presentation
on moments.

00:00:04.390 --> 00:00:07.680
So just if you were
wondering, I have

00:00:07.680 --> 00:00:09.310
already covered moments.

00:00:09.310 --> 00:00:11.760
You just may not have recognized
it, because I

00:00:11.760 --> 00:00:14.410
covered it in mechanical
advantage and torque.

00:00:14.410 --> 00:00:17.500
But I do realize that when I
covered it in mechanical

00:00:17.500 --> 00:00:22.200
advantage and torque, I think
I maybe over-complicated it.

00:00:22.200 --> 00:00:26.100
And if anything, I didn't cover
some of the most basic

00:00:26.100 --> 00:00:29.400
moment to force problems that
you see in your standards

00:00:29.400 --> 00:00:32.900
physics class, especially
physics classes that aren't

00:00:32.900 --> 00:00:36.250
focused on calculus or going
to make you a mechanical

00:00:36.250 --> 00:00:37.850
engineer the very next year.

00:00:37.850 --> 00:00:40.660
So we did that with-- why did
I write down the word

00:00:40.660 --> 00:00:43.980
"mechanical?" Oh yeah,
mechanical advantage.

00:00:43.980 --> 00:00:46.970
If you do a search for
mechanical advantage, I cover

00:00:46.970 --> 00:00:50.730
some things on moments
and also on torque.

00:00:50.730 --> 00:00:53.620
So what is moment of force?

00:00:53.620 --> 00:00:56.850
Well, it essentially is the
same thing as torque.

00:00:56.850 --> 00:00:58.490
It's just another word for it.

00:00:58.490 --> 00:01:02.730
And it's essentially force times
the distance to your

00:01:02.730 --> 00:01:03.650
axis of rotation.

00:01:03.650 --> 00:01:04.489
What do I mean by that?

00:01:04.489 --> 00:01:05.690
Let me take a simple example.

00:01:05.690 --> 00:01:07.870
Let's say that I have
a pivot point here.

00:01:14.210 --> 00:01:17.470
Let's say I have some type
of seesaw or whatever.

00:01:21.770 --> 00:01:23.260
There's a seesaw.

00:01:23.260 --> 00:01:28.290
And let's say that I were to
apply some force here and the

00:01:28.290 --> 00:01:31.750
forces that we care about-- this
was the exact same case

00:01:31.750 --> 00:01:33.850
with torque, because there's
essentially the same thing.

00:01:33.850 --> 00:01:36.370
The forces we care about
are the forces that are

00:01:36.370 --> 00:01:40.910
perpendicular to the distance
from our axis of rotation.

00:01:40.910 --> 00:01:45.000
So, in this case, if we're here,
the distance from our

00:01:45.000 --> 00:01:48.830
axis of rotation is this.

00:01:48.830 --> 00:01:50.990
That's our distance from
our axis of rotation.

00:01:50.990 --> 00:01:53.870
So we care about a perpendicular
force, either a

00:01:53.870 --> 00:01:57.220
force going up like that or a
force going down like that.

00:01:57.220 --> 00:02:01.490
Let's say I have a force
going up like that.

00:02:01.490 --> 00:02:06.830
Let's call that F, F1, d1.

00:02:06.830 --> 00:02:10.110
So essentially, the moment of
force created by this force is

00:02:10.110 --> 00:02:16.500
equal to F1 times d1, or the
perpendicular force times the

00:02:16.500 --> 00:02:17.990
moment arm distance.

00:02:17.990 --> 00:02:19.240
This is the moment
arm distance.

00:02:22.670 --> 00:02:25.450
That's also often called the
lever arm, if you're talking

00:02:25.450 --> 00:02:29.820
about a simple machine, and I
think that's the term I used

00:02:29.820 --> 00:02:33.480
when I did a video on
torque: moment arm.

00:02:33.480 --> 00:02:34.590
And why is this interesting?

00:02:34.590 --> 00:02:37.810
Well, first of all, this force
times distance, or this moment

00:02:37.810 --> 00:02:42.330
of force, or this torque, if it
has nothing balancing it or

00:02:42.330 --> 00:02:45.310
no offsetting moment or torque,
it's going to cause

00:02:45.310 --> 00:02:49.830
this seesaw in this example to
rotate clockwise, right?

00:02:49.830 --> 00:02:52.100
This whole thing, since it's
pivoting here, is going to

00:02:52.100 --> 00:02:53.380
rotate clockwise.

00:02:53.380 --> 00:02:56.150
The only way that it's not going
to rotate clockwise is

00:02:56.150 --> 00:02:59.360
if I have something keep-- so
right now, this end is going

00:02:59.360 --> 00:03:02.500
to want go down like that, and
the only way that I can keep

00:03:02.500 --> 00:03:05.320
it from happening is if I exert
some upward force here.

00:03:05.320 --> 00:03:08.820
So let's say that I exert some
upward force here that

00:03:08.820 --> 00:03:13.880
perfectly counterbalances, that
keeps this whole seesaw

00:03:13.880 --> 00:03:15.060
from rotating.

00:03:15.060 --> 00:03:21.530
F2, and it is a distance d2
away from our axis of

00:03:21.530 --> 00:03:23.930
rotation, but it's going in a
counterclockwise direction, so

00:03:23.930 --> 00:03:25.830
it wants to go like that.

00:03:25.830 --> 00:03:28.890
So the Law of Moments
essentially tells us, and we

00:03:28.890 --> 00:03:33.790
learned this when we talked
about the net torque, that

00:03:33.790 --> 00:03:36.910
this force times this distance
is equal to this force times

00:03:36.910 --> 00:03:37.500
this distance.

00:03:37.500 --> 00:03:47.780
So F1 d1 is equal to F2 d2, or
if you subtract this from both

00:03:47.780 --> 00:03:55.470
sides, you could get F2 d2 minus
F1 d1 is equal to 0.

00:03:55.470 --> 00:03:57.820
And actually, this is how we
dealt with it when we talked

00:03:57.820 --> 00:03:58.640
about torque.

00:03:58.640 --> 00:04:02.060
Because just the convention with
torque is if we have a

00:04:02.060 --> 00:04:04.890
counterclockwise rotation, it's
positive, and this is a

00:04:04.890 --> 00:04:07.940
counterclockwise rotation
in the example

00:04:07.940 --> 00:04:09.260
that I've drawn here.

00:04:09.260 --> 00:04:13.750
And if we have a clockwise
rotation, it has a negative

00:04:13.750 --> 00:04:15.540
torque, and that's just the
convention we did, and that's

00:04:15.540 --> 00:04:17.089
because torque is a
pseudovector, but I don't want

00:04:17.089 --> 00:04:18.310
to confuse right now.

00:04:18.310 --> 00:04:20.390
What you'll see is that these
moment problems are actually

00:04:20.390 --> 00:04:21.709
quite, quite straightforward.

00:04:21.709 --> 00:04:23.240
So let's do a couple.

00:04:23.240 --> 00:04:29.640
It always becomes a lot easier
when you do a problem, except

00:04:29.640 --> 00:04:33.780
when you try to erase
things with green.

00:04:33.780 --> 00:04:36.410
So let's say that --
let me plug in real

00:04:36.410 --> 00:04:38.070
numbers for these values.

00:04:38.070 --> 00:04:39.250
Let me erase all of this.

00:04:39.250 --> 00:04:43.210
Let me just erase everything.

00:04:43.210 --> 00:04:44.450
There you go.

00:04:44.450 --> 00:04:46.170
All right, let me draw
a lever arm again.

00:04:48.980 --> 00:04:51.290
So what we learned when we
learned about torque is that

00:04:51.290 --> 00:04:55.130
an object won't rotate if the
net torque, the sum of all the

00:04:55.130 --> 00:04:58.670
torques around it, are zero,
and we're going to apply

00:04:58.670 --> 00:05:00.280
essentially that same
principle here.

00:05:04.250 --> 00:05:08.700
So let's do it with masses,
because I think that helps

00:05:08.700 --> 00:05:11.980
explain a lot of things and
makes this seesaw example a

00:05:11.980 --> 00:05:13.230
little bit more tangible.

00:05:15.600 --> 00:05:21.940
Let's say I have a 5-kilogram
mass here, and let's say that

00:05:21.940 --> 00:05:25.640
gravity is 10 meters
per second squared.

00:05:25.640 --> 00:05:28.480
So what is the downward
force here?

00:05:28.480 --> 00:05:29.450
What is the downward force?

00:05:29.450 --> 00:05:32.060
It's going to be the mass times
acceleration, so it's

00:05:32.060 --> 00:05:35.140
going to be 50 Newtons.

00:05:35.140 --> 00:05:38.350
And let's say that the distance,
the moment arm

00:05:38.350 --> 00:05:42.570
distance or the lever arm
distance here, let's say that

00:05:42.570 --> 00:05:47.880
this distance right
here is 10 meters.

00:05:47.880 --> 00:05:50.800
Let's say that I have
another mass.

00:05:50.800 --> 00:05:58.830
Let's say it's a 25 kilogram--
no, that's too much.

00:05:58.830 --> 00:06:01.090
Let's say it's 10 kilograms.
Let's say I have

00:06:01.090 --> 00:06:05.490
a 10-kilogram mass.

00:06:05.490 --> 00:06:09.590
And I want to place it some
distance d from the fulcrum or

00:06:09.590 --> 00:06:12.600
from the axis of rotation so
that it completely balances

00:06:12.600 --> 00:06:14.140
this 5-kilogram mass.

00:06:14.140 --> 00:06:17.550
So how far from the axis of
rotation do I put this

00:06:17.550 --> 00:06:19.390
10-kilogram mass?

00:06:19.390 --> 00:06:20.310
This is the distance, right?

00:06:20.310 --> 00:06:21.270
Because we actually carry
the distance to the

00:06:21.270 --> 00:06:22.720
center of the mass.

00:06:22.720 --> 00:06:25.750
Well, how much force
is this 10-kilogram

00:06:25.750 --> 00:06:27.400
mass exerting downwards?

00:06:27.400 --> 00:06:30.120
Well, it's 10 kilograms times 10
meters per second squared,

00:06:30.120 --> 00:06:34.620
it's 100 Newtons.

00:06:34.620 --> 00:06:35.540
This is acting what?

00:06:35.540 --> 00:06:37.390
This is acting clockwise,
right?

00:06:37.390 --> 00:06:39.830
This one's acting clockwise
and this one's acting

00:06:39.830 --> 00:06:41.130
counterclockwise, right?

00:06:41.130 --> 00:06:42.750
So they are offsetting
each other.

00:06:42.750 --> 00:06:43.840
So we could do it a
couple of ways.

00:06:43.840 --> 00:06:50.190
We could say that 50 Newtons,
the moment in the

00:06:50.190 --> 00:06:54.950
counterclockwise direction, 50
Newtons times 10 meters, in

00:06:54.950 --> 00:06:57.890
order for this thing to not
rotate has to be equal to the

00:06:57.890 --> 00:07:00.560
moment in the clockwise
direction.

00:07:00.560 --> 00:07:02.520
And so the moment in the
clockwise direction is equal

00:07:02.520 --> 00:07:12.140
to 100 Newtons times some
distance, let's call that d,

00:07:12.140 --> 00:07:14.230
100 Newtons times d, and
then we could just

00:07:14.230 --> 00:07:15.210
solve for d, right?

00:07:15.210 --> 00:07:18.650
We get 50 times 10 is 500.

00:07:18.650 --> 00:07:24.730
500 Newton-meters is equal
to 100 Newtons times d.

00:07:24.730 --> 00:07:25.740
That's 100.

00:07:25.740 --> 00:07:29.970
Divide both sides by 100, you
get 5 meters is equal to d.

00:07:29.970 --> 00:07:32.410
So d is equal to 5.

00:07:32.410 --> 00:07:33.420
That's interesting.

00:07:33.420 --> 00:07:35.950
And I think this kind of
confirms your intuition from

00:07:35.950 --> 00:07:40.390
playing at the playground that
you can put a heavier weight

00:07:40.390 --> 00:07:44.090
closer to the axis of rotation
to offset a light weight

00:07:44.090 --> 00:07:44.790
that's further away.

00:07:44.790 --> 00:07:47.530
Or the other way to put it is
you could put a light weight

00:07:47.530 --> 00:07:50.040
further away and you kind of get
a mechanical advantage in

00:07:50.040 --> 00:07:53.030
terms of offsetting the
heavier weight.

00:07:53.030 --> 00:07:58.240
So let's do a more difficult
problem.

00:07:58.240 --> 00:08:01.090
I think the more problems we
do here, the more sense

00:08:01.090 --> 00:08:03.680
everything will make.

00:08:03.680 --> 00:08:07.430
So let's say that we have
a bunch of masses.

00:08:15.450 --> 00:08:16.470
Actually, let's not
do it with masses.

00:08:16.470 --> 00:08:17.820
Let's just do it with forces
because I want to

00:08:17.820 --> 00:08:20.070
complicate the issue.

00:08:20.070 --> 00:08:22.410
So this is the pivot.

00:08:22.410 --> 00:08:28.940
And let's say I have a force
here that's 10 Newtons going

00:08:28.940 --> 00:08:34.360
in the clockwise direction, and
let's say it is at-- let's

00:08:34.360 --> 00:08:37.440
say if this is 0, let's say that
this is at minus 8, so

00:08:37.440 --> 00:08:41.190
this distance is 8, right?

00:08:41.190 --> 00:08:47.820
Let's say that I have another
force going down at 5 Newtons.

00:08:47.820 --> 00:08:52.060
And let's say that its
x-coordinate is minus 6.

00:08:52.060 --> 00:08:55.980
Let's say I have another force
that's going up here, and

00:08:55.980 --> 00:08:57.790
let's say that it
is 50 Newtons.

00:08:57.790 --> 00:08:58.790
This might get complicated.

00:08:58.790 --> 00:09:01.510
50 Newtons, and it's at minus
2, so this distance

00:09:01.510 --> 00:09:04.970
right here is 2.

00:09:04.970 --> 00:09:10.750
Let's say that I need to figure
out-- and I'm making

00:09:10.750 --> 00:09:12.000
this up on the fly.

00:09:12.000 --> 00:09:16.750
Let's say that I have another
force here that is 5 Newtons.

00:09:16.750 --> 00:09:20.360
No, let's make it a weird
number, 6 Newtons, and this

00:09:20.360 --> 00:09:22.840
distance right here
is 3 meters.

00:09:22.840 --> 00:09:26.000
And let's say that I need to
figure out what force I need

00:09:26.000 --> 00:09:28.780
to apply here upwards or
downwards-- I actually don't

00:09:28.780 --> 00:09:31.380
know, because I'm doing this on
the fly-- to make sure that

00:09:31.380 --> 00:09:34.660
this whole thing
doesn't rotate.

00:09:34.660 --> 00:09:36.950
So to make sure this whole
thing doesn't rotate,

00:09:36.950 --> 00:09:40.090
essentially what we have to
say is that all of the

00:09:40.090 --> 00:09:44.770
counterclockwise moments or all
of the counter clockwise

00:09:44.770 --> 00:09:49.170
torques have to offset all
of the clockwise torques.

00:09:49.170 --> 00:09:50.880
And notice, they're not
all on the same side.

00:09:50.880 --> 00:09:52.350
So what are all of the things
that are acting in the

00:09:52.350 --> 00:09:53.570
counterclockwise direction?

00:09:53.570 --> 00:09:56.790
So counter clockwise
is that way, right?

00:09:56.790 --> 00:09:59.850
So this is acting
counterclockwise, this is

00:09:59.850 --> 00:10:04.080
acting counterclockwise,
and that's it, right?

00:10:04.080 --> 00:10:05.530
So the other ones
are clockwise.

00:10:05.530 --> 00:10:07.000
And we don't know this one.

00:10:07.000 --> 00:10:10.210
Let's assume for a second.

00:10:10.210 --> 00:10:11.190
We could assume either way.

00:10:11.190 --> 00:10:12.680
And if we get a negative, that
means it's the opposite.

00:10:12.680 --> 00:10:16.830
So let's assume that this is a--
all of the clockwise ones

00:10:16.830 --> 00:10:17.770
I'll do in this dark brown.

00:10:17.770 --> 00:10:19.950
Let's assume this is clockwise,
let's assume that

00:10:19.950 --> 00:10:23.940
this is clockwise, and let's
assume that our mystery force

00:10:23.940 --> 00:10:25.190
is also clockwise.

00:10:29.380 --> 00:10:32.060
All of the counterclockwise
moments have to offset all the

00:10:32.060 --> 00:10:33.340
clockwise moments.

00:10:33.340 --> 00:10:37.700
So what are the counterclockwise
moments?

00:10:37.700 --> 00:10:40.170
Well, this one's
counterclockwise, so it's 10

00:10:40.170 --> 00:10:43.440
Newtons, 10 times its distance
from its moment arm.

00:10:43.440 --> 00:10:45.600
We said it's 8, because it's
at the x-coordinate minus 8

00:10:45.600 --> 00:10:50.310
from 0, so it's 10
times 8, plus 50.

00:10:50.310 --> 00:10:58.360
This is also counterclockwise
times 6, 50 times 6, and those

00:10:58.360 --> 00:11:00.840
are all of our counterclockwise
moments and

00:11:00.840 --> 00:11:02.340
that has to equal the
clockwise moments.

00:11:02.340 --> 00:11:03.880
So clockwise moments,
let's see.

00:11:03.880 --> 00:11:07.450
We have 5 Newtons that's going
clockwise times 6.

00:11:10.560 --> 00:11:12.880
5 Newtons.

00:11:12.880 --> 00:11:14.400
Actually, was this 6?

00:11:14.400 --> 00:11:18.820
No, if this is 6, I must have
written some other number here

00:11:18.820 --> 00:11:19.860
that I can't read now.

00:11:19.860 --> 00:11:22.070
How far did I say this was?

00:11:22.070 --> 00:11:23.770
Let's say that this is 2.

00:11:23.770 --> 00:11:28.840
So that 50, let's say this is
2, it's negative 2, because

00:11:28.840 --> 00:11:30.010
that's what it looks like.

00:11:30.010 --> 00:11:31.430
I apologize for confusing you.

00:11:31.430 --> 00:11:33.650
So what were all the
counterclockwise moments?

00:11:33.650 --> 00:11:38.130
This 10 Newtons times its
distance 8, the 50 Newtons

00:11:38.130 --> 00:11:39.790
times this distance, 2.

00:11:39.790 --> 00:11:40.750
Don't get confused
by the negative.

00:11:40.750 --> 00:11:42.890
I just kind of said we're in
the x-coordinate axis or at

00:11:42.890 --> 00:11:45.620
minus 8 if this is 0, but it's
8 units away, right?

00:11:45.620 --> 00:11:49.810
And this 50, its moment arm
distance is 2 units.

00:11:49.810 --> 00:11:53.640
So that has to equal all of
the clockwise moments.

00:11:53.640 --> 00:11:59.430
So the clockwise moments
is 5 Newtons times 6.

00:11:59.430 --> 00:12:01.760
Its distance is 6 and it's
5 Newtons going in

00:12:01.760 --> 00:12:03.720
the clockwise direction.

00:12:03.720 --> 00:12:07.170
And then we have plus
6 Newtons times 3,

00:12:07.170 --> 00:12:08.690
plus 6 times 3.

00:12:08.690 --> 00:12:10.550
And then we're just assuming,
we don't know for sure.

00:12:13.730 --> 00:12:14.840
Let's say we're applying
the force.

00:12:14.840 --> 00:12:16.010
I should have told you
ahead of time so you

00:12:16.010 --> 00:12:16.620
could do this problem.

00:12:16.620 --> 00:12:20.430
Let's say that we're applying
the force at 10 meters away

00:12:20.430 --> 00:12:21.480
from our fulcrum arm.

00:12:21.480 --> 00:12:23.140
So force times 10.

00:12:23.140 --> 00:12:25.240
So now let's just solve
for the force.

00:12:25.240 --> 00:12:35.310
We get 80 plus 100 is equal
to 30 plus 18 plus 10F.

00:12:35.310 --> 00:12:40.950
We get 180 is equal
to 48 plus 10F.

00:12:40.950 --> 00:12:42.500
What's 180 minus 48?

00:12:42.500 --> 00:12:50.350
It's 132 is equal to
10F, or we get F is

00:12:50.350 --> 00:12:54.780
equal to 13.2 Newtons.

00:12:54.780 --> 00:12:59.530
So we guessed correctly that
this is going to be a-- sorry,

00:12:59.530 --> 00:13:03.490
this is going to be a-- I keep
mixing up all of the clockwise

00:13:03.490 --> 00:13:04.740
and counterclockwise.

00:13:06.670 --> 00:13:09.360
This is going to be
a clockwise force.

00:13:09.360 --> 00:13:11.540
These were all of the-- sorry,
this is going to be a

00:13:11.540 --> 00:13:13.010
counterclockwise force, right?

00:13:13.010 --> 00:13:15.040
A clock, this is
counterclockwise.

00:13:15.040 --> 00:13:17.140
Let me label that because I
think I said it wrong several

00:13:17.140 --> 00:13:19.240
times in the video.

00:13:19.240 --> 00:13:23.180
So these go clockwise.

00:13:26.510 --> 00:13:29.440
And it's this one
and this one.

00:13:29.440 --> 00:13:31.650
And what were the
counterclockwise?

00:13:31.650 --> 00:13:34.480
These go counterclockwise.

00:13:34.480 --> 00:13:39.830
So we have to apply a 13.10
Newton force 10 meters away,

00:13:39.830 --> 00:13:45.380
which will generate 132
Newton-meters moment in the

00:13:45.380 --> 00:13:48.410
counterclockwise direction,
which will perfectly offset

00:13:48.410 --> 00:13:52.100
all of the other moments, and
our lever will not move.

00:13:52.100 --> 00:13:54.280
Anyway, I might have confused
you with all the

00:13:54.280 --> 00:13:56.170
counterclockwise/clockwise.

00:13:56.170 --> 00:13:58.940
But just keep in mind that all
the moments in one rotational

00:13:58.940 --> 00:14:01.270
direction have to offset all
the moments in the other

00:14:01.270 --> 00:14:02.510
rotational direction.

00:14:02.510 --> 00:14:06.440
All a moment is is the force
times the distance from the

00:14:06.440 --> 00:14:11.260
fulcrum arm, so force times
distance from fulcrum arm.

00:14:11.260 --> 00:14:13.570
I'll see you in the
next video.


Capacitance

WEBVTT
Kind: captions
Language: en

00:00:00.740 --> 00:00:04.150
We learned several videos ago
that if I had an infinite

00:00:04.150 --> 00:00:08.284
uniformly charged plane-- let me
draw one right here, and I

00:00:08.284 --> 00:00:09.960
won't draw it infinite and
I'll tell you why in a

00:00:09.960 --> 00:00:13.450
second-- that if we had an
infinite uniformly charged

00:00:13.450 --> 00:00:19.600
plane, and let's say this
one's positive, that the

00:00:19.600 --> 00:00:23.935
electric field generated
by it is constant.

00:00:29.030 --> 00:00:30.290
Those are the field lines.

00:00:30.290 --> 00:00:32.890
They should all be
the same size.

00:00:32.890 --> 00:00:38.210
And the strength of the field,
or the magnitude of the field,

00:00:38.210 --> 00:00:45.820
is equal to 2 times Coulomb's
constant times pi times the

00:00:45.820 --> 00:00:47.750
charge density of the plate.

00:00:47.750 --> 00:00:50.130
So if this is infinite-- so
what was charge density?

00:00:50.130 --> 00:00:54.450
We defined it when we proved
that this truly is a uniform

00:00:54.450 --> 00:00:57.140
electric field, but what
is charge density?

00:00:57.140 --> 00:01:03.280
Charge density is just the total
amount of charge divided

00:01:03.280 --> 00:01:05.290
by the area, or charge
per area.

00:01:05.290 --> 00:01:10.560
Well, if we have an infinite
plane, the area's going to be

00:01:10.560 --> 00:01:13.110
infinite, and so if this is a
constant number, this is also

00:01:13.110 --> 00:01:16.740
going to be infinite, so it's
kind of hard to work with.

00:01:16.740 --> 00:01:22.350
But what we also know is that
when we have a non-infinite

00:01:22.350 --> 00:01:27.210
plane that has some finite area,
that near the center of

00:01:27.210 --> 00:01:32.250
it and fairly close to it, it
approximates an infinite

00:01:32.250 --> 00:01:34.780
uniformly charged plane.

00:01:34.780 --> 00:01:37.180
So with that said, let's see if
we can figure out some of

00:01:37.180 --> 00:01:40.830
the properties of the voltage
and how the voltage relates to

00:01:40.830 --> 00:01:42.350
the charge.

00:01:42.350 --> 00:01:48.130
If we were to have two
parallel-- let me draw it

00:01:48.130 --> 00:01:50.040
before I say it, because I
think saying it'll just

00:01:50.040 --> 00:01:51.850
confuse it.

00:01:51.850 --> 00:02:02.350
So let's say I have two plates,
that plate-- and then

00:02:02.350 --> 00:02:05.290
I'll do this one in a different
color-- and I have

00:02:05.290 --> 00:02:11.650
that plate, and let's say
they're the same size and they

00:02:11.650 --> 00:02:13.470
both have area A.

00:02:13.470 --> 00:02:19.860
Let's say that I place plus
Q worth of charges here.

00:02:19.860 --> 00:02:22.460
So this is plus Q so this is
positively charged, right?

00:02:22.460 --> 00:02:24.010
I could draw a bunch
of charges here.

00:02:24.010 --> 00:02:30.590
Let's say this is minus Q, so
this is negatively charged.

00:02:30.590 --> 00:02:32.860
So what's the electric field
going to look like

00:02:32.860 --> 00:02:34.730
between these two?

00:02:34.730 --> 00:02:37.070
Well, it's essentially going to
be the combination of the

00:02:37.070 --> 00:02:40.400
electric field generated by
this plate on top of the

00:02:40.400 --> 00:02:42.400
electric field generated
by this plate.

00:02:42.400 --> 00:02:45.290
And they're both going to be
constant close to the center,

00:02:45.290 --> 00:02:46.970
assuming that they're
reasonably-- and let's say

00:02:46.970 --> 00:02:49.220
that they're d apart.

00:02:49.220 --> 00:02:52.140
Assuming that d isn't too big,
near the center we're going to

00:02:52.140 --> 00:02:53.660
have a constant electric
field.

00:02:53.660 --> 00:02:58.070
For example, this green one is
going to be generating-- its

00:02:58.070 --> 00:03:00.470
field lines are going to look
something like this.

00:03:00.470 --> 00:03:02.200
Near the center,
it's constant.

00:03:02.200 --> 00:03:03.450
These are meant to
look constant.

00:03:06.500 --> 00:03:10.250
Near the center, it'll look like
that, and it'll start to

00:03:10.250 --> 00:03:12.250
bulge out when you
get to the edges.

00:03:14.770 --> 00:03:18.440
Once again, near the center,
it's constant.

00:03:18.440 --> 00:03:19.635
That one should've
been at an angle.

00:03:19.635 --> 00:03:22.330
They start to bulge out,
and it'll look

00:03:22.330 --> 00:03:23.830
something like that.

00:03:23.830 --> 00:03:28.120
And similarly, this purple plate
will generate a constant

00:03:28.120 --> 00:03:30.630
electric field, and since it's
negatively charged, the field

00:03:30.630 --> 00:03:33.470
lines will be going towards it,
not away from it, so its

00:03:33.470 --> 00:03:35.020
field lines are going to look
something like this.

00:03:35.020 --> 00:03:40.890
Near the center, they'll be
constant, and its field lines

00:03:40.890 --> 00:03:42.140
are going to look something
like that.

00:03:44.640 --> 00:03:48.380
As you can see, they're going
to be of the same magnitude

00:03:48.380 --> 00:03:52.730
and in the same direction,
and they also

00:03:52.730 --> 00:03:54.820
will bulge out there.

00:03:54.820 --> 00:03:59.090
So the big picture is that you
just kind of have twice the

00:03:59.090 --> 00:04:02.530
electric field as you would have
if you just had one of

00:04:02.530 --> 00:04:03.920
these plates.

00:04:03.920 --> 00:04:06.690
So let's say we're operating
near the center of these,

00:04:06.690 --> 00:04:09.940
where we have roughly a constant
electric field and

00:04:09.940 --> 00:04:12.620
see if we can figure out the
relationship between the

00:04:12.620 --> 00:04:17.760
voltage across these two plates
and the area, and maybe

00:04:17.760 --> 00:04:20.120
the distance between
the two plates.

00:04:20.120 --> 00:04:23.260
So we know that the electric
field generated by any one of

00:04:23.260 --> 00:04:27.100
these charge plates-- I'll do it
in the blue of this color.

00:04:27.100 --> 00:04:29.190
So for the bottom plate right
here, what is the electric

00:04:29.190 --> 00:04:29.810
field generated?

00:04:29.810 --> 00:04:34.930
It's 2K pi times sigma.

00:04:34.930 --> 00:04:40.270
Sigma is just the total charge
divided by the area.

00:04:40.270 --> 00:04:45.640
So Q/A, right?

00:04:45.640 --> 00:04:48.570
And we know that the total
electric field generated by

00:04:48.570 --> 00:04:50.890
this one is going to be
essentially the same thing.

00:04:50.890 --> 00:04:53.370
I mean, we could say it's a
minus, a negative, because

00:04:53.370 --> 00:04:56.110
it's going towards it, but it's

00:04:56.110 --> 00:04:57.140
essentially the same thing.

00:04:57.140 --> 00:04:58.800
Because we see that they overlap
just drawing the field

00:04:58.800 --> 00:05:02.750
line, so the electric field
from that one, and we know

00:05:02.750 --> 00:05:04.570
that they go in the
same direction.

00:05:04.570 --> 00:05:08.155
If this was somehow-- well, this
is negative, so the field

00:05:08.155 --> 00:05:08.850
lines go towards it.

00:05:08.850 --> 00:05:14.300
So plus 2K pi and this is Q/A.

00:05:14.300 --> 00:05:16.640
We could have said minus and
then had a minus Q/A, but we

00:05:16.640 --> 00:05:18.730
know that they go into same
direction, so we know that

00:05:18.730 --> 00:05:19.820
they're going to be additive.

00:05:19.820 --> 00:05:22.950
And so we know that the total
electric field is

00:05:22.950 --> 00:05:29.625
going to be 4K pi Q/A.

00:05:32.670 --> 00:05:34.320
So now we know the
exact strength of

00:05:34.320 --> 00:05:35.490
the electric field.

00:05:35.490 --> 00:05:41.220
Let's see if we can figure out
the voltage difference between

00:05:41.220 --> 00:05:46.850
this point and this point.

00:05:46.850 --> 00:05:49.420
What was voltage difference,
just as a review?

00:05:49.420 --> 00:05:53.680
Well, voltage difference is
the electrical potential

00:05:53.680 --> 00:05:59.200
energy per charge if the charge
was here versus here.

00:05:59.200 --> 00:06:02.500
So how much more potential
energy per coulomb is there

00:06:02.500 --> 00:06:04.390
for a charge to be here
relative to here?

00:06:04.390 --> 00:06:07.220
So another way to view it is a
charge here, a positive charge

00:06:07.220 --> 00:06:10.170
here, because by default we're
always assuming a positive

00:06:10.170 --> 00:06:14.100
charge when we talk about
positive numbers and the

00:06:14.100 --> 00:06:15.820
direction of the field lines
or what the positive

00:06:15.820 --> 00:06:16.840
charge would do.

00:06:16.840 --> 00:06:21.180
So by default, a positive charge
here really wants to go

00:06:21.180 --> 00:06:24.500
up to this negative plate,
although we later learned that

00:06:24.500 --> 00:06:28.500
most of the movement in
electronics and electricity,

00:06:28.500 --> 00:06:30.080
it's actually the negative
charge that's moving.

00:06:30.080 --> 00:06:31.385
It's the electrons moving.

00:06:31.385 --> 00:06:33.370
But let's say we did
have a positive ion

00:06:33.370 --> 00:06:34.500
or a positive charge.

00:06:34.500 --> 00:06:39.170
The voltage is a measure of if
any charge is here, how badly

00:06:39.170 --> 00:06:42.550
does it want to move to this
point if it has a way to move?

00:06:42.550 --> 00:06:46.500
If we have air here or if we
have a vacuum here, it might

00:06:46.500 --> 00:06:49.740
be difficult or impossible
for it to move up here.

00:06:49.740 --> 00:06:52.310
But maybe if we were to connect
a wire where the

00:06:52.310 --> 00:06:55.360
charges could freely conduct,
then it will move.

00:06:55.360 --> 00:06:57.420
And the voltage is just
kind of how badly

00:06:57.420 --> 00:06:58.210
does it want to move?

00:06:58.210 --> 00:07:00.990
You could almost view it
as electrical pressure.

00:07:00.990 --> 00:07:03.290
And maybe I'll do a whole video
on trying to get an

00:07:03.290 --> 00:07:05.330
intuitive understanding of
voltage, because that really

00:07:05.330 --> 00:07:08.040
is probably the most important
thing to get an intuitive

00:07:08.040 --> 00:07:10.240
understanding of, if you ever
want to study electrical

00:07:10.240 --> 00:07:11.900
engineering or whatever.

00:07:11.900 --> 00:07:13.190
But anyway, back
to the problem.

00:07:13.190 --> 00:07:17.060
We know that the combined
electric field is this, right?

00:07:17.060 --> 00:07:19.590
It goes upwards in
that direction.

00:07:19.590 --> 00:07:25.840
So what is the electric
potential at this point

00:07:25.840 --> 00:07:28.430
relative to this point or
the potential difference

00:07:28.430 --> 00:07:30.380
from here to here?

00:07:30.380 --> 00:07:34.220
Well, that's the amount of
energy per charge it would

00:07:34.220 --> 00:07:42.650
take to move a positive charge
from here to there, right?

00:07:42.650 --> 00:07:44.810
Remember, electric potential
energy is the amount of work

00:07:44.810 --> 00:07:48.210
necessary to move a charge from
there to there, and then

00:07:48.210 --> 00:07:52.810
the voltage is how much
to do it per charge.

00:07:52.810 --> 00:07:53.910
Let me write that down.

00:07:53.910 --> 00:07:58.730
So the work necessary to move a
charge from there to there--

00:07:58.730 --> 00:08:07.010
let's say a 1-coulomb charge, it
will be 1 coulomb times the

00:08:07.010 --> 00:08:09.060
electric field, because we're
always going to have to be

00:08:09.060 --> 00:08:10.660
going against the
electric field.

00:08:10.660 --> 00:08:13.260
So we have to apply an equal
and opposite force.

00:08:13.260 --> 00:08:17.360
So the force that is going to
be the electric field-- so

00:08:17.360 --> 00:08:19.750
far, this just generates this
force. coulomb times electric

00:08:19.750 --> 00:08:23.430
field, charge times electric
field, tells us the force on

00:08:23.430 --> 00:08:25.200
the charge, right?

00:08:25.200 --> 00:08:26.410
That's force, and
then we have to

00:08:26.410 --> 00:08:28.380
multiply that times distance.

00:08:28.380 --> 00:08:31.020
Force times distance.

00:08:31.020 --> 00:08:36.590
So we see the work necessary
is going to be the electric

00:08:36.590 --> 00:08:42.929
field times d joules-- the J is
joules-- and so what is the

00:08:42.929 --> 00:08:48.210
voltage difference or the
electric potential difference

00:08:48.210 --> 00:08:50.560
between this point
and this point?

00:08:50.560 --> 00:08:54.720
Let's call that point a.

00:08:54.720 --> 00:08:56.450
Let's call that point b.

00:08:56.450 --> 00:09:03.040
So Va minus Vb, which is the
voltage difference, that's

00:09:03.040 --> 00:09:06.000
essentially the electric
potential energy difference

00:09:06.000 --> 00:09:08.580
divided by the charge.

00:09:08.580 --> 00:09:09.330
Or, per charge.

00:09:09.330 --> 00:09:11.900
Well, here, the charge was just
1, so we can just divide

00:09:11.900 --> 00:09:18.380
by 1, and we see that it is
equal to the electric field

00:09:18.380 --> 00:09:20.410
times the distance.

00:09:20.410 --> 00:09:23.200
And the units are going to be
joules because we divided both

00:09:23.200 --> 00:09:27.570
sides by charge joules per
coulomb, or volts, right?

00:09:27.570 --> 00:09:29.600
That's just the units.

00:09:29.600 --> 00:09:30.380
So what does that equal?

00:09:30.380 --> 00:09:36.250
So the voltage difference-- so
we can say change in voltage.

00:09:36.250 --> 00:09:39.130
The voltage difference is equal
to the electric field,

00:09:39.130 --> 00:09:51.720
which we know is constant 4K
pi Q over A times distance.

00:09:51.720 --> 00:09:53.020
Or we could rewrite this.

00:09:53.020 --> 00:10:00.300
Let's see if we could write
Q as a function of V.

00:10:00.300 --> 00:10:03.220
So if we just do a little bit of
algebraic manipulation, we

00:10:03.220 --> 00:10:08.110
can get Q is equal to what?

00:10:08.110 --> 00:10:13.800
We would essentially divide
both sides by 4 pi Kd and

00:10:13.800 --> 00:10:19.350
multiply both sides by
A, so we would get A

00:10:19.350 --> 00:10:29.680
over 4K pi d voltage.

00:10:29.680 --> 00:10:30.960
And why is this interesting?

00:10:30.960 --> 00:10:33.030
Why did I go through all of
this work to get this

00:10:33.030 --> 00:10:33.870
relationship?

00:10:33.870 --> 00:10:37.780
Well, what it shows you, if you
look at this, if we assume

00:10:37.780 --> 00:10:40.150
that the area of the plates
aren't changing-- that's a

00:10:40.150 --> 00:10:43.630
constant; this is definitely a
constant-- and if we assume

00:10:43.630 --> 00:10:46.980
that the distance between the
plates don't change, what we

00:10:46.980 --> 00:10:49.690
see is that there's a
proportional difference

00:10:49.690 --> 00:10:54.910
between the voltage and the
amount of the combined charge

00:10:54.910 --> 00:10:56.080
in the plates.

00:10:56.080 --> 00:10:59.680
And that's interesting because,
before doing this,

00:10:59.680 --> 00:11:03.240
maybe voltage is somehow
proportional to the square of

00:11:03.240 --> 00:11:06.435
the charges or to the square
root, but now we know that

00:11:06.435 --> 00:11:08.280
it's directly proportionally.

00:11:08.280 --> 00:11:14.430
And actually, this term right
here has a name, and it is

00:11:14.430 --> 00:11:15.290
called capacitance.

00:11:15.290 --> 00:11:18.220
And so another way of rewriting
this, if we divide

00:11:18.220 --> 00:11:33.660
both sides by voltage, we get
Q/V is equal to 1 over 4K pi

00:11:33.660 --> 00:11:37.270
area over distance.

00:11:37.270 --> 00:11:41.340
And so what it essentially says
is that the amount of

00:11:41.340 --> 00:11:43.730
energy that-- well, actually,
I don't want to

00:11:43.730 --> 00:11:45.520
go into that yet.

00:11:45.520 --> 00:11:48.630
But for a given configuration,
and the configuration is

00:11:48.630 --> 00:11:53.030
defined by the area of the
plates and the distance-- for

00:11:53.030 --> 00:11:55.890
a given configuration, if I know
the amount of charge that

00:11:55.890 --> 00:11:59.000
I put onto the plates, if I did
a minus Q here and a plus

00:11:59.000 --> 00:12:00.900
Q here, I know the voltage
across the

00:12:00.900 --> 00:12:02.875
plates or vice versa.

00:12:02.875 --> 00:12:05.090
If I know the voltage across
the plates and I know its

00:12:05.090 --> 00:12:09.300
configuration, I know how much
charge there is, and this is

00:12:09.300 --> 00:12:12.010
called capacitance, and the
unit for capacitance

00:12:12.010 --> 00:12:13.990
is called the Farad.

00:12:13.990 --> 00:12:15.590
And if you become an electrical
engineer or even

00:12:15.590 --> 00:12:17.350
take a couple of electrical
engineering courses, you'll

00:12:17.350 --> 00:12:19.370
become very familiar
with this.

00:12:19.370 --> 00:12:22.650
And one other thing to point
out; this term right here,

00:12:22.650 --> 00:12:26.200
just so you know a little
bit of terminology.

00:12:26.200 --> 00:12:27.360
This term right here.

00:12:27.360 --> 00:12:36.630
This 1 over 4K pi, this is often
called epsilon nought,

00:12:36.630 --> 00:12:39.220
or just epsilon, and that's
called the permittivity of

00:12:39.220 --> 00:12:41.560
free space or permittivity
of the vacuum.

00:12:41.560 --> 00:12:45.460
And maybe in a future lecture
or a future video, I'll talk

00:12:45.460 --> 00:12:47.010
more about why it's
called that.

00:12:47.010 --> 00:12:49.910
But anyway, I'm already well
over the time limit.

00:12:49.910 --> 00:12:55.260
So I just wanted to give you a
sense of, one, that you can

00:12:55.260 --> 00:12:58.230
calculate the voltage across
what we call, in

00:12:58.230 --> 00:12:59.600
this case, a capacitor.

00:12:59.600 --> 00:13:01.430
It has capacitance.

00:13:01.430 --> 00:13:03.385
That voltage, you can
kind of view it as

00:13:03.385 --> 00:13:04.170
the electric pressure.

00:13:04.170 --> 00:13:06.800
How bad does the charge here
want to move here?

00:13:06.800 --> 00:13:09.750
And if you put a wire here,
you'll learn in a second-- not

00:13:09.750 --> 00:13:11.380
in a second, in several
videos-- that

00:13:11.380 --> 00:13:12.575
that charge will flow.

00:13:12.575 --> 00:13:15.610
Or actually the negative charges
will flow this way and

00:13:15.610 --> 00:13:16.310
generate current.

00:13:16.310 --> 00:13:17.780
And we'll do that when we start
learning a little bit

00:13:17.780 --> 00:13:19.360
more about electricity.

00:13:19.360 --> 00:13:24.120
For any given configuration,
it has a corresponding

00:13:24.120 --> 00:13:27.030
capacitance, and then given
that capacitance, if I put

00:13:27.030 --> 00:13:28.910
some amount of charge, I can
figure out the voltage, or if

00:13:28.910 --> 00:13:31.070
I know there's some voltage, I
can figure out the charge.

00:13:31.070 --> 00:13:34.350
Anyway, I will see you
in the next video.


Voltage

WEBVTT
Kind: captions
Language: en

00:00:00.830 --> 00:00:03.510
Before we move on, I want to
clarify something that I've

00:00:03.510 --> 00:00:04.490
inadvertently done.

00:00:04.490 --> 00:00:06.660
I think I was not exact
with some of the

00:00:06.660 --> 00:00:07.550
terminology I used.

00:00:07.550 --> 00:00:10.920
So I want to highlight the
difference between two things

00:00:10.920 --> 00:00:12.590
that I've used almost
interchangeably up to this

00:00:12.590 --> 00:00:15.100
point, but now that we are about
to embark on learning

00:00:15.100 --> 00:00:18.260
what voltage is, I think it's
important that I highlight the

00:00:18.260 --> 00:00:20.200
difference, because initially,
this can be very confusing.

00:00:20.200 --> 00:00:23.430
I remember when I first learned
this, I found I often

00:00:23.430 --> 00:00:26.680
mixed up these words and didn't
quite understand why

00:00:26.680 --> 00:00:27.540
there was a difference.

00:00:27.540 --> 00:00:31.280
So the two words are
electrical-- or sometimes

00:00:31.280 --> 00:00:33.580
you'll see electric instead
of electrical.

00:00:33.580 --> 00:00:49.110
So "electric potential energy"
and "electric potential." I

00:00:49.110 --> 00:00:51.380
think even in the last video,
I used these almost

00:00:51.380 --> 00:00:53.630
interchangeably, and I shouldn't
have. I really

00:00:53.630 --> 00:00:56.500
should have always used
electrical or electric

00:00:56.500 --> 00:00:57.390
potential energy.

00:00:57.390 --> 00:00:58.850
And what's the difference?

00:00:58.850 --> 00:01:05.379
Electrical potential energy is
associated with a charge.

00:01:05.379 --> 00:01:08.830
It's associated with a particle
that has some charge.

00:01:08.830 --> 00:01:12.390
Only that particle
can have energy.

00:01:12.390 --> 00:01:16.520
Electrical potential, or
electric potential, this is

00:01:16.520 --> 00:01:18.860
associated with a position.

00:01:18.860 --> 00:01:23.170
So, for example, if I have a
charge and I know that it's at

00:01:23.170 --> 00:01:26.720
some point with a given electric
potential, I can

00:01:26.720 --> 00:01:29.590
figure out the electric
potential energy at that point

00:01:29.590 --> 00:01:32.710
by just multiplying actually
this value by the charge.

00:01:32.710 --> 00:01:34.970
Let me give you some examples.

00:01:34.970 --> 00:01:38.380
Let's say that I have
an infinite

00:01:38.380 --> 00:01:39.740
uniformly charged plate.

00:01:39.740 --> 00:01:41.290
So that we don't have to do
calculus, we can have a

00:01:41.290 --> 00:01:43.050
uniform electric field.

00:01:43.050 --> 00:01:44.640
Let's say that this
is the plate.

00:01:44.640 --> 00:01:47.130
I'll make it vertical just so we
get a little bit of change

00:01:47.130 --> 00:01:55.760
of pace, and let's say it's
positively charged plate.

00:01:55.760 --> 00:01:57.170
And let's say that the
electric field

00:01:57.170 --> 00:01:59.010
is constant, right?

00:01:59.010 --> 00:02:00.060
It's constant.

00:02:00.060 --> 00:02:05.580
No matter what point we pick,
these field vectors should all

00:02:05.580 --> 00:02:08.156
be the same length because the
electric field does not change

00:02:08.156 --> 00:02:12.290
in magnitude it's pushing out,
because we assume when we draw

00:02:12.290 --> 00:02:14.810
field lines that we're using a
test charge with a positive

00:02:14.810 --> 00:02:16.060
charge so it's pushing
outward.

00:02:18.370 --> 00:02:22.640
Let's say I have a
1-coulomb charge.

00:02:22.640 --> 00:02:24.420
Actually, let me make
it 2 coulombs just

00:02:24.420 --> 00:02:26.320
to hit a point home.

00:02:26.320 --> 00:02:33.532
Say I have a 2-coulomb charge
right here, and it's positive.

00:02:33.532 --> 00:02:40.750
A positive 2-coulomb charge, and
it starts off at 3 meters

00:02:40.750 --> 00:02:46.430
away, and I want to bring
it in 2 meters.

00:02:46.430 --> 00:02:48.560
I want to bring it in 2 meters,
so it's 1 meter away.

00:02:51.800 --> 00:02:56.250
So what is the electric-- or
electrical-- potential energy

00:02:56.250 --> 00:03:00.600
difference between the particle
at this point and at

00:03:00.600 --> 00:03:02.200
this point?

00:03:02.200 --> 00:03:05.270
Well, the electrical potential
energy difference is the

00:03:05.270 --> 00:03:07.860
amount of work, as we've learned
in the previous two

00:03:07.860 --> 00:03:11.390
videos, we need to apply to this
particle to take it from

00:03:11.390 --> 00:03:12.770
here to here.

00:03:12.770 --> 00:03:14.200
So how much work do
we have to apply?

00:03:14.200 --> 00:03:21.290
We have to apply a force that
directly-- that exactly-- we

00:03:21.290 --> 00:03:22.990
assume that maybe this is
already moving with a constant

00:03:22.990 --> 00:03:24.840
velocity, or maybe we have to
start with a slightly higher

00:03:24.840 --> 00:03:27.210
force just to get it moving, but
we have to apply a force

00:03:27.210 --> 00:03:34.000
that's exactly opposite the
force provided by Coulomb's

00:03:34.000 --> 00:03:37.570
Law, the electrostatic force.

00:03:37.570 --> 00:03:40.030
And so what is that force we're
going to have to apply?

00:03:40.030 --> 00:03:42.620
Well, we actually have to know
what the electric field is,

00:03:42.620 --> 00:03:44.650
which I have not told you yet.

00:03:44.650 --> 00:03:46.220
I just realized that,
as you can tell.

00:03:46.220 --> 00:03:54.330
So let's say all of these
electric field lines are 3

00:03:54.330 --> 00:03:57.100
newtons per coulomb.

00:03:57.100 --> 00:04:01.260
So at any point, what is the
force being exerted from this

00:04:01.260 --> 00:04:02.940
field onto this particle?

00:04:02.940 --> 00:04:07.630
Well, the electrostatic force
on this particle is equal to

00:04:07.630 --> 00:04:16.269
the electric field times the
charge, which is equal to-- I

00:04:16.269 --> 00:04:19.829
just defined the electric field
as being 3 newtons per

00:04:19.829 --> 00:04:25.220
coulomb times 2 coulombs.

00:04:25.220 --> 00:04:27.000
It equals 6 newtons.

00:04:27.000 --> 00:04:30.940
So at any point, the electric
field is pushing this way 6

00:04:30.940 --> 00:04:33.416
newtons, so in order to push the
particle this way, I have

00:04:33.416 --> 00:04:35.930
to completely offset that, and
actually, I have to get it

00:04:35.930 --> 00:04:37.170
moving initially, and I'll
keep saying that.

00:04:37.170 --> 00:04:39.570
I just want to hit
that point home.

00:04:39.570 --> 00:04:42.690
So I have to apply a force of
6 newtons in the leftward

00:04:42.690 --> 00:04:45.560
direction and I have to apply
it for 2 meters to get the

00:04:45.560 --> 00:04:46.660
point here.

00:04:46.660 --> 00:04:54.370
So the total work is equal to
6 newtons times 2 meters,

00:04:54.370 --> 00:04:58.920
which is equal to 12
newton-meters or 12 joules.

00:04:58.920 --> 00:05:04.200
So we could say that the
electrical potential energy--

00:05:04.200 --> 00:05:05.570
and energy is always joules.

00:05:05.570 --> 00:05:07.950
The electrical potential energy
difference between this

00:05:07.950 --> 00:05:10.850
point and this point
is 12 joules.

00:05:10.850 --> 00:05:13.520
Or another way to say it
is-- and which one

00:05:13.520 --> 00:05:14.530
has a higher potential?

00:05:14.530 --> 00:05:16.140
Well, this one does, right?

00:05:16.140 --> 00:05:19.610
Because at this point, we're
closer to the thing that's

00:05:19.610 --> 00:05:22.170
trying to repel it, so if we
were to just let go, it would

00:05:22.170 --> 00:05:25.530
start accelerating in this
direction, and a lot of that

00:05:25.530 --> 00:05:27.250
energy would be converted to
kinetic energy by the time we

00:05:27.250 --> 00:05:28.480
get to this point, right?

00:05:28.480 --> 00:05:33.520
So we could also say that the
electric potential energy at

00:05:33.520 --> 00:05:38.400
this point right here is 12
joules higher than the

00:05:38.400 --> 00:05:41.480
electric potential energy
at this point.

00:05:41.480 --> 00:05:43.680
Now that's potential energy.

00:05:43.680 --> 00:05:46.300
What is electric potential?

00:05:46.300 --> 00:05:51.330
Well, electric potential tells
us essentially how much work

00:05:51.330 --> 00:05:55.550
is necessary per unit
of charge, right?

00:05:55.550 --> 00:05:58.220
Electric potential energy was
just how much total work is

00:05:58.220 --> 00:06:01.650
needed to move it from
here to here.

00:06:01.650 --> 00:06:05.890
Electric potential says, per
unit charge, how much work

00:06:05.890 --> 00:06:09.340
does it take to move any charge
per unit charge from

00:06:09.340 --> 00:06:11.010
here to here?

00:06:11.010 --> 00:06:14.070
Well, in our example we just
did, the total work to move it

00:06:14.070 --> 00:06:15.780
from here to here
was 12 joules.

00:06:15.780 --> 00:06:20.130
But how much work did it take to
move it from there to there

00:06:20.130 --> 00:06:21.500
per charge?

00:06:21.500 --> 00:06:29.640
Well, work per charge is equal
to 12 joules for what?

00:06:29.640 --> 00:06:32.280
What was the charge
that we moved?

00:06:32.280 --> 00:06:35.040
Well, it was 2 coulombs.

00:06:35.040 --> 00:06:41.520
It equals 6 joules
per coulomb.

00:06:41.520 --> 00:06:48.930
That is the electric potential
difference between this point

00:06:48.930 --> 00:06:49.760
and this point.

00:06:49.760 --> 00:06:51.180
So what is the distinction?

00:06:51.180 --> 00:06:54.150
Electric potential energy was
associated with a particle.

00:06:54.150 --> 00:06:57.980
How much more energy did the
particle have here than here?

00:06:57.980 --> 00:07:00.140
When we say electric potential,
because we

00:07:00.140 --> 00:07:03.490
essentially divide by the
size of the particle, it

00:07:03.490 --> 00:07:05.720
essentially is independent of
the size of the particle.

00:07:05.720 --> 00:07:07.960
It actually just depends
on our position.

00:07:07.960 --> 00:07:12.130
So electric potential, we're
just saying how much more

00:07:12.130 --> 00:07:15.180
potential, irrespective of the
charge we're using, does this

00:07:15.180 --> 00:07:18.240
position have relative
to this position?

00:07:18.240 --> 00:07:21.960
And this electric potential,
that's just another way of

00:07:21.960 --> 00:07:27.980
saying voltage, and the unit
for voltage is volts.

00:07:27.980 --> 00:07:30.600
So 6 joules per coulomb,
that's the

00:07:30.600 --> 00:07:34.030
same thing as 6 volts.

00:07:34.030 --> 00:07:42.060
And so if we think of the
analogy to gravitation, we

00:07:42.060 --> 00:07:46.170
said gravitational potential
energy was mgh, right?

00:07:46.170 --> 00:07:46.860
This was force.

00:07:46.860 --> 00:07:49.040
This was distance, right?

00:07:49.040 --> 00:07:52.970
Electric potential is
essentially the amount of

00:07:52.970 --> 00:07:55.820
gravitational-- if we extend
the analogy, the amount of

00:07:55.820 --> 00:07:58.890
gravitational potential energy
per mass, right?

00:07:58.890 --> 00:08:04.500
So if we wanted a quick way of
knowing what the gravitational

00:08:04.500 --> 00:08:06.640
potential is at any point
without having to care about

00:08:06.640 --> 00:08:09.340
the mass, we divide by the
mass, and it would be the

00:08:09.340 --> 00:08:11.130
acceleration of gravity
times height.

00:08:11.130 --> 00:08:13.750
Ignore that if it
confused you.

00:08:13.750 --> 00:08:15.590
So what is useful
about voltage?

00:08:15.590 --> 00:08:19.650
It tells us regardless of how
small or big or actually

00:08:19.650 --> 00:08:23.170
positive or negative a charge
is, what the difference in

00:08:23.170 --> 00:08:26.980
potential energy would be if
we're at two different points.

00:08:26.980 --> 00:08:31.390
So electric potential, we're
comparing points in space.

00:08:31.390 --> 00:08:37.760
Electric potential energy, we're
comparing charges at

00:08:37.760 --> 00:08:39.330
points in space.

00:08:39.330 --> 00:08:40.789
Hopefully, I didn't
confuse you.

00:08:40.789 --> 00:08:43.059
In the next video, we'll
actually do a couple of

00:08:43.059 --> 00:08:45.690
problems where we figure out
the electric potential

00:08:45.690 --> 00:08:48.960
difference or the voltage
difference between two points

00:08:48.960 --> 00:08:51.050
in space as opposed
to a charge at two

00:08:51.050 --> 00:08:52.190
different points in space.

00:08:52.190 --> 00:08:54.760
I will see you in
the next video.