Kirchhoff's voltage law

WEBVTT
Kind: captions
Language: en

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- [Voiceover] Now we're
ready to start hooking up

00:00:01.692 --> 00:00:06.111
our components into circuits,
and one of the two things

00:00:06.111 --> 00:00:09.583
that are going to be very useful
to us are Kirchhoff's laws.

00:00:09.583 --> 00:00:11.279
In this video we're gonna talk

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about Kirchhoff's voltage law.

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If we look at this circuit here,

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this is a voltage source, let's
just say this is 10 volts.

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We'll put a resistor connected to it

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and let's say the resistor is 200 ohms.

00:00:27.662 --> 00:00:31.212
Just for something to talk about.

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One of the things I can do
here is I can label this

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with voltages on the different nodes.

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Here's one node down here.

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I'm going to arbitrarily
call this zero volts.

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Then if I go through this voltage source,

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this node up here is
going to be at 10 volts.

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10 volts.

00:00:50.413 --> 00:00:52.602
So here's a little bit of jargon.

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We call this voltage here.

00:00:54.739 --> 00:00:58.411
The voltage goes up as we go
through the voltage source,

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and that's called a voltage rise.

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Over on this side, if we are standing

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at this point in the circuit right here

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and we went from this
node down to this node,

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like that, the voltage
would go from 10 volts

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down to zero volts in this circuit,

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and that's called a voltage drop.

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That's just a little
bit of slang, or jargon

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that we use to talk
about changes in voltage.

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Now I can make an observation about this.

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If I look at this voltage
rise here, it's 10 volts,

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and if I look at that voltage
drop, the drop is 10 volts.

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I can say the drop is 10 volts,

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or I could say the rise on
this side is minus 10 volts.

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A rise of minus 10.

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These two expressions mean
exactly the same thing.

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It meant that the voltage
went from 10 volts

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to zero volts, sort of going
through this 200 ohm resistor.

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So I ran a little expression for this,

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which is, v-rise minus v-drop equals what?

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Equals zero.

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I went up 10 volts, back down 10 volts,

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I end up back at zero volts,
and that's this right here.

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This is a form of Kirchhoff's voltage law.

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It says the voltage rises minus

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the voltage drops is equal to zero.

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So if we just plug our
actual numbers in here

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what we get is 10 minus 10 equals zero.

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I'm gonna draw this circuit again.

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Let's draw another
version of this circuit.

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This time we'll have two
resistors instead of one.

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We'll make it...

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We'll make it two 100 ohm resistors.

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Let's go through and label these.

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This is again 10 volts.

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So this node is at zero volts.

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This node is at 10 volts.

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What's this node?

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This node here is...

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These are equal resistors,

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so this is gonna be at five volts.

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That's this node voltage
here with respect to here.

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So that is five volts.

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This is five volts.

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And this is 10 volts.

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So let's just do our visit again.

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Let's start here and
count the rises and drops.

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We go up 10 volts, then we
have a voltage drop of five,

00:03:56.727 --> 00:03:58.891
then we have another voltage drop of five,

00:03:58.891 --> 00:04:00.706
and then we get back to zero.

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We can write the sum of the rises

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and the falls just like we did before.

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We can say 10 volts minus
five minus five equals zero.

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Alright.

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So I can generalize this.

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We can say this is general
we can do the summation,

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that's the summation symbol,

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of the v-rise minus the sum
of the v-fall equals zero.

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This is a form of Kirchhoff's voltage law.

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The sum of the voltage rises minus the sum

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of the voltage falls is
always equal to zero.

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There's a more compact way to write this

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that I like better, and that
is, we start at this corner...

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We start at any corner of the circuit.

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Let's say we start here.

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We're gonna go up 10
volts, down five volts,

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and down five volts.

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So what we're adding is the voltage rises.

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We're adding all the voltage rises.

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Rise plus 10.

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That's a rise of minus five
and a rise of minus five.

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So I can write this with
just one summation symbol.

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The voltages around the
loop, where i takes us all

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the way around the loop, equals zero.

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So this means I start
any place on the circuit,

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go around in some direction,
this way or this way,

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up, down, down, and I end up back

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at the same voltage I started at.

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So let's put a box around that too.

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This is Kvl, Kirchhoff's voltage law.

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Now I started over here in this corner,

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but I could start anywhere.

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If I started at the top and went

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around clockwise, if I started here say,

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I would go minus five,
minus five, plus 10,

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and I'd get the same answer.

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I'd still get back to zero.

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If I start here and I
go around the other way,

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the same thing happens.

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Plus five rise, plus five rise,

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and this is a 10 volt drop,

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so it works whichever way
you go around the loop,

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and it works for whatever
node you start at.

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That's the essence of
Kirchhoff's voltage law.

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We're gonna pair this
with the current law,

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Kirchhoff's current
law, and with those two,

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that's our tools for
doing circuit analysis.


Efficacy of Khan Academy

WEBVTT
Kind: captions
Language: en

00:00:00.589 --> 00:00:02.980
- [Voiceover] As a teacher
thinking about using a tool

00:00:02.980 --> 00:00:04.953
inside or outside of your classroom,

00:00:04.953 --> 00:00:06.788
the first natural question is,

00:00:06.788 --> 00:00:09.329
well does that tool work?

00:00:09.329 --> 00:00:11.110
And that's also very important to us

00:00:11.110 --> 00:00:13.479
here at Khan Academy with our mission.

00:00:13.479 --> 00:00:15.313
We don't want just people to use it.

00:00:15.313 --> 00:00:17.635
We want to feel good that that usage

00:00:17.635 --> 00:00:20.094
is actually driving real learning.

00:00:20.094 --> 00:00:24.064
And so what I'm going to give
an overview of in this video,

00:00:24.064 --> 00:00:28.499
is a very large study conducted
in the state of Idaho.

00:00:28.499 --> 00:00:30.682
It was across the entire state,

00:00:30.682 --> 00:00:34.849
understanding whether Khan
Academy is driving real learning.

00:00:35.744 --> 00:00:38.623
And this is the largest
study that has ever been done

00:00:38.623 --> 00:00:41.479
on a personalized learning tool.

00:00:41.479 --> 00:00:43.035
And so I'm going to summarize this.

00:00:43.035 --> 00:00:44.939
We'll also give a link to the study,

00:00:44.939 --> 00:00:47.307
later on in this tutorial.

00:00:47.307 --> 00:00:49.769
It was done and funded in conjunction with

00:00:49.769 --> 00:00:53.856
the J.A. and Kathryn
Albertson Family Foundation.

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And so I'm just going to
summarize the report here.

00:00:57.269 --> 00:00:59.498
So just as a big picture,

00:00:59.498 --> 00:01:00.891
we'll go right down here.

00:01:00.891 --> 00:01:02.726
There's a lot of really
cool stories from teachers

00:01:02.726 --> 00:01:05.860
and educators and district officials here

00:01:05.860 --> 00:01:08.298
talking about how they
implemented the pilot.

00:01:08.298 --> 00:01:09.599
But the big picture,

00:01:09.599 --> 00:01:13.599
this was 47 schools, 33
districts, 173 teachers,

00:01:14.568 --> 00:01:18.735
several thousand students
throughout the state of Idaho.

00:01:20.442 --> 00:01:21.998
And what they did in the study,

00:01:21.998 --> 00:01:25.272
is the students took the NWEA map exam

00:01:25.272 --> 00:01:26.990
at the beginning of the year.

00:01:26.990 --> 00:01:28.755
They worked on Khan Academy,

00:01:28.755 --> 00:01:33.027
and then they took the NWEA map
exam at the end of the year,

00:01:33.027 --> 00:01:35.280
and the way that efficacy was measured

00:01:35.280 --> 00:01:38.136
is well the map exam
can see for any student,

00:01:38.136 --> 00:01:40.504
whether they are a student
who is more advanced

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or a student who is re-mediating,

00:01:41.990 --> 00:01:43.685
they can see what their expected growth

00:01:43.685 --> 00:01:45.636
is in a traditional model

00:01:45.636 --> 00:01:47.586
and then they can compare
that expected growth

00:01:47.586 --> 00:01:51.905
to what the actual growth
was using Khan Academy.

00:01:51.905 --> 00:01:53.647
And so let's just cut to the chase

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and see what the results are.

00:01:54.854 --> 00:01:57.942
There's a lot of videos that
we have on our educator portal

00:01:57.942 --> 00:02:01.100
that talks about how
the different teachers

00:02:01.100 --> 00:02:04.119
use Khan Academy and
what they found valuable.

00:02:04.119 --> 00:02:06.069
But I'll go straight to the data here

00:02:06.069 --> 00:02:08.577
for the sake of this video.

00:02:08.577 --> 00:02:10.040
And so if we go down here,

00:02:10.040 --> 00:02:13.221
this is just the distribution
of students by grade level.

00:02:13.221 --> 00:02:16.332
You can see kind of late
elementary and middle schools

00:02:16.332 --> 00:02:18.306
were the bulk of the
students in the study were.

00:02:18.306 --> 00:02:19.235
But even in third grade,

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we're talking about over 200 students.

00:02:21.069 --> 00:02:23.986
So this is a very large scale study

00:02:25.411 --> 00:02:27.594
and this first one says mission completion

00:02:27.594 --> 00:02:29.591
versus spring percentile.

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Mission completion,

00:02:30.543 --> 00:02:33.956
these are the grade level
personalized learning experiences

00:02:33.956 --> 00:02:35.117
that the students can pick.

00:02:35.117 --> 00:02:36.534
So there is a third grade mission.

00:02:36.534 --> 00:02:38.600
There's actually an
early learning mission.

00:02:38.600 --> 00:02:39.761
There's a third, fourth, fifth,

00:02:39.761 --> 00:02:43.244
all the way up to Algebra,
Geometry, Trigonometry,

00:02:43.244 --> 00:02:44.916
there's even a calculus mission.

00:02:44.916 --> 00:02:48.167
And these are aligned to the
important state standards,

00:02:48.167 --> 00:02:49.862
especially the common core standards

00:02:49.862 --> 00:02:51.743
for K through pre-calculus.

00:02:51.743 --> 00:02:55.226
And they're aligned to the
AP standards for calculus.

00:02:55.226 --> 00:02:57.269
And so what you see here is,

00:02:57.269 --> 00:03:01.333
depending on how much a student
completed of their mission,

00:03:01.333 --> 00:03:02.981
over the course of the pilot,

00:03:02.981 --> 00:03:05.420
it correlates very strongly with

00:03:05.420 --> 00:03:07.441
how they performed on the map exam

00:03:07.441 --> 00:03:09.529
during the spring assessment.

00:03:09.529 --> 00:03:11.666
Now you might say, well
of course, naturally,

00:03:11.666 --> 00:03:13.105
a student who completes more,

00:03:13.105 --> 00:03:14.684
well that's maybe a student

00:03:14.684 --> 00:03:15.869
who's a little bit more advanced,

00:03:15.869 --> 00:03:17.819
and so they're going to
be in a higher percentile.

00:03:17.819 --> 00:03:18.701
And I would agree with you.

00:03:18.701 --> 00:03:19.746
That makes sense.

00:03:19.746 --> 00:03:23.554
So this is, this right
here, is not evidence of,

00:03:23.554 --> 00:03:26.875
or clear evidence of efficacy just yet,

00:03:26.875 --> 00:03:28.477
but you definitely wanna see this trend.

00:03:28.477 --> 00:03:31.519
If for whatever reason
this was a flat line,

00:03:31.519 --> 00:03:33.609
if it had a downward
slope for some reason,

00:03:33.609 --> 00:03:35.745
then you would have an issue.

00:03:35.745 --> 00:03:37.231
But this is the direction
that you wanna see,

00:03:37.231 --> 00:03:38.392
but we wanna see more evidence.

00:03:38.392 --> 00:03:40.087
We wanna see for a given student,

00:03:40.087 --> 00:03:41.968
regardless of where they started,

00:03:41.968 --> 00:03:44.151
that usage of Khan Academy is not

00:03:44.151 --> 00:03:45.915
driving just expected learning.

00:03:45.915 --> 00:03:47.146
For all we know, this might be just

00:03:47.146 --> 00:03:49.398
what you would expect
for different students.

00:03:49.398 --> 00:03:53.717
It's driving learning above
and beyond the expectations.

00:03:53.717 --> 00:03:56.527
And so that's where we
see this data down here.

00:03:56.527 --> 00:03:57.850
And they boiled it out,

00:03:57.850 --> 00:03:59.870
students who completed zero to 10%

00:03:59.870 --> 00:04:02.843
of their mission on
average, grew as expected.

00:04:02.843 --> 00:04:04.793
These students barely used Khan Academy.

00:04:04.793 --> 00:04:07.045
So once again, grew as expected,

00:04:07.045 --> 00:04:09.275
this means if you are an advanced student

00:04:09.275 --> 00:04:11.364
and you are learning
at a fairly quick pace,

00:04:11.364 --> 00:04:14.360
well you grew as expected,

00:04:14.360 --> 00:04:16.589
you grew at that quick pace.

00:04:16.589 --> 00:04:19.375
And if you are a student who
took a little bit more time.

00:04:19.375 --> 00:04:21.140
Well you also grew as expected

00:04:21.140 --> 00:04:22.463
and so when you didn't use Khan Academy,

00:04:22.463 --> 00:04:25.111
just what you would expect happened.

00:04:25.111 --> 00:04:27.595
But then when you see students who

00:04:27.595 --> 00:04:29.290
had significant usage of Khan Academy,

00:04:29.290 --> 00:04:31.426
students who completed 40% of more

00:04:31.426 --> 00:04:34.608
of their mission on
average grew 1.5 times more

00:04:34.608 --> 00:04:36.697
than their expected growth in one year.

00:04:36.697 --> 00:04:38.880
Students who completed 60%
or more of their mission

00:04:38.880 --> 00:04:42.851
grew an average 1.8 times
their expected growth.

00:04:42.851 --> 00:04:47.018
So they almost had two
years of growth in one year.

00:04:47.982 --> 00:04:49.422
And once again, I want to be very clear,

00:04:49.422 --> 00:04:53.114
this is, what we're plotting
on the vertical axis here.

00:04:53.114 --> 00:04:54.646
This isn't just growth,

00:04:54.646 --> 00:04:59.406
this is average actual growth
divided by target growth.

00:04:59.406 --> 00:05:01.241
So in a normal model,

00:05:01.241 --> 00:05:03.958
if you just look at the map
data on a nationwide basis,

00:05:03.958 --> 00:05:06.047
whether a student is strong or weak,

00:05:06.047 --> 00:05:08.548
if Khan Academy had no effect

00:05:08.548 --> 00:05:12.654
you would expect just a
flat line right over here.

00:05:12.654 --> 00:05:17.246
You would expect everything
here to be just at one.

00:05:17.246 --> 00:05:19.359
If Khan Academy was
actually less effective

00:05:19.359 --> 00:05:21.379
than whatever students were doing before,

00:05:21.379 --> 00:05:22.912
then you would say well these students

00:05:22.912 --> 00:05:24.792
who are spending a lot
of time on Khan Academy,

00:05:24.792 --> 00:05:26.254
then it would be taking away from those,

00:05:26.254 --> 00:05:27.834
so you would see a downward slope.

00:05:27.834 --> 00:05:29.552
But over here we see that the students

00:05:29.552 --> 00:05:32.826
who are actually using
Khan Academy deeply,

00:05:32.826 --> 00:05:35.195
and you can imagine any
large scale studies like this

00:05:35.195 --> 00:05:37.610
you have variation, and
the various fidelity

00:05:37.610 --> 00:05:39.467
to which folks are using Khan Academy,

00:05:39.467 --> 00:05:41.394
how integrated it is in the classroom.

00:05:41.394 --> 00:05:44.390
But the classrooms that
are using it more deeply,

00:05:44.390 --> 00:05:47.687
more regularly, are not
just seeing expected growth,

00:05:47.687 --> 00:05:49.770
they're seeing 1.8 times.

00:05:51.031 --> 00:05:53.562
They're seeing a significant multiple

00:05:53.562 --> 00:05:56.557
of what you would expect
their growth to be.

00:05:56.557 --> 00:05:59.227
So this is nearly two years of growth

00:05:59.227 --> 00:06:01.644
in one year of learning time.

00:06:02.641 --> 00:06:05.404
And that's once again, this is 60% plus,

00:06:05.404 --> 00:06:07.378
so you could only imagine what it would be

00:06:07.378 --> 00:06:10.675
if students complete 70%,
80%, 90% of the mission

00:06:10.675 --> 00:06:14.195
or if it's used in an even deeper way

00:06:14.195 --> 00:06:16.195
in different classrooms.


Khan Academy and the Common Core

WEBVTT
Kind: captions
Language: en

00:00:00.522 --> 00:00:02.571
- [Voiceover] A lot of
users of Khan Academy

00:00:02.571 --> 00:00:03.832
especially teachers

00:00:03.832 --> 00:00:06.525
don't fully know how much we have mapped

00:00:06.525 --> 00:00:08.053
and how much we have invested

00:00:08.053 --> 00:00:10.876
in the actual Common Core

00:00:10.876 --> 00:00:12.922
and as I often point out to folks,

00:00:12.922 --> 00:00:14.424
a standard is one thing

00:00:14.424 --> 00:00:15.978
and the Common Core standards

00:00:15.978 --> 00:00:19.038
are definitely more rigorous
than traditional standards,

00:00:19.038 --> 00:00:21.054
much more focused on conceptual learning

00:00:21.054 --> 00:00:22.934
but what really matters for a standard

00:00:22.934 --> 00:00:24.333
is how it's implemented

00:00:24.333 --> 00:00:26.098
and how it is assessed.

00:00:26.098 --> 00:00:27.288
So over the last few years,

00:00:27.288 --> 00:00:28.661
we've taken great effort

00:00:28.661 --> 00:00:31.436
to create over a 150 thousand exercises

00:00:31.436 --> 00:00:33.610
and many thousands of videos

00:00:33.610 --> 00:00:36.515
that are directly aligned
to the Common Core,

00:00:36.515 --> 00:00:38.763
explicitly created for the Common Core

00:00:38.763 --> 00:00:39.623
and not only that

00:00:39.623 --> 00:00:40.768
but they have been vetted

00:00:40.768 --> 00:00:42.486
by the authors of the Common Core

00:00:42.486 --> 00:00:44.131
and we've correlated them

00:00:44.131 --> 00:00:47.477
with performance on Common Core exams.

00:00:47.477 --> 00:00:50.422
So if you're a teacher,
a student or a parent

00:00:50.422 --> 00:00:51.281
and want to explore

00:00:51.281 --> 00:00:53.429
the Common Core resources we have,

00:00:53.429 --> 00:00:57.330
I suggest that you go to
khanacademy.org/commoncore

00:00:57.330 --> 00:00:58.199
or from there

00:00:58.199 --> 00:01:00.624
and you can see that we
have some resources here

00:01:00.624 --> 00:01:04.225
that describe what we have on Common Core

00:01:04.225 --> 00:01:05.747
and how our materials

00:01:05.747 --> 00:01:08.847
have even involved some of the people

00:01:08.847 --> 00:01:10.559
who are assessing the Common Core

00:01:10.559 --> 00:01:12.850
or some of the Illustrative Mathematics

00:01:12.850 --> 00:01:13.920
is run by Bill McCallum

00:01:13.920 --> 00:01:15.640
who's one of the authors
of the Common Core

00:01:15.640 --> 00:01:16.918
on the math side.

00:01:16.918 --> 00:01:19.612
But if you actually want to look at

00:01:19.612 --> 00:01:22.659
what we have by standard,

00:01:22.659 --> 00:01:27.355
you can click on Browse
our Common Core map

00:01:27.355 --> 00:01:29.082
and you will go right over here

00:01:29.082 --> 00:01:30.676
and you can see you can download it

00:01:30.676 --> 00:01:35.667
as a kind of comma file or
CSV comma separated files

00:01:35.667 --> 00:01:40.667
and that you can read on
Excel or on a spreadsheet

00:01:40.906 --> 00:01:42.740
but you could also navigate it over here

00:01:42.740 --> 00:01:45.851
and so you can see all of
the different grade levels

00:01:45.851 --> 00:01:47.314
that are associated with the Common Core.

00:01:47.314 --> 00:01:48.140
Once you get into high school,

00:01:48.140 --> 00:01:50.838
it's much more by I
guess you can say class

00:01:50.838 --> 00:01:52.389
or subject area

00:01:52.389 --> 00:01:54.797
and if we pick a grade level,

00:01:54.797 --> 00:01:57.168
let's say grade six

00:01:57.168 --> 00:01:58.315
and you could see already here

00:01:58.315 --> 00:02:00.197
that there's 107 skills

00:02:00.197 --> 00:02:02.568
but each of those skills
has many questions involved

00:02:02.568 --> 00:02:05.145
so there's 2678 questions

00:02:05.145 --> 00:02:06.528
and you could click there

00:02:06.528 --> 00:02:08.174
and you can see the different standards

00:02:08.174 --> 00:02:09.481
and this is the actual description

00:02:09.481 --> 00:02:11.924
of the Common Core standards

00:02:11.924 --> 00:02:14.223
and then you can see visual pictures

00:02:14.223 --> 00:02:17.045
of the different exercises

00:02:17.045 --> 00:02:19.177
that we have for those standards

00:02:19.177 --> 00:02:20.276
and so if you,

00:02:20.276 --> 00:02:23.468
over here you see these
major themes in grade six,

00:02:23.468 --> 00:02:25.719
geometry, ratios and
proportional relationships,

00:02:25.719 --> 00:02:27.763
number system, expression and equations,

00:02:27.763 --> 00:02:29.321
statistics and probability

00:02:29.321 --> 00:02:30.911
and so you can click on any one of them

00:02:30.911 --> 00:02:33.522
until you can see the types of things

00:02:33.522 --> 00:02:35.927
that Khan Academy actually has

00:02:35.927 --> 00:02:39.249
and you can click on any of these

00:02:39.249 --> 00:02:41.168
to go to the exercises

00:02:41.168 --> 00:02:42.391
and if you are a teacher,

00:02:42.391 --> 00:02:43.783
this is actually a good way to explore,

00:02:43.783 --> 00:02:45.373
hey, is this something
that might be appropriate

00:02:45.373 --> 00:02:46.560
for my students?

00:02:46.560 --> 00:02:49.735
You can then look at the URL up here

00:02:49.735 --> 00:02:51.870
and then you can email it to your students

00:02:51.870 --> 00:02:53.912
or send it on your
learning management system

00:02:53.912 --> 00:02:56.940
or on a playlist of some kind

00:02:56.940 --> 00:02:57.676
and then they can do it

00:02:57.676 --> 00:02:58.977
and if you sign up as a coach

00:02:58.977 --> 00:02:59.802
then you can track

00:02:59.802 --> 00:03:01.237
whether the students have worked on it.

00:03:01.237 --> 00:03:03.202
Also, you can assign it directly

00:03:03.202 --> 00:03:05.248
through the Khan Academy
interface on missions

00:03:05.248 --> 00:03:07.702
and there's other videos that
go into a lot of detail there.

00:03:07.702 --> 00:03:09.304
And so you can see this exercise,

00:03:09.304 --> 00:03:11.833
every student will get as
many exercises as they need.

00:03:11.833 --> 00:03:14.415
If they don't know how to tackle it,

00:03:14.415 --> 00:03:16.298
there are hints

00:03:16.298 --> 00:03:19.037
which are essentially
step by step solutions

00:03:19.037 --> 00:03:20.427
for that exercise

00:03:20.427 --> 00:03:22.676
and every one of these
Common Core exercises,

00:03:22.676 --> 00:03:25.181
these 150 thousand exercises,

00:03:25.181 --> 00:03:27.935
we have videos that were
also explicitly created

00:03:27.935 --> 00:03:30.346
for the Common Core associated with them.

00:03:30.346 --> 00:03:33.527
So here, Writing
expressions word problems.

00:03:33.527 --> 00:03:35.773
You can go into the library

00:03:35.773 --> 00:03:37.977
and you can see the video

00:03:37.977 --> 00:03:39.461
and this video in particular

00:03:39.461 --> 00:03:40.961
does some example problems

00:03:40.961 --> 00:03:43.174
from that Common Core exercise.

00:03:43.174 --> 00:03:45.088
So you'll have some videos

00:03:45.088 --> 00:03:47.554
that are more introductory.

00:03:47.554 --> 00:03:50.614
We also have articles
aligned with the Common Core

00:03:50.614 --> 00:03:53.352
that go deeper into it

00:03:53.352 --> 00:03:54.824
and these could actually be printed out

00:03:54.824 --> 00:03:56.081
and used as worksheets

00:03:56.081 --> 00:03:57.484
or the students can use it directly

00:03:57.484 --> 00:03:59.851
if they have access to
a computer or tablet

00:03:59.851 --> 00:04:01.076
or even on a phone.

00:04:01.076 --> 00:04:03.860
And of course, we have the actual,

00:04:03.860 --> 00:04:06.477
we have the actual exercises here.

00:04:06.477 --> 00:04:08.266
So in general, I encourage you,

00:04:08.266 --> 00:04:10.568
let me go back to,

00:04:10.568 --> 00:04:12.973
let me go back to the map.

00:04:12.973 --> 00:04:14.864
Oh, it's actually right over here.

00:04:14.864 --> 00:04:17.469
I encourage you to go back.

00:04:17.469 --> 00:04:19.029
I encourage you to explore

00:04:19.029 --> 00:04:22.296
our Common Core map on Khan Academy.

00:04:22.296 --> 00:04:24.423
As you can see, it is very comprehensive

00:04:24.423 --> 00:04:26.353
and as I said, it's done in conjunction

00:04:26.353 --> 00:04:29.909
with some of the creators
of the actual Common Core

00:04:29.909 --> 00:04:30.970
and above and beyond that,

00:04:30.970 --> 00:04:33.811
if you're a teacher who's
teaching the Common Core,

00:04:33.811 --> 00:04:35.814
there's a ton of other resources we have

00:04:35.814 --> 00:04:39.197
on just even understanding
what the standards speak to

00:04:39.197 --> 00:04:41.160
and how we can work together,

00:04:41.160 --> 00:04:42.823
Khan Academy and you as a teacher,

00:04:42.823 --> 00:04:45.386
to make sure that the students
have good mastery of it.

00:04:45.386 --> 00:04:47.260
And all of that is actually encapsulated

00:04:47.260 --> 00:04:48.451
as well in our missions

00:04:48.451 --> 00:04:50.006
and the missions are really valuable.

00:04:50.006 --> 00:04:53.030
You can use our library
and assign skill by skill

00:04:53.030 --> 00:04:54.818
or video by video during the year

00:04:54.818 --> 00:04:56.216
but in parallel to that,

00:04:56.216 --> 00:04:58.380
our missions allow the
students to fill in their gaps,

00:04:58.380 --> 00:04:59.741
work at their own pace

00:04:59.741 --> 00:05:01.074
and usage of missions

00:05:01.074 --> 00:05:02.619
correlates with out performance

00:05:02.619 --> 00:05:04.773
on Common Core benchmark exams.

00:05:04.773 --> 00:05:07.868
So encourage you to explore all of this.

00:05:07.868 --> 00:05:09.640
We put a lot of work in this

00:05:09.640 --> 00:05:11.255
and we'd love to hear your feedback

00:05:11.255 --> 00:05:13.817
on how we can make it better.


The Power of Persistence

WEBVTT
Kind: captions
Language: en

00:00:00.768 --> 00:00:02.788
Hi my name is Morey Aldeeb.

00:00:02.788 --> 00:00:04.188
I was born in Egypt.

00:00:04.188 --> 00:00:05.648
Worked on a farm til third grade

00:00:05.648 --> 00:00:08.048
and then I came with my family to the USA.

00:00:08.048 --> 00:00:10.868
And I continued working and also going

00:00:11.848 --> 00:00:13.504
to school since we had to.

00:00:13.504 --> 00:00:15.184
But working full time didn't

00:00:15.184 --> 00:00:17.124
make school go well.

00:00:17.124 --> 00:00:18.424
I was mostly sleeping,

00:00:18.424 --> 00:00:20.124
and I wasn't doing well at all.

00:00:20.124 --> 00:00:21.564
And that continued that same

00:00:21.564 --> 00:00:23.344
exact way til eighth grade.

00:00:23.344 --> 00:00:25.104
And my family was also in the middle

00:00:25.104 --> 00:00:26.464
going back and forth between

00:00:26.464 --> 00:00:27.864
Egypt and here and nobody had

00:00:27.864 --> 00:00:29.584
decided yet exactly what we were doing.

00:00:29.584 --> 00:00:31.484
But then when high school started,

00:00:31.484 --> 00:00:33.424
two weeks in, my house burned.

00:00:33.424 --> 00:00:35.064
And I was like, that's it for school.

00:00:35.064 --> 00:00:38.124
There's no way it's
gonna work out anymore.

00:00:38.124 --> 00:00:40.112
But after a year and a
half of being homeless

00:00:40.112 --> 00:00:42.392
and in a shelter, my
family was able to move

00:00:42.392 --> 00:00:43.838
in some where stable.

00:00:43.838 --> 00:00:45.498
And life was getting a little stable so

00:00:45.498 --> 00:00:47.238
I was willing to give
high school another shot

00:00:47.238 --> 00:00:49.158
and let's see ya know, if I could really,

00:00:49.158 --> 00:00:50.958
if school would actually work out for me.

00:00:50.958 --> 00:00:52.718
Thank God that I found Khan Academy

00:00:52.718 --> 00:00:54.578
and they had everything that I needed.

00:00:54.578 --> 00:00:57.408
'Cause I needed Pre Pre
Algebra to actually start

00:00:57.408 --> 00:01:00.186
my way and actually be able
to learn at an equal level.

00:01:00.186 --> 00:01:01.946
So they had it all for me.

00:01:01.946 --> 00:01:03.566
Ya know, they had Pre Algebra and then

00:01:03.566 --> 00:01:05.566
Pre, and then they had
Algebra, and then they

00:01:05.566 --> 00:01:08.166
had the whole path just
set up right there for you.

00:01:08.166 --> 00:01:10.026
Where I didn't even have to organize it or

00:01:10.026 --> 00:01:11.846
find someone to help me organize it or

00:01:11.846 --> 00:01:13.046
figure out what I would do.

00:01:13.046 --> 00:01:14.786
And I went down through every video and

00:01:14.786 --> 00:01:16.746
as I learned and I learned then things

00:01:16.746 --> 00:01:19.246
were getting easier and
the pace was what I wanted.

00:01:19.246 --> 00:01:21.446
It motivated me a lot
that I felt like I could

00:01:21.446 --> 00:01:22.536
actually learn.

00:01:22.536 --> 00:01:24.256
And I was learning and getting happier.

00:01:24.256 --> 00:01:25.726
And things were working out ya know.

00:01:25.726 --> 00:01:27.806
And I continued that
same way and that even

00:01:27.806 --> 00:01:30.366
drove in a love for math for me and after

00:01:30.366 --> 00:01:32.346
finishing every video that was there,

00:01:32.346 --> 00:01:34.626
I finished high school
and that year and a half

00:01:34.626 --> 00:01:36.546
I graduated in 11th grade.

00:01:36.546 --> 00:01:39.466
After finishing the 11th
grade and I went through

00:01:40.726 --> 00:01:44.206
Queens College and I
knew I could learn math

00:01:44.206 --> 00:01:47.486
so I continued learning
math and Khan Academy

00:01:47.486 --> 00:01:48.946
was still there for me.

00:01:48.946 --> 00:01:51.304
They had Calculus and
they continued through

00:01:51.304 --> 00:01:54.124
Statistics and Probability,
and every class that I needed

00:01:54.124 --> 00:01:57.584
to continue to get my,
to do well in math and

00:01:57.584 --> 00:02:00.164
I was able to finish in
my Applied Math degree in

00:02:00.164 --> 00:02:01.784
two and a half years.

00:02:01.784 --> 00:02:03.704
And now I'm doing my
second bachelor's here at

00:02:03.704 --> 00:02:06.444
Columbia University
after transferring here.


Kirchhoff's current law

WEBVTT
Kind: captions
Language: en

00:00:01.131 --> 00:00:03.000
- [Voiceover] Up to now we've talked about

00:00:03.000 --> 00:00:06.169
resistors and capacitors
and other components,

00:00:06.169 --> 00:00:07.400
and we've connected them up

00:00:07.400 --> 00:00:10.209
and learned about Ohm's
law, for resistors,

00:00:10.209 --> 00:00:14.400
and we've also learned some
things about series resistors,

00:00:14.400 --> 00:00:15.922
like we show here.

00:00:15.922 --> 00:00:18.243
The idea of Kirchhoff's Laws,

00:00:18.243 --> 00:00:20.566
these are basically common sense laws

00:00:20.566 --> 00:00:23.328
that we can derive from
looking at simple circuits,

00:00:23.328 --> 00:00:25.047
and in this video we're gonna

00:00:25.047 --> 00:00:29.558
work out Kirchhoff's Current Law.

00:00:30.585 --> 00:00:32.686
Let's take a look at these
series resistors here.

00:00:32.686 --> 00:00:34.869
There's a connection point right there,

00:00:34.869 --> 00:00:37.580
and that's called a node, a junction.

00:00:40.778 --> 00:00:43.158
And one of the things we know is that

00:00:43.158 --> 00:00:45.934
when we put current through this,

00:00:45.934 --> 00:00:49.196
let's say we put a current through here.

00:00:49.196 --> 00:00:51.018
And we know that current
is flowing charge,

00:00:51.018 --> 00:00:53.840
so we know that the charge
does not collect anywhere.

00:00:53.840 --> 00:00:56.509
So that means it comes
out of this resistor

00:00:56.509 --> 00:00:57.868
and flows into the node,

00:00:57.868 --> 00:01:01.015
and that goes across and
it comes out on this side,

00:01:01.015 --> 00:01:04.579
all the current that comes in comes out.

00:01:04.579 --> 00:01:05.519
That's something we know,

00:01:05.519 --> 00:01:06.796
that's the conservation of charge,

00:01:06.796 --> 00:01:10.018
and we know that the charge
does not pile up anywhere.

00:01:11.452 --> 00:01:13.966
We'll call this current i1.

00:01:14.888 --> 00:01:17.007
And we'll call this current i2.

00:01:19.636 --> 00:01:24.636
And we know, we can just write
right away, i1 equals i2.

00:01:26.858 --> 00:01:31.270
That seems pretty clear from
our argument about charge.

00:01:31.270 --> 00:01:32.756
Now let me add something else here,

00:01:32.756 --> 00:01:35.363
we'll add another resistor to our node.

00:01:36.448 --> 00:01:38.131
Like that.

00:01:38.131 --> 00:01:41.173
And this now, there's gonna be
some current going this way.

00:01:41.173 --> 00:01:43.305
Let's call that i3.

00:01:45.109 --> 00:01:46.676
And now this doesn't work anymore,

00:01:46.676 --> 00:01:49.800
this i1 and i2 are not
necessarily the same.

00:01:49.800 --> 00:01:52.551
But what we do know is
any current that goes in

00:01:52.551 --> 00:01:54.432
has to come out of this node.

00:01:54.432 --> 00:01:59.412
So we can say that i1 equals i2 plus i3.

00:01:59.412 --> 00:02:01.131
That seems pretty reasonable.

00:02:01.131 --> 00:02:03.975
And in general, what we have here isn't,

00:02:03.975 --> 00:02:06.216
if we take all the current flowing in,

00:02:06.216 --> 00:02:09.678
it equals all the current flowing out.

00:02:11.065 --> 00:02:13.618
And that's Kirchhoff's Current Law.

00:02:13.618 --> 00:02:14.849
That's a one way to say it,

00:02:14.849 --> 00:02:19.849
in mathematical notation,
we would say i in,

00:02:21.384 --> 00:02:24.786
the summation of currents going in,

00:02:24.786 --> 00:02:26.845
this is the summation sign,

00:02:26.845 --> 00:02:31.310
is the summation of i out.

00:02:33.660 --> 00:02:36.476
That's one expression of
Kirchhoff's Current Law.

00:02:38.386 --> 00:02:42.345
So now I want to generalize
this a little bit.

00:02:42.345 --> 00:02:44.318
Let's say we have a node,

00:02:44.318 --> 00:02:46.606
and we have some wires going into it,

00:02:46.606 --> 00:02:49.096
here's some wires connecting up to a node.

00:02:49.937 --> 00:02:52.288
And there's current going into each one.

00:02:53.200 --> 00:02:54.883
I'm gonna define the current arrows,

00:02:54.883 --> 00:02:58.784
this looks a little odd,
but it's okay to do.

00:02:58.784 --> 00:03:00.479
All going in.

00:03:00.479 --> 00:03:03.300
And what Kirchhoff's Current Law says

00:03:03.300 --> 00:03:07.109
is that the sum of the currents

00:03:07.109 --> 00:03:09.257
going into that node

00:03:09.257 --> 00:03:11.458
has to be equal to zero.

00:03:12.450 --> 00:03:14.249
Let's work out how that works.

00:03:14.249 --> 00:03:18.243
Let's say this is one
amp, and this is one amp,

00:03:18.243 --> 00:03:21.584
and this is one amp.

00:03:21.584 --> 00:03:24.918
And the question is, what is this one?

00:03:24.918 --> 00:03:27.936
What's that current there?

00:03:27.936 --> 00:03:32.936
If I use my Kirchhoff's
Current Law, express this way,

00:03:32.953 --> 00:03:37.268
it says that one plus one plus one

00:03:37.268 --> 00:03:42.268
plus i, whatever this i
here, has to equal zero.

00:03:43.305 --> 00:03:48.305
And what that says is
that i equals minus three.

00:03:48.623 --> 00:03:51.327
So that says, minus three amps flowing in

00:03:51.327 --> 00:03:55.762
is the same exact thing as
plus three amps flowing out.

00:03:55.762 --> 00:03:58.770
So one amp, one amp, one amp comes in,

00:03:58.770 --> 00:04:01.472
three amperes flows out.

00:04:02.754 --> 00:04:05.680
Another way we could do it, equally valid,

00:04:05.680 --> 00:04:08.513
this is just three ways to
say exactly the same thing.

00:04:08.513 --> 00:04:13.152
I have a bunch of wires going
to a junction, like this.

00:04:14.317 --> 00:04:16.361
And this time I define
the currents going out,

00:04:16.361 --> 00:04:19.003
let's say I define them all going out.

00:04:22.433 --> 00:04:24.012
And this same thing works.

00:04:24.012 --> 00:04:26.739
The sum of the currents,

00:04:26.739 --> 00:04:29.316
this time going out,

00:04:29.316 --> 00:04:31.638
I'll go back over here, I'll write in,

00:04:31.638 --> 00:04:34.320
all the currents going in.

00:04:34.320 --> 00:04:37.225
That has to equal zero as well.

00:04:37.225 --> 00:04:38.464
And you can do the same exercise,

00:04:38.464 --> 00:04:41.131
if I make all these one amp,

00:04:42.889 --> 00:04:47.602
and ask, what is this
one here, what is i here,

00:04:47.602 --> 00:04:48.659
outgoing current,

00:04:48.659 --> 00:04:53.562
it's one plus one plus one plus one,

00:04:53.562 --> 00:04:55.245
those are the four that I know,

00:04:55.245 --> 00:04:57.811
and those are the ones going out,

00:04:57.811 --> 00:05:00.110
so what's the last one going
out, it has to equal zero.

00:05:00.110 --> 00:05:04.441
The last one has to be
minus four equals zero.

00:05:04.441 --> 00:05:09.441
So this is a current
of minus four amperes.

00:05:10.520 --> 00:05:12.901
So that's the idea of
Kirchhoff's Current Law.

00:05:12.901 --> 00:05:13.597
It's basically,

00:05:13.597 --> 00:05:16.581
we've reasoned through
it from first principles,

00:05:16.581 --> 00:05:19.622
because everything that comes in

00:05:19.622 --> 00:05:21.375
has to leave by some route,

00:05:21.375 --> 00:05:23.175
and when we've talked about it that way,

00:05:23.175 --> 00:05:25.637
we ended up with this expression

00:05:25.637 --> 00:05:28.179
for Kirchhoff's Current Law.

00:05:28.179 --> 00:05:30.467
And we can come up with a slightly smaller

00:05:30.467 --> 00:05:33.125
mathematical expression, if we say,

00:05:33.125 --> 00:05:36.236
let's define all the
currents to be pointing in.

00:05:36.236 --> 00:05:38.361
Some of them may turn out to be negative,

00:05:38.361 --> 00:05:41.155
but then that's another way

00:05:41.155 --> 00:05:43.674
to write Kirchhoff's Current Law.

00:05:43.674 --> 00:05:45.253
And in the same way,

00:05:45.253 --> 00:05:46.717
if we define all the currents going out,

00:05:46.717 --> 00:05:48.656
and you actually have
your choice of any of

00:05:48.656 --> 00:05:51.117
these three any time
you want to use these.

00:05:51.117 --> 00:05:53.560
If we define them all going out.

00:05:55.191 --> 00:05:58.860
This is Kirchhoff's Current Law,

00:05:58.860 --> 00:06:01.804
and we'll use this all the time
when we do circuit analysis.


Voltage divider

WEBVTT
Kind: captions
Language: en

00:00:01.018 --> 00:00:01.851
- [Voiceover] Now I'm gonna show you

00:00:01.851 --> 00:00:04.174
what a circuit, that's
called a voltage divider.

00:00:04.174 --> 00:00:06.229
This is the name we
give to a simple circuit

00:00:06.229 --> 00:00:08.617
of two series resistors.

00:00:08.617 --> 00:00:11.416
So, I'm just gonna draw
two series resistors here.

00:00:11.416 --> 00:00:13.566
And it's a nickname, in the sense of,

00:00:13.566 --> 00:00:15.939
it's just a pattern that we see

00:00:15.939 --> 00:00:18.647
when we look at circuits.

00:00:18.647 --> 00:00:20.643
And, I'll show you what the pattern is.

00:00:20.643 --> 00:00:22.711
The pattern is,

00:00:22.711 --> 00:00:23.544
we have

00:00:25.051 --> 00:00:26.131
two resistors in series.

00:00:26.131 --> 00:00:28.103
It's no more than that.

00:00:28.103 --> 00:00:32.400
And we assume that there's
a voltage over here.

00:00:32.400 --> 00:00:35.823
We hook up a voltage over here like this.

00:00:35.823 --> 00:00:38.162
So, that's called an input voltage.

00:00:38.162 --> 00:00:41.393
We'll call it 'VI', for 'V in'.

00:00:41.393 --> 00:00:43.476
And then, the midpoint of

00:00:44.535 --> 00:00:46.040
the two resistors,

00:00:46.040 --> 00:00:48.363
and typically the bottom,

00:00:48.363 --> 00:00:50.041
that's called the 'out'.

00:00:50.041 --> 00:00:51.717
So, we basically

00:00:51.717 --> 00:00:54.396
just have a pattern here
with the series resistor,

00:00:54.396 --> 00:00:57.763
driven by some voltage from
the ends of the two resistors.

00:00:57.763 --> 00:01:00.918
And we're curious about the
voltage across one of them.

00:01:00.918 --> 00:01:03.523
So now we're gonna develop
an expression for this.

00:01:03.523 --> 00:01:06.129
Let's also label our resistors.

00:01:06.129 --> 00:01:08.202
This will be 'R1'.

00:01:08.202 --> 00:01:10.035
And this will be 'R2'.

00:01:10.976 --> 00:01:13.989
That's how we tell our resistors apart.

00:01:13.989 --> 00:01:16.525
And we're gonna develop
an expression for this.

00:01:16.525 --> 00:01:17.358
So,

00:01:18.195 --> 00:01:20.262
let's first put a current through here.

00:01:20.262 --> 00:01:22.675
We'll call that current 'i'.

00:01:22.675 --> 00:01:24.277
We'll make an assumption

00:01:24.277 --> 00:01:26.822
that this current here, is zero.

00:01:26.822 --> 00:01:28.803
There's no current going out of our

00:01:28.803 --> 00:01:29.915
little circuit here.

00:01:29.915 --> 00:01:31.142
And that means, of course,

00:01:31.142 --> 00:01:33.972
that this current here is also 'i'.

00:01:33.972 --> 00:01:36.212
So, it's continuous all the way down.

00:01:36.212 --> 00:01:37.941
And now we want to develop an expression

00:01:37.941 --> 00:01:40.103
that tells us what 'V out' is,

00:01:40.103 --> 00:01:42.304
in terms of these two resistors

00:01:42.304 --> 00:01:44.106
and the input voltage.

00:01:44.106 --> 00:01:45.910
So let's go over here and do that.

00:01:45.910 --> 00:01:48.062
First thing we're gonna write is,

00:01:48.062 --> 00:01:49.860
we know that,

00:01:49.860 --> 00:01:51.095
using Ohm's law,

00:01:51.095 --> 00:01:53.270
we can write an expression for

00:01:53.270 --> 00:01:56.446
these series resistors on this side here.

00:01:56.446 --> 00:01:58.562
Ohm's law, we'll put over here.

00:01:58.562 --> 00:02:01.645
'V' equals 'iR'.

00:02:02.766 --> 00:02:05.333
In a specific case here,

00:02:05.333 --> 00:02:09.443
'V in' equals 'i' times what?

00:02:09.443 --> 00:02:12.553
Times the series combination
of 'R1' and 'R2'.

00:02:12.553 --> 00:02:14.702
And the series combination is the sum:

00:02:14.702 --> 00:02:17.035
'R1' plus 'R2'.

00:02:19.959 --> 00:02:22.280
I'm gonna solve this for 'i'.

00:02:22.280 --> 00:02:23.697
'i' equals

00:02:25.459 --> 00:02:28.326
'V in' divided by

00:02:28.326 --> 00:02:30.909
'R1' plus 'R2'.

00:02:33.981 --> 00:02:35.665
Alright, next step is gonna be,

00:02:35.665 --> 00:02:36.767
let's solve for--

00:02:36.767 --> 00:02:40.055
let's write an expression
that's related to 'V out'.

00:02:40.055 --> 00:02:43.749
And 'V out' only depends on
'R2' and this current here.

00:02:43.749 --> 00:02:46.161
So we can write 'V out'

00:02:46.161 --> 00:02:49.411
equals 'i' times 'R2'.

00:02:52.110 --> 00:02:55.675
And I'll solve this equation
for 'i' the same way.

00:02:55.675 --> 00:02:59.175
Equals 'V zero' over 'R2'

00:03:00.483 --> 00:03:02.712
And now we have two expressions for 'i'

00:03:02.712 --> 00:03:03.567
in our circuit,

00:03:03.567 --> 00:03:06.759
because we made this assumption
of zero current going out,

00:03:06.759 --> 00:03:08.898
those two 'i's' are the same.

00:03:08.898 --> 00:03:11.233
So, let's set those equal to each other

00:03:11.233 --> 00:03:12.696
and see what we get.

00:03:12.696 --> 00:03:14.363
'i' is

00:03:15.775 --> 00:03:19.192
'V zero' over 'R2',

00:03:20.772 --> 00:03:23.522
equals 'V1'

00:03:25.150 --> 00:03:27.983
over 'R1' plus 'R2'.

00:03:29.944 --> 00:03:31.570
So now I'm gonna take 'R2'

00:03:31.570 --> 00:03:34.061
and move it over to the
other side of the equation.

00:03:34.061 --> 00:03:38.228
And we get 'V out' equals 'V1'.

00:03:39.230 --> 00:03:42.691
Sorry, 'V in' times

00:03:42.691 --> 00:03:46.516
'R2' over

00:03:46.516 --> 00:03:49.183
'R1' plus 'R2'.

00:03:52.647 --> 00:03:54.398
And this is called,

00:03:54.398 --> 00:03:56.810
this is called the voltage
divider expression.

00:03:56.810 --> 00:03:57.727
Right here.

00:04:01.463 --> 00:04:03.846
It gives us an expression for 'V out',

00:04:03.846 --> 00:04:04.793
in terms of 'V in',

00:04:04.793 --> 00:04:06.897
and the ratio of resistors.

00:04:06.897 --> 00:04:09.513
Resistors are always positive numbers.

00:04:09.513 --> 00:04:12.013
And so this fraction is always

00:04:13.341 --> 00:04:14.441
less than one.

00:04:14.441 --> 00:04:15.574
Which means that 'V out'

00:04:15.574 --> 00:04:17.760
is always somewhat less than 'V in'.

00:04:17.760 --> 00:04:18.926
And it's adjustable,

00:04:18.926 --> 00:04:20.774
by adjusting the resistor values.

00:04:20.774 --> 00:04:24.304
It's a really handy circuit to have.

00:04:24.304 --> 00:04:25.976
Let's do some examples.

00:04:25.976 --> 00:04:30.059
We'll put that up in the
corner so we can see it.

00:04:30.945 --> 00:04:31.778
Then real quick,

00:04:31.778 --> 00:04:35.945
I'm gonna build a voltage
divider that we can practice on.

00:04:37.659 --> 00:04:41.120
Let's make this '2k'
ohms, two thousand ohms.

00:04:41.120 --> 00:04:43.350
We'll make this 6000 ohms,

00:04:43.350 --> 00:04:46.166
or '6k' ohms.

00:04:46.166 --> 00:04:48.255
And we'll hook it up to

00:04:48.255 --> 00:04:50.922
an input source that looks like,

00:04:52.124 --> 00:04:54.041
let's say it's 6 volts.

00:04:56.478 --> 00:04:57.311
Like that.

00:04:59.600 --> 00:05:01.488
And we'll take an output off of this.

00:05:01.488 --> 00:05:05.221
Right here, is where the output
of our voltage divider is.

00:05:05.221 --> 00:05:08.054
And we'll say that that is

00:05:09.904 --> 00:05:10.737
'V out'.

00:05:12.208 --> 00:05:13.239
So let's solve this

00:05:13.239 --> 00:05:16.133
using the voltage divider expression.

00:05:16.133 --> 00:05:18.453
'V out' equals

00:05:18.453 --> 00:05:20.536
'V in', which is 6 volts.

00:05:21.493 --> 00:05:23.910
Times the ratio of resistors.

00:05:24.777 --> 00:05:27.610
'R2' is '6k' ohms,

00:05:28.967 --> 00:05:31.885
divided by '2k' ohms,

00:05:31.885 --> 00:05:35.218
plus '6k' ohms.

00:05:36.337 --> 00:05:37.911
And notice this always happens,

00:05:37.911 --> 00:05:39.371
the 'k's' all cancel out.

00:05:39.371 --> 00:05:40.986
That's nice.

00:05:40.986 --> 00:05:42.901
And that equals

00:05:42.901 --> 00:05:44.920
six times,

00:05:44.920 --> 00:05:47.587
six over, two plus six is eight.

00:05:48.848 --> 00:05:51.189
And if I do my calculations right,

00:05:51.189 --> 00:05:55.356
'V out' is 4.5 volts.

00:05:56.976 --> 00:05:58.677
So that's what a voltage divider is.

00:05:58.677 --> 00:06:00.909
And if you remember at the beginning,

00:06:00.909 --> 00:06:02.075
if you remember at the beginning,

00:06:02.075 --> 00:06:03.739
we made an assumption

00:06:03.739 --> 00:06:05.729
that this current going out here,

00:06:05.729 --> 00:06:08.314
was appr-- about zero.

00:06:08.314 --> 00:06:09.542
If that current is really small,

00:06:09.542 --> 00:06:12.057
you can use this voltage
divider expression.

00:06:12.057 --> 00:06:14.243
Which as, we see up here,

00:06:14.243 --> 00:06:17.633
is the ratio of the bottom
resistor to both resistors.

00:06:17.633 --> 00:06:19.040
That's how I remember it.

00:06:19.040 --> 00:06:20.514
It's the bottom resistor,

00:06:20.514 --> 00:06:24.274
over the two resistors added together.

00:06:24.274 --> 00:06:27.059
If you think the current
is not very small,

00:06:27.059 --> 00:06:29.513
what you do is you go back
and you do this analysis.

00:06:29.513 --> 00:06:31.633
You do the same analysis again

00:06:31.633 --> 00:06:35.495
but you account for the
current that's in here.

00:06:35.495 --> 00:06:38.659
So that's the story on voltage dividers


Prepositions of neither space nor time

WEBVTT
Kind: captions
Language: en

00:00:00.817 --> 00:00:01.815
- [Voiceover] Hey grammarians,

00:00:01.815 --> 00:00:04.853
we've talked about prepositions of time

00:00:04.853 --> 00:00:06.954
and we've talked about
prepositions of space

00:00:06.954 --> 00:00:09.218
and I couldn't come up
with a cute name for these

00:00:09.218 --> 00:00:11.877
because the following five prepositions

00:00:11.877 --> 00:00:14.315
are examples of what we
would call prepositions

00:00:14.315 --> 00:00:18.658
that have connotations for
neither time nor space.

00:00:18.658 --> 00:00:20.677
Some of them do have time connotations

00:00:20.677 --> 00:00:22.937
and some of them do have
physical connotations

00:00:22.937 --> 00:00:25.489
and what we're going to
talk about today, however,

00:00:25.489 --> 00:00:30.489
are the uses of these
words, these prepositions,

00:00:31.212 --> 00:00:33.077
that don't have anything
to do with time or space,

00:00:33.077 --> 00:00:37.013
they just have, they
encode other relationships.

00:00:37.013 --> 00:00:39.335
Let's get to it, I'll
show you what I mean.

00:00:39.335 --> 00:00:41.684
When we say about it can mean

00:00:41.684 --> 00:00:45.318
you're talking about a specific subject.

00:00:45.318 --> 00:00:50.062
So I could say to you,
"Tell me about yourself!"

00:00:50.062 --> 00:00:55.062
The word by can be used to
denote agency or doing this.

00:00:56.227 --> 00:00:57.466
You'll see what I mean by that.

00:00:57.466 --> 00:01:01.726
I mean we can figure out who
is responsible for something

00:01:01.726 --> 00:01:03.734
with the use of the word by.

00:01:03.734 --> 00:01:06.568
The book was written by Sudhir.

00:01:06.568 --> 00:01:07.496
So who did the thing?

00:01:07.496 --> 00:01:08.750
Sudhir did the thing,

00:01:08.750 --> 00:01:12.978
he's the person with
agency, he's the doer.

00:01:12.978 --> 00:01:15.428
The word for denotes use.

00:01:15.428 --> 00:01:17.835
So if you were to ask me, for example,

00:01:17.835 --> 00:01:21.269
"David what's a wood chipper used to do?"

00:01:21.269 --> 00:01:23.866
I would say, "It's for chipping wood,

00:01:23.866 --> 00:01:28.866
"for turning wood into chips,
it's purpose is chipping."

00:01:29.253 --> 00:01:31.362
Of has this connotation of belonging

00:01:31.362 --> 00:01:33.683
or being part of a place.

00:01:33.683 --> 00:01:36.976
So we can talk about the great
green dragon of Inverness.

00:01:36.976 --> 00:01:41.140
Inverness is a place, it's in Scotland.

00:01:41.140 --> 00:01:42.046
Are there dragons there?

00:01:42.046 --> 00:01:44.526
I don't know, I've never been.

00:01:44.526 --> 00:01:49.526
And with means together or part of.

00:01:50.145 --> 00:01:53.826
There goes that snail
with the painted shell

00:01:53.826 --> 00:01:56.214
which indicates that
the snail and the shell

00:01:56.214 --> 00:01:58.496
are part and parcel, they're together.

00:01:58.496 --> 00:02:00.981
So yeah, so these prepositions can be used

00:02:00.981 --> 00:02:02.304
for all sorts of things.

00:02:02.304 --> 00:02:04.691
I understand this can be confusing.

00:02:04.691 --> 00:02:05.875
Prepositions are probably

00:02:05.875 --> 00:02:08.530
the most complicated part of English

00:02:08.530 --> 00:02:10.318
and the problem is you
just need to memorize them.

00:02:10.318 --> 00:02:12.623
But the good thing is that
there aren't that many

00:02:12.623 --> 00:02:14.179
because, as I've said before,

00:02:14.179 --> 00:02:18.057
prepositions are a closed
group, we don't mint new ones.

00:02:18.057 --> 00:02:19.334
So you don't have to be

00:02:19.334 --> 00:02:22.295
constantly trying to collect
more ones, or pick them up,

00:02:22.295 --> 00:02:23.432
or figure them out.

00:02:23.432 --> 00:02:26.256
You have a limited set
that you need to master

00:02:26.256 --> 00:02:28.114
and the way to do that is to read,

00:02:28.114 --> 00:02:30.912
and listen, and talk a lot.

00:02:30.912 --> 00:02:35.070
You can do that, you can
learn anything, David out.


Meet the preposition

WEBVTT
Kind: captions
Language: en

00:00:00.434 --> 00:00:01.362
- [Voiceover] Hey grammarians,

00:00:01.362 --> 00:00:03.262
I want to talk about prepositions

00:00:03.262 --> 00:00:06.712
but before I do I'm going to
draw you a little hamster.

00:00:12.348 --> 00:00:13.179
Is it a hamster?

00:00:13.179 --> 00:00:14.097
Is it a tiny bear?

00:00:14.097 --> 00:00:15.281
Who knows?

00:00:15.281 --> 00:00:16.426
We're just going to call it a hamster,

00:00:16.426 --> 00:00:19.843
a little rodent type creature.

00:00:20.784 --> 00:00:22.765
Now I'm going to use
this critter to establish

00:00:22.765 --> 00:00:26.015
what prepositions are and what they do

00:00:26.015 --> 00:00:28.454
because in addition to
there being a hamster

00:00:28.454 --> 00:00:32.193
there's also going to be this box.

00:00:34.777 --> 00:00:35.961
So what prepositions do

00:00:35.961 --> 00:00:39.612
is they establish
relationships between stuff

00:00:39.612 --> 00:00:43.444
in place and time so it can show us

00:00:43.444 --> 00:00:48.444
where things are, when things
are, and how things are.

00:00:52.336 --> 00:00:53.791
Let me demonstrate.

00:00:53.791 --> 00:00:57.610
So, okay, using just
this hamster and this box

00:00:57.610 --> 00:00:59.886
we can move this box around

00:00:59.886 --> 00:01:04.367
and talk about how the hamster
relates to the box, right.

00:01:04.367 --> 00:01:07.760
So right now the box is under the hamster,

00:01:07.760 --> 00:01:09.511
let's write that down.

00:01:12.338 --> 00:01:13.958
Right, the box is under the hamster,

00:01:13.958 --> 00:01:16.188
that word under is a preposition

00:01:16.188 --> 00:01:19.728
because it's establishing
this relationship of where.

00:01:19.728 --> 00:01:22.271
It's connecting the box to the hamster.

00:01:22.271 --> 00:01:26.108
The box is under the hamster.

00:01:30.015 --> 00:01:31.257
But if I move it up like so,

00:01:31.257 --> 00:01:35.384
now we can say the box
is over the hamster.

00:01:37.058 --> 00:01:40.033
But let's get rid of the
box and let's imagine

00:01:40.033 --> 00:01:44.316
that our hamster is
having a midlife crisis.

00:01:45.249 --> 00:01:47.115
And our hamster decides
it's going to go out

00:01:47.115 --> 00:01:50.795
and it's going to splurge
on a fabulous, new hat,

00:01:50.795 --> 00:01:55.795
just an enormous top hat, a
little band in the center,

00:01:55.915 --> 00:01:59.074
just a big, old, silly, Abe Lincoln style,

00:01:59.074 --> 00:02:01.984
stove pipe, top hat.

00:02:03.354 --> 00:02:06.100
Now, another use for
prepositions is we can talk about

00:02:06.100 --> 00:02:08.899
when things are in relation to each other.

00:02:08.899 --> 00:02:13.899
So I could say, "Before
the hamster got the hat

00:02:14.716 --> 00:02:18.925
"and after the hamster got the hat."

00:02:18.925 --> 00:02:21.723
Right, and these words after and before

00:02:21.723 --> 00:02:24.347
express relationships in time.

00:02:24.347 --> 00:02:26.518
But another interesting thing
that prepositions can do

00:02:26.518 --> 00:02:30.186
is they can also help
express how something is

00:02:30.186 --> 00:02:33.122
or how it's, what it's
for, what its use is.

00:02:33.122 --> 00:02:38.122
So we could say that
this hat is for parties

00:02:39.407 --> 00:02:41.957
or is for wearing at parties.

00:02:41.957 --> 00:02:45.702
Oh, and at, also, is a preposition.

00:02:45.702 --> 00:02:48.171
This hat is for wearing at parties.

00:02:48.171 --> 00:02:53.171
So this is the how and
this part is the where.

00:02:54.964 --> 00:02:56.450
So what's the purpose of the hat?

00:02:56.450 --> 00:02:58.563
Well, we established
that with the word for,

00:02:58.563 --> 00:03:00.195
the hat is for wearing.

00:03:00.195 --> 00:03:02.563
The where is it supposed
to be worn, at parties,

00:03:02.563 --> 00:03:04.335
that's the where.

00:03:04.335 --> 00:03:08.409
We can also use a word like of to express

00:03:08.409 --> 00:03:13.409
the how relationship and
that's just sort of to say

00:03:14.679 --> 00:03:15.840
what belongs to whom.

00:03:15.840 --> 00:03:18.556
So we could say, "That is
the hat of the hamster."

00:03:18.556 --> 00:03:23.556
That is the hat of the hamster.

00:03:25.746 --> 00:03:27.868
So that's what prepositions are

00:03:27.868 --> 00:03:30.256
in the most basic sense they can

00:03:30.256 --> 00:03:32.938
help you figure out
what the relationship is

00:03:32.938 --> 00:03:37.079
between two things in time and space

00:03:37.079 --> 00:03:40.845
or how one thing relates to another.

00:03:40.845 --> 00:03:41.609
So you can figure out

00:03:41.609 --> 00:03:44.948
when, where, and how using prepositions.

00:03:46.120 --> 00:03:48.576
You can learn anything, David out.


Prepositions of space

WEBVTT
Kind: captions
Language: en

00:00:00.332 --> 00:00:01.901
- [Voiceover] Hello grammarians!

00:00:01.901 --> 00:00:06.092
So we had said previously
that prepositions express

00:00:06.092 --> 00:00:08.759
relationships between two ideas.

00:00:10.191 --> 00:00:12.132
And we can do that either in time

00:00:12.132 --> 00:00:14.037
or in space or in other ways.

00:00:14.037 --> 00:00:15.250
But today I wanna talk about

00:00:15.250 --> 00:00:18.417
prepositions in space.

00:00:22.519 --> 00:00:23.601
Because this is, again,

00:00:23.601 --> 00:00:26.070
one of the things that prepositions do,

00:00:26.070 --> 00:00:29.803
is they can set up
relationships between objects

00:00:29.803 --> 00:00:31.388
and their locations.

00:00:31.388 --> 00:00:32.592
So I could say,

00:00:32.592 --> 00:00:35.259
the triangle is over the square,

00:00:36.538 --> 00:00:38.885
or on top of the square.

00:00:38.885 --> 00:00:39.885
I could say,

00:00:40.850 --> 00:00:44.017
the circle is inside the square.

00:00:46.615 --> 00:00:47.615
Over,

00:00:49.119 --> 00:00:50.669
inside.

00:00:50.669 --> 00:00:53.289
What I would like to do is
review some of the major ones,

00:00:53.289 --> 00:00:56.489
and talk about what their uses are.

00:00:56.489 --> 00:00:59.324
So when we use the word at in a sentence,

00:00:59.324 --> 00:01:01.305
and here I'm talking about,
something we should note,

00:01:01.305 --> 00:01:04.017
is that some of these prepositions

00:01:04.017 --> 00:01:07.110
can be used in multiple ways.

00:01:07.110 --> 00:01:10.341
So at has a space connotation,

00:01:10.341 --> 00:01:12.763
but it also can have a time connotation.

00:01:12.763 --> 00:01:15.537
But I don't want you to really
worry about that right now,

00:01:15.537 --> 00:01:17.091
I think it makes the most sense to just

00:01:17.091 --> 00:01:19.758
think of their uses as separate,

00:01:20.885 --> 00:01:23.552
and just think of them separately.

00:01:23.552 --> 00:01:27.135
So when we talk about
at, at means a point.

00:01:29.313 --> 00:01:30.837
It's talking about a point.

00:01:30.837 --> 00:01:33.047
So we could say something like,

00:01:33.047 --> 00:01:35.964
we stood at the entrance to a cave.

00:01:37.557 --> 00:01:40.844
But you can also have this
connotation of direction.

00:01:40.844 --> 00:01:44.594
As in, the creature
launched itself at Amina.

00:01:49.468 --> 00:01:53.034
The word by when we're talking
about space means near.

00:01:53.034 --> 00:01:57.201
As in, the house by the old
mill is totally haunted.

00:02:02.162 --> 00:02:06.002
Man all these sentences
are like really spooky,

00:02:06.002 --> 00:02:08.303
ooooh, I don't know what I was thinking.

00:02:08.303 --> 00:02:12.470
The preposition from has this
connotation of coming from

00:02:13.804 --> 00:02:15.721
somewhere else to here.

00:02:17.065 --> 00:02:19.148
As in, we came from Mars.

00:02:25.126 --> 00:02:27.459
In denotes an enclosed area,

00:02:28.722 --> 00:02:30.124
so you could say something like

00:02:30.124 --> 00:02:32.374
there's a bunny in the box.

00:02:36.021 --> 00:02:37.854
Off denotes away from,

00:02:42.726 --> 00:02:44.726
she hopped off the rock.

00:02:48.562 --> 00:02:52.145
On, which usually notes
being on a surface,

00:02:54.139 --> 00:02:57.446
as opposed to in which is an
enclosed area like I said.

00:02:57.446 --> 00:03:01.613
So we could say, there's a
goblin on the front steps.

00:03:11.754 --> 00:03:14.004
The goblin is on the steps.

00:03:17.819 --> 00:03:20.272
The bunny is in the box.

00:03:20.272 --> 00:03:22.086
Do you see the difference?

00:03:22.086 --> 00:03:26.253
Out is another direction
word. Away from something.

00:03:28.074 --> 00:03:31.685
And off and on and in
and out mean the opposite

00:03:31.685 --> 00:03:32.722
of each other.

00:03:32.722 --> 00:03:36.889
So away from, out means
away from an enclosed area,

00:03:40.097 --> 00:03:42.930
and off means away from a surface.

00:03:45.430 --> 00:03:48.950
So if you can imagine, there's
someone who's on the rock,

00:03:48.950 --> 00:03:51.754
and then they hop off the rock.

00:03:51.754 --> 00:03:54.131
There's a goblin on the front steps,

00:03:54.131 --> 00:03:56.082
the goblin leaves the front
steps he's off the front steps.

00:03:56.082 --> 00:03:57.682
There's a bunny in the box,

00:03:57.682 --> 00:04:02.604
if the bunny leaves the box
it will go out of the box.

00:04:02.604 --> 00:04:04.996
And there's plenty of other prepositions

00:04:04.996 --> 00:04:08.425
but let's talk about to,
which when you're talking

00:04:08.425 --> 00:04:10.147
about to in the physical sense it has this

00:04:10.147 --> 00:04:12.230
connotation of direction.

00:04:16.126 --> 00:04:19.626
So you could say, I'm going to Mozambique.

00:04:22.230 --> 00:04:24.516
These are some of but certainly not all

00:04:24.516 --> 00:04:27.335
of the spacial prepositions of English.

00:04:27.335 --> 00:04:30.718
Now we're lucky because
prepositions are a closed group

00:04:30.718 --> 00:04:33.502
in English, a closed group.

00:04:33.502 --> 00:04:36.656
We don't add many of them to the language

00:04:36.656 --> 00:04:38.774
the way that we add nouns and adverbs

00:04:38.774 --> 00:04:40.785
and verbs and adjectives.

00:04:40.785 --> 00:04:42.736
There are a lot of them
and you have to memorize

00:04:42.736 --> 00:04:46.012
all of them and their
various obnoxious nuances,

00:04:46.012 --> 00:04:50.218
but there isn't a limitless
number of prepositions.

00:04:50.218 --> 00:04:53.905
There's maybe 100 plus,
and of those maybe 50

00:04:53.905 --> 00:04:56.488
are quite useful, and of those,

00:04:57.669 --> 00:05:00.336
maybe 20 to 25 are super useful.

00:05:01.433 --> 00:05:03.841
And it's the super
useful, most common ones

00:05:03.841 --> 00:05:06.797
that are in the exercises,
so give those a go,

00:05:06.797 --> 00:05:09.630
you can learn anything. David out.


Prepositions of time

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.143
- [Voiceover] Hello, Grammarians.

00:00:01.143 --> 00:00:04.347
We are once again learning
how to master time

00:00:04.347 --> 00:00:06.728
and become Time Wizards,

00:00:06.728 --> 00:00:07.541
which is, of course,

00:00:07.541 --> 00:00:09.445
what you will be if you master all

00:00:09.445 --> 00:00:11.140
the tenses of English.

00:00:11.140 --> 00:00:14.718
But, if you want to become
an additional Time Wizard,

00:00:14.718 --> 00:00:16.111
if you want to get, I don't know,

00:00:16.111 --> 00:00:17.434
a second hat,

00:00:17.434 --> 00:00:20.617
because everyone knows
all wizards wear multiple,

00:00:20.617 --> 00:00:21.961
simultaneous hats.

00:00:21.961 --> 00:00:23.755
If you want to wear a second hat on top of

00:00:23.755 --> 00:00:25.496
your other Time Wizard hat,

00:00:25.496 --> 00:00:27.486
that's the silliest thing I've ever said,

00:00:27.486 --> 00:00:31.054
then you will have to learn
the Prepositions of Time.

00:00:31.054 --> 00:00:33.863
Now here's something weird and cool about

00:00:33.863 --> 00:00:36.464
Prepositions of Time is
that once upon a time

00:00:36.464 --> 00:00:40.876
all of these were physical prepositions.

00:00:40.876 --> 00:00:43.397
Like "Before" and "After"

00:00:43.397 --> 00:00:48.275
just used to mean behind and in front of.

00:00:48.275 --> 00:00:52.902
They later took on this
additional connotation of time

00:00:52.902 --> 00:00:56.708
just over the course of
English-Speaking history.

00:00:56.708 --> 00:01:01.708
People took this literal
meaning of "Before" and "After"

00:01:03.034 --> 00:01:05.799
and made it representational.

00:01:05.799 --> 00:01:09.253
This moment occurred

00:01:09.253 --> 00:01:11.459
in front of this one in time,

00:01:11.459 --> 00:01:13.455
but behind this other one in time.

00:01:13.455 --> 00:01:14.384
It's a metaphor.

00:01:14.384 --> 00:01:17.380
We're using space to represent time.

00:01:17.380 --> 00:01:19.151
Anyway, I just thought
that was really cool.

00:01:19.151 --> 00:01:21.542
Let's talk about how all of these work.

00:01:21.542 --> 00:01:24.632
I'm just going to list
a couple of the most

00:01:24.632 --> 00:01:28.370
famous Prepositions of Time
and write an example sentence.

00:01:28.370 --> 00:01:29.603
So let's go through these.

00:01:29.603 --> 00:01:32.014
"After" and "Before,"
as we've established,

00:01:32.014 --> 00:01:35.020
these are time relationships that refer to

00:01:35.020 --> 00:01:36.761
something happening after.

00:01:36.761 --> 00:01:38.779
So when something is completed,

00:01:38.779 --> 00:01:43.779
say, "The bats come out
after the sun goes down."

00:01:44.011 --> 00:01:49.011
And before this occurs
prior to some point in time,

00:01:49.929 --> 00:01:52.924
so it is behind an action.

00:01:52.924 --> 00:01:56.431
So you can say, "Can
you take out the garbage

00:01:56.431 --> 00:02:00.495
"before you leave the house?"

00:02:00.495 --> 00:02:03.880
"At" is very precise.

00:02:03.880 --> 00:02:05.291
When we're talking about
"at" we're talking about

00:02:05.291 --> 00:02:07.776
a single moment in time.

00:02:07.776 --> 00:02:11.471
We could say, "The
vampire wakes at 10 p.m."

00:02:13.604 --> 00:02:14.774
There he is

00:02:14.774 --> 00:02:16.329
emerging from his coffin.

00:02:16.329 --> 00:02:18.620
There's the,

00:02:18.620 --> 00:02:19.644
oh that's not the sun.

00:02:19.644 --> 00:02:20.875
The sun would burn a vampire.

00:02:20.875 --> 00:02:23.596
No that's a little clock.

00:02:25.582 --> 00:02:28.682
It's got a tail because it's
like a little wacky cat clock.

00:02:28.682 --> 00:02:31.962
No, Bat Clock.

00:02:31.962 --> 00:02:32.928
That doesn't have a tail.

00:02:32.928 --> 00:02:35.454
It's got a little stubby tail.

00:02:35.454 --> 00:02:37.739
Doop.

00:02:37.739 --> 00:02:39.572
Ah, I really want a Bat Clock now.

00:02:39.572 --> 00:02:40.751
Anyway, okay.

00:02:40.751 --> 00:02:45.606
"By," this is a really precise end time,

00:02:45.606 --> 00:02:49.135
but not a very precise beginning time.

00:02:49.135 --> 00:02:51.175
So you could say something like,

00:02:51.175 --> 00:02:56.050
"This place had better be
clean by 3 p.m., buddy."

00:02:56.050 --> 00:02:57.112
If you say something like that,

00:02:57.112 --> 00:02:59.260
you're not especially
concerned that the place

00:02:59.260 --> 00:03:01.703
might be clean before three.

00:03:01.703 --> 00:03:03.119
That would be nice,

00:03:03.119 --> 00:03:04.694
but it's only relevant to you that the

00:03:04.694 --> 00:03:06.714
cutoff time is at three o'clock.

00:03:06.714 --> 00:03:08.224
So the end is precise.

00:03:08.224 --> 00:03:09.454
That's the connotation there.

00:03:09.454 --> 00:03:11.839
But the beginning is not.

00:03:11.839 --> 00:03:13.750
"For" denotes duration.

00:03:13.750 --> 00:03:16.235
How long something has been going on.

00:03:16.235 --> 00:03:17.744
So you could say,

00:03:17.744 --> 00:03:21.436
"I've been a chef for 40 years."

00:03:21.436 --> 00:03:22.086
I haven't,

00:03:22.086 --> 00:03:24.810
but that would be cool and difficult.

00:03:24.810 --> 00:03:25.368
But you know what,

00:03:25.368 --> 00:03:26.180
this is Khan Academy,

00:03:26.180 --> 00:03:28.015
you can cook anything.

00:03:28.015 --> 00:03:30.704
"In" denotes a bounded duration.

00:03:30.704 --> 00:03:34.382
So it's something that lasts
for a specific amount of time,

00:03:34.382 --> 00:03:36.352
like a limited period.

00:03:36.352 --> 00:03:41.352
Okay, so let's just say bounded duration.

00:03:43.654 --> 00:03:45.632
So that covers usage like,

00:03:45.632 --> 00:03:50.632
"In March" or "In the Middle Ages."

00:03:51.758 --> 00:03:54.674
Both of those things are like set periods.

00:03:54.674 --> 00:03:57.554
March has a beginning and an end.

00:03:57.554 --> 00:04:02.478
The Middle Ages have a
beginning and an end.

00:04:02.478 --> 00:04:06.157
It's a bounded duration.

00:04:06.157 --> 00:04:09.980
"On" has a specific connotation.

00:04:09.980 --> 00:04:14.384
It's something that
happens on a specific day.

00:04:14.384 --> 00:04:15.287
You could say something like,

00:04:15.287 --> 00:04:16.727
"On the 4th of July,

00:04:16.727 --> 00:04:20.953
"many Americans watch fireworks
and eat encaged meats."

00:04:20.953 --> 00:04:24.111
Mind you not everybody eats
hot dogs or likes fireworks,

00:04:24.111 --> 00:04:27.872
so I said many not all.

00:04:27.872 --> 00:04:32.050
"Since" is kind of like "By"

00:04:32.050 --> 00:04:33.800
except it's more about the precision of

00:04:33.800 --> 00:04:36.399
the start point rather than the end point.

00:04:36.399 --> 00:04:39.436
So, precise beginning.

00:04:39.436 --> 00:04:42.253
"Since 1974, our company has made

00:04:42.253 --> 00:04:45.318
"nothing but toasters."

00:04:45.318 --> 00:04:49.242
"Until" is also precise,

00:04:49.242 --> 00:04:52.719
but it's a precise ending time.

00:04:52.719 --> 00:04:55.947
"You have until midnight
to rescue the Ambassador,

00:04:55.947 --> 00:04:59.636
break the curse and save Prince Wilbur.

00:04:59.636 --> 00:05:02.037
All right. So there's
a precise ending there.

00:05:02.037 --> 00:05:03.319
You have "until midnight,"

00:05:03.319 --> 00:05:05.408
and then you can't rescue the Ambassador,

00:05:05.408 --> 00:05:07.774
break the curse or save any princes.

00:05:07.774 --> 00:05:11.576
But what you can do is learn anything.

00:05:11.576 --> 00:05:14.619
These are some of the most
essential Time Prepositions.

00:05:14.619 --> 00:05:15.885
David out.


Terminal prepositions

WEBVTT
Kind: captions
Language: en

00:00:00.939 --> 00:00:02.247
- [Voiceover] Hello grammarians.

00:00:02.247 --> 00:00:03.369
Today, I wanna talk about

00:00:03.369 --> 00:00:05.472
ending sentences with prepositions,

00:00:05.472 --> 00:00:08.649
and I wanna tell you, straight
up, it is totally okay.

00:00:08.649 --> 00:00:12.174
Like, it is perfectly
grammatically correct and sensible

00:00:12.174 --> 00:00:16.341
and fine to end sentences
with prepositions in English.

00:00:17.461 --> 00:00:20.559
And if you don't know
what I mean, that's fine.

00:00:20.559 --> 00:00:23.837
Let me throw out some examples.

00:00:23.837 --> 00:00:26.287
"It's a crazy world we
live in," for example,

00:00:26.287 --> 00:00:29.437
is a sentence that ends in
"in," which is a preposition.

00:00:29.437 --> 00:00:32.520
And for years, for hundreds of years,

00:00:33.550 --> 00:00:35.713
there have been people,
language authorities

00:00:35.713 --> 00:00:38.116
that have been telling you it's not okay

00:00:38.116 --> 00:00:39.958
to end a sentence with a preposition.

00:00:39.958 --> 00:00:41.828
Let me tell you, by
the power vested in me,

00:00:41.828 --> 00:00:43.109
it is totally okay.

00:00:43.109 --> 00:00:45.613
This is one of those
language superstitions

00:00:45.613 --> 00:00:47.113
that will not die.

00:00:47.989 --> 00:00:49.779
Taking away the terminal preposition

00:00:49.779 --> 00:00:51.274
takes away sentences like,

00:00:51.274 --> 00:00:53.597
"That's not behavior I'll put up with."

00:00:53.597 --> 00:00:55.760
And, in fact, some of you have maybe heard

00:00:55.760 --> 00:00:59.685
the statement that is
supposedly attributed

00:00:59.685 --> 00:01:02.602
to Winston Churchill where he says,

00:01:03.504 --> 00:01:06.014
"That is something with
which up I will not put,"

00:01:06.014 --> 00:01:10.680
which kinda emphasizes how
clunky that is, you know?

00:01:10.680 --> 00:01:13.217
If that's supposed to
be formal high language,

00:01:13.217 --> 00:01:15.587
it sounds really inarticulate.

00:01:15.587 --> 00:01:16.869
Not a fan.

00:01:16.869 --> 00:01:21.036
This is ultimately a question
not of grammar but of style

00:01:22.363 --> 00:01:24.072
because there's nothing about

00:01:24.072 --> 00:01:27.623
"It's a crazy world we live
in," that doesn't make sense

00:01:27.623 --> 00:01:30.507
that doesn't function as a sentence.

00:01:30.507 --> 00:01:32.964
Indeed, there's nothing
grammatically incorrect

00:01:32.964 --> 00:01:36.435
with, "This is behavior with
which up I will not put,"

00:01:36.435 --> 00:01:41.268
it's just needlessly verbose
and twisting back on itself

00:01:41.268 --> 00:01:43.164
for the sake of avoiding something

00:01:43.164 --> 00:01:46.021
that doesn't need to be avoided.

00:01:46.021 --> 00:01:48.365
And we can trace all of
this back to Robert Lowth,

00:01:48.365 --> 00:01:50.661
a man who was the Bishop of London

00:01:50.661 --> 00:01:52.824
during part of the 18th century,

00:01:52.824 --> 00:01:56.429
and he wrote about terminal prepositions

00:01:56.429 --> 00:02:00.775
in his 1762 "Short Introduction
to English Grammar,"

00:02:00.775 --> 00:02:03.846
which reads in part, "This is an idiom

00:02:03.846 --> 00:02:06.569
"which our language is
strongly inclined to;

00:02:06.569 --> 00:02:08.439
"it prevails in common conversation

00:02:08.439 --> 00:02:11.242
"and suits very well with the
familiar style in writing;

00:02:11.242 --> 00:02:12.871
"but the placing of the preposition

00:02:12.871 --> 00:02:15.114
"before the relative is more graceful,

00:02:15.114 --> 00:02:18.586
"and agrees much better with
the solemn and elevated style."

00:02:18.586 --> 00:02:21.490
But, Bishop Lowth, may
I direct your attention

00:02:21.490 --> 00:02:24.494
to this part of your statement?

00:02:24.494 --> 00:02:25.962
"This is an idiom which our language

00:02:25.962 --> 00:02:28.199
"is strongly inclined to."

00:02:28.199 --> 00:02:31.637
Even when Bishop Lowth
is using what he calls

00:02:31.637 --> 00:02:33.666
this solemn and elevated style,

00:02:33.666 --> 00:02:36.897
he himself can not avoid ending a clause,

00:02:36.897 --> 00:02:38.413
boom, with a preposition.

00:02:38.413 --> 00:02:40.246
Game, set, match, sir.

00:02:42.044 --> 00:02:45.222
The question is, why did Lowth
have such a bee in his bonnet

00:02:45.222 --> 00:02:47.518
about prepositions at
the end of sentences?

00:02:47.518 --> 00:02:50.162
And the answer can be found in Latin.

00:02:50.162 --> 00:02:52.752
Follow me over to the next screen.

00:02:52.752 --> 00:02:54.134
Here is the deal with Latin.

00:02:54.134 --> 00:02:57.338
In Latin, prepositions have
a very particular function,

00:02:57.338 --> 00:03:00.910
similar to how they work in English.

00:03:00.910 --> 00:03:05.077
But let's break apart what
the word preposition is.

00:03:06.063 --> 00:03:10.230
In Latin, the word "preposition"
comes from "prae positio,"

00:03:12.038 --> 00:03:16.525
which means "placed before,"
right here, placed before,

00:03:16.525 --> 00:03:19.783
because here's something cool about Latin:

00:03:19.783 --> 00:03:22.663
Latin's word order rules are different

00:03:22.663 --> 00:03:24.601
than English's word order rules.

00:03:24.601 --> 00:03:25.963
I'll explain.

00:03:25.963 --> 00:03:28.707
You know, in English,
we have this expression,

00:03:28.707 --> 00:03:30.416
"To put the cart before the horse,"

00:03:30.416 --> 00:03:32.686
which means to embark on a project

00:03:32.686 --> 00:03:34.728
before you're really ready.

00:03:34.728 --> 00:03:38.253
And this is a very ancient
expression, in fact,

00:03:38.253 --> 00:03:41.753
one that can be attested in Latin like so.

00:03:43.293 --> 00:03:46.711
"Ante equum carrum ponere," right?

00:03:46.711 --> 00:03:50.878
Okay, so this is, "Before
the horse, the cart to put."

00:03:51.998 --> 00:03:54.722
Here's the thing about
prepositions in Latin

00:03:54.722 --> 00:03:58.033
is that in Latin, this, "ante," before,

00:03:58.033 --> 00:04:00.283
always has to be positioned

00:04:01.338 --> 00:04:05.505
before the word it's attached
to, so before the horse.

00:04:07.105 --> 00:04:10.203
But in Latin, you can rearrange

00:04:10.203 --> 00:04:11.832
this sentence any way you like.

00:04:11.832 --> 00:04:15.665
So, you could say, "Carrum
ponere ante equum."

00:04:22.513 --> 00:04:24.369
And just because of the way Latin works,

00:04:24.369 --> 00:04:25.677
because of its case endings

00:04:25.677 --> 00:04:29.309
and because of this
prepositional relationship,

00:04:29.309 --> 00:04:32.807
we can always tell, no matter
what order the words are in,

00:04:32.807 --> 00:04:36.272
how the sentence parts
relate to one another.

00:04:36.272 --> 00:04:38.808
Or we could also switch it around:

00:04:38.808 --> 00:04:40.905
"Ponere carrum ante equum," right?

00:04:40.905 --> 00:04:45.072
It could in any order, as
long as ante was before equum.

00:04:47.600 --> 00:04:50.030
Now, admittedly, in English,
if you wanted to end this

00:04:50.030 --> 00:04:52.567
with a preposition, it would
still sound pretty awkward,

00:04:52.567 --> 00:04:56.619
like, "The cart is the thing
that the horse is before,"

00:04:56.619 --> 00:04:58.622
but it is still grammatical.

00:04:58.622 --> 00:05:02.861
If you move this thing, if
you move "ante" out of order,

00:05:02.861 --> 00:05:06.279
there's no way to tell what's
going on in this sentence.

00:05:06.279 --> 00:05:09.403
Latin, during the time that
Lowth was Bishop of London,

00:05:09.403 --> 00:05:12.340
was the language of scholarship, right?

00:05:12.340 --> 00:05:14.503
It was this language that enabled people

00:05:14.503 --> 00:05:16.132
all over the European continent

00:05:16.132 --> 00:05:17.387
to communicate with each other

00:05:17.387 --> 00:05:19.530
in a common language of knowledge.

00:05:19.530 --> 00:05:23.447
It was the language of
religion and philosophy.

00:05:24.790 --> 00:05:28.957
And all of that added up
to make Latin really cool,

00:05:29.917 --> 00:05:32.074
and also very powerful.

00:05:32.074 --> 00:05:35.191
And because of the history
of the English language,

00:05:35.191 --> 00:05:37.835
which basically entails people in boats

00:05:37.835 --> 00:05:39.250
coming over the North Sea

00:05:39.250 --> 00:05:42.000
to beat the tar out of
Celts and Anglo-Saxons

00:05:42.000 --> 00:05:44.564
and leave Latin- or Norse-

00:05:44.564 --> 00:05:48.429
or French-shaped dents in their language,

00:05:48.429 --> 00:05:50.699
English has this kind of

00:05:50.699 --> 00:05:54.090
uncomfortable relationship with Latin.

00:05:54.090 --> 00:05:58.257
English scholars kinda had
an inferiority complex.

00:05:59.190 --> 00:06:01.701
And so, during the 17th and 18th century,

00:06:01.701 --> 00:06:05.706
you really see this move
towards Latinizing English,

00:06:05.706 --> 00:06:08.403
trying to make English grammar

00:06:08.403 --> 00:06:11.474
behave more like Latin grammar.

00:06:11.474 --> 00:06:14.892
But English comes from a
different language heritage;

00:06:14.892 --> 00:06:16.547
it's a Germanic language.

00:06:16.547 --> 00:06:18.550
And that doesn't mean it's
better or worse than Latin,

00:06:18.550 --> 00:06:21.354
it just means it's different,
and it behaves differently.

00:06:21.354 --> 00:06:24.291
We shouldn't try to treat English

00:06:24.291 --> 00:06:28.430
as though it were anything
other than English.

00:06:28.430 --> 00:06:30.032
So, if anyone ever tells you

00:06:30.032 --> 00:06:33.130
that you can't end a
sentence with a preposition,

00:06:33.130 --> 00:06:34.919
send them this page.

00:06:34.919 --> 00:06:38.544
Or if you prefer, you know
where to send them to,

00:06:38.544 --> 00:06:42.416
which is here on Khan Academy,
where you can learn anything.

00:06:42.416 --> 00:06:43.249
David out.


Prepositional phrases

WEBVTT
Kind: captions
Language: en

00:00:00.134 --> 00:00:01.070
- [Voiceover] Hey grammarians,

00:00:01.070 --> 00:00:02.892
let's talk about prepositional phrases:

00:00:02.892 --> 00:00:04.459
what they are, and how they're used.

00:00:04.459 --> 00:00:06.411
Their care and feeding, you know.

00:00:07.451 --> 00:00:09.754
So a prepositional
phrase, simply speaking,

00:00:09.754 --> 00:00:13.979
is anything that follows
a preposition, frankly.

00:00:13.979 --> 00:00:16.395
So, if we look at the sentence:

00:00:16.395 --> 00:00:21.395
Danielle blew the horn with
the strength of a giant-

00:00:27.459 --> 00:00:28.771
quick little doodle there.

00:00:28.771 --> 00:00:30.234
There's Danielle blowing the horn

00:00:30.234 --> 00:00:31.278
with the strength of a giant.

00:00:31.278 --> 00:00:33.357
So this part with the strength

00:00:33.357 --> 00:00:37.073
of a giant, is a prepositional phrase.

00:00:37.073 --> 00:00:39.997
Actually, it's two prepositional phrases,

00:00:39.997 --> 00:00:42.679
because there's with the strength,

00:00:42.679 --> 00:00:45.094
and then, of a giant.

00:00:45.094 --> 00:00:46.349
What is a prepositional phrase?

00:00:46.349 --> 00:00:49.111
It is a word chunk that begins

00:00:49.111 --> 00:00:50.192
with a preposition.

00:00:50.192 --> 00:00:53.198
So, with is a preposition,
of is a preposition,

00:00:53.198 --> 00:00:55.997
and this entire thing, with
the strength of a giant,

00:00:55.997 --> 00:00:59.073
is one prepositional phrase, altogether,

00:00:59.073 --> 00:01:02.069
composed of two smaller ones.

00:01:02.069 --> 00:01:05.458
And what's cool, is you can use

00:01:05.458 --> 00:01:07.536
prepositional phrases in a couple

00:01:07.536 --> 00:01:08.817
of different ways.

00:01:08.817 --> 00:01:12.470
You can use them as nouns.

00:01:12.470 --> 00:01:16.256
You can use them as adverbs.

00:01:16.256 --> 00:01:19.391
And you can use them as adjectives.

00:01:19.391 --> 00:01:22.549
So we've got two different examples here,

00:01:22.549 --> 00:01:25.195
just even within this first sentence here.

00:01:25.195 --> 00:01:27.308
So Danielle blew the
horn with the strength

00:01:27.308 --> 00:01:29.851
of a giant. How did she blow the horn?

00:01:29.851 --> 00:01:32.197
With the strength of a giant.

00:01:32.197 --> 00:01:33.299
And so she blew the horn

00:01:33.299 --> 00:01:35.030
with the strength of a giant.

00:01:35.030 --> 00:01:36.433
So, with the strength of a giant,

00:01:36.433 --> 00:01:40.114
this prepositional phrase is modifying

00:01:40.114 --> 00:01:42.668
the verb blew.

00:01:42.668 --> 00:01:44.933
You can really see, her hair's

00:01:44.933 --> 00:01:46.013
being blown back just by the strength

00:01:46.013 --> 00:01:47.718
of this (trumpet noise).

00:01:47.718 --> 00:01:51.713
So this whole thing
together is being treated

00:01:51.713 --> 00:01:53.211
as an adverb, but if we look

00:01:53.211 --> 00:01:54.650
at the word strength, strength

00:01:54.650 --> 00:01:57.331
is being modified by of a giant.

00:01:57.331 --> 00:01:59.816
So this is a noun,
right, the word strength

00:01:59.816 --> 00:02:02.696
is a noun, but this of a giant thing

00:02:02.696 --> 00:02:05.389
is modifying it, so this part

00:02:05.389 --> 00:02:09.290
is actually behaving as an adjective.

00:02:09.290 --> 00:02:12.099
Kinda cool, right?

00:02:12.099 --> 00:02:17.046
Let's look at some more examples.

00:02:20.700 --> 00:02:22.596
To steal the queen's diamonds

00:02:22.596 --> 00:02:24.638
would be a terrible crime.

00:02:24.638 --> 00:02:26.032
This is actually something we'd call,

00:02:26.032 --> 00:02:28.656
in addition to being a
prepositional phrase,

00:02:28.656 --> 00:02:31.037
this is something we'd call an infinitive.

00:02:31.037 --> 00:02:33.856
The verb to steal, when
it's presented like this,

00:02:33.856 --> 00:02:36.399
in the to form never conjugates.

00:02:36.399 --> 00:02:37.755
It's not affected by time, so it's

00:02:37.755 --> 00:02:40.730
kind of infinitive and infinite.

00:02:40.730 --> 00:02:42.529
But we are treating this whole thing

00:02:42.529 --> 00:02:45.095
as a noun, right, because

00:02:45.095 --> 00:02:46.895
to steal the queen's diamonds

00:02:46.895 --> 00:02:48.811
is kind of all being considered one thing,

00:02:48.811 --> 00:02:50.377
this big, old prepositional phrase,

00:02:50.377 --> 00:02:53.292
would, right, to steal
the queen's diamonds

00:02:53.292 --> 00:02:55.578
would be a terrible crime.

00:02:55.578 --> 00:02:58.377
So, this prepositional phrase is acting

00:02:59.947 --> 00:03:02.474
like a noun.

00:03:02.474 --> 00:03:05.474
Let's try another one.

00:03:05.474 --> 00:03:06.207
I don't know what that is,

00:03:06.207 --> 00:03:07.352
I just made it up.

00:03:07.352 --> 00:03:09.291
Let's pay attention to how

00:03:09.291 --> 00:03:12.495
the prepositional phrase of glass

00:03:12.495 --> 00:03:14.956
works in the rest of the sentence.

00:03:14.956 --> 00:03:16.291
You know, what part of this

00:03:16.291 --> 00:03:17.556
is it attached to?

00:03:17.556 --> 00:03:21.179
It's not I of glass, or enjoy of glass.

00:03:21.179 --> 00:03:24.139
It's the cathedral of glass,

00:03:24.139 --> 00:03:25.917
and that means that this of glass thing

00:03:25.917 --> 00:03:27.937
is describing cathedral.

00:03:27.937 --> 00:03:30.293
A cathedral is a place or a structure,

00:03:30.293 --> 00:03:33.231
so it's a noun, right, so if of glass

00:03:33.231 --> 00:03:35.111
is modifying this noun, that would make it

00:03:35.111 --> 00:03:36.690
an adjective.

00:03:36.690 --> 00:03:39.256
So of glass here, this
prepositional phrase,

00:03:39.256 --> 00:03:42.449
is behaving like an adjective.

00:03:42.449 --> 00:03:45.375
Prepositional phrases
can be really powerful

00:03:45.375 --> 00:03:47.696
and really elegant, and really cool.

00:03:47.696 --> 00:03:49.612
Like in Hamlet, in the
"to be, or not to be"

00:03:49.612 --> 00:03:52.479
speech, Hamlet describes death as

00:03:57.269 --> 00:03:59.606
the undiscovered country,
from whose bourn,

00:03:59.606 --> 00:04:02.556
no traveler returns.

00:04:02.556 --> 00:04:04.949
And bourn is an Early Modern English word

00:04:04.949 --> 00:04:06.795
meaning, like, boundary.

00:04:06.795 --> 00:04:09.279
What Hamlet is saying in the soliloquy

00:04:09.279 --> 00:04:11.010
is that death is a mystery.

00:04:11.010 --> 00:04:12.657
People don't come back from it.

00:04:12.657 --> 00:04:15.235
And I think that's like a really powerful

00:04:15.235 --> 00:04:17.929
use of a prepositional phrase.

00:04:19.419 --> 00:04:23.587
All of this is describing country

00:04:24.697 --> 00:04:27.298
in a way that undiscovered is also doing.

00:04:27.298 --> 00:04:31.210
So country is being
modified from both sides,

00:04:31.210 --> 00:04:33.811
which is really cool, and it imbues

00:04:33.811 --> 00:04:36.353
the word country with
a really strange power.

00:04:36.353 --> 00:04:38.258
But, you have to be careful

00:04:38.258 --> 00:04:39.476
because you can set yourself up

00:04:39.476 --> 00:04:41.010
for a lot of ambiguity

00:04:41.010 --> 00:04:43.320
with prepositional phrases.

00:04:43.320 --> 00:04:45.154
You may remember this terrible joke

00:04:45.154 --> 00:04:47.650
from Mary Poppins. One man says,

00:04:47.650 --> 00:04:51.354
"I knew a man with a
wooden leg named Smith."

00:04:51.354 --> 00:04:54.791
Other guy says, "But what was
the name of his other leg?"

00:04:56.411 --> 00:05:00.154
It's silly, but it's
a good way to indicate

00:05:00.154 --> 00:05:03.533
where confusion can arise

00:05:03.533 --> 00:05:05.774
with prepositional phrases.

00:05:05.774 --> 00:05:09.279
So I would say, generally,
that the solution

00:05:09.279 --> 00:05:11.637
to a problem like this is to just put

00:05:11.637 --> 00:05:14.179
the named Smith part
earlier in the sentence.

00:05:14.179 --> 00:05:16.628
I knew a man named Smith
who had a wooden leg.

00:05:16.628 --> 00:05:19.474
Maybe lose the prepositional phrase.

00:05:19.474 --> 00:05:22.457
That solves the problem.

00:05:22.457 --> 00:05:24.756
What I'm trying to say
is, prepositional phrases

00:05:24.756 --> 00:05:26.590
are very powerful, but
you have to be careful

00:05:26.590 --> 00:05:28.692
about how you use them, because

00:05:28.692 --> 00:05:29.899
if you're not careful, you can create

00:05:29.899 --> 00:05:31.756
confusion or ambiguity.

00:05:31.756 --> 00:05:34.032
Anyway, you can learn anything.

00:05:34.032 --> 00:05:36.238
Sorry for the terrible cockney accent.

00:05:36.238 --> 00:05:37.479
David out.


Units of the rate constant

WEBVTT
Kind: captions
Language: en

00:00:00.173 --> 00:00:01.985
- [Voiceover] In this video,
we're going to be talking about

00:00:01.985 --> 00:00:05.305
how you can find the units
for your rate constant k.

00:00:05.305 --> 00:00:08.321
So the two things you should
know before we get started

00:00:08.321 --> 00:00:12.945
are that, one, rate constant k has units.

00:00:14.265 --> 00:00:18.419
So this isn't always true
of constants in chemistry,

00:00:18.419 --> 00:00:22.159
but it is true of k.

00:00:22.159 --> 00:00:24.435
The second thing to remember is that

00:00:24.435 --> 00:00:28.639
your rate constant, the units of k depend

00:00:28.639 --> 00:00:31.843
on your rate law.

00:00:31.843 --> 00:00:36.348
And so we're going to
use this second point

00:00:36.348 --> 00:00:40.317
to use the rate law to
derive the units of k.

00:00:40.317 --> 00:00:42.129
And this is really
handy because that means

00:00:42.129 --> 00:00:45.077
you don't have to memorize
what the units of k are

00:00:45.077 --> 00:00:47.773
for different orders of reactions.

00:00:47.773 --> 00:00:51.625
So we're going to focus on the
three most common rate laws

00:00:51.625 --> 00:00:53.925
that you see in chemistry class.

00:00:53.925 --> 00:00:55.551
So we're going to talk about

00:00:55.551 --> 00:00:59.175
zeroth, first, and second

00:00:59.175 --> 00:01:01.355
order reactions.

00:01:01.355 --> 00:01:05.559
And we will derive their units.

00:01:08.929 --> 00:01:11.482
So first, let's look at zeroth order.

00:01:11.482 --> 00:01:14.100
So zeroth order reactions

00:01:16.450 --> 00:01:20.002
have a rate law that look like this.

00:01:20.002 --> 00:01:22.554
So the rate is equal to k times

00:01:22.554 --> 00:01:25.270
the concentration of your reactant A

00:01:25.270 --> 00:01:30.193
to the zeroth power.

00:01:31.170 --> 00:01:34.838
And anything to the
zeroth power is just one.

00:01:34.838 --> 00:01:37.834
So our rate is equal
to the rate constant k.

00:01:37.834 --> 00:01:40.622
The units of rate are
always going to be the same.

00:01:40.622 --> 00:01:43.406
So the units of rate are
always molar per second

00:01:43.406 --> 00:01:46.217
and you can also just think
of units almost like numbers.

00:01:46.217 --> 00:01:48.280
If you have an equal sign,
the units on both sides

00:01:48.280 --> 00:01:50.696
of your equal sign have to be the same

00:01:50.696 --> 00:01:52.484
and they have to match.

00:01:52.484 --> 00:01:55.896
So here, since we have rate equal to k,

00:01:55.896 --> 00:01:59.588
that means k must also have
units of molars per second.

00:01:59.588 --> 00:02:03.328
So this tell us that the units
for a zeroth order reaction

00:02:03.328 --> 00:02:05.508
are molar per second.

00:02:05.508 --> 00:02:08.552
We can use that same idea
to figure out the units of k

00:02:08.552 --> 00:02:11.060
for first and second order reactions, too.

00:02:11.060 --> 00:02:14.424
So for a first order reaction,

00:02:14.424 --> 00:02:16.790
so for first order,

00:02:17.908 --> 00:02:20.368
a first order reaction rate law is

00:02:20.368 --> 00:02:23.572
rate is equal to our rate constant k

00:02:23.572 --> 00:02:26.408
times the concentration of our reactant

00:02:26.408 --> 00:02:27.940
raised to the first power.

00:02:27.940 --> 00:02:30.588
Units of rate are molar per second,

00:02:30.588 --> 00:02:32.584
and the units of concentration are always

00:02:32.584 --> 00:02:33.952
going to be molar.

00:02:33.952 --> 00:02:37.320
So now we know that the
units of k times molar

00:02:37.320 --> 00:02:39.509
equals molar per second.

00:02:40.467 --> 00:02:42.091
So we have molar on both sides,

00:02:42.091 --> 00:02:43.391
so we don't have to worry about that,

00:02:43.391 --> 00:02:45.643
but we're missing a
one over a second term.

00:02:45.643 --> 00:02:49.861
So that tells us that the units
of k are one over seconds.

00:02:51.241 --> 00:02:54.109
The other way that we can try
to figure out the units here,

00:02:54.109 --> 00:02:56.733
if you're not comfortable
with back-calculating

00:02:56.733 --> 00:02:58.545
what the units are, is we can actually

00:02:58.545 --> 00:03:00.541
rearrange this rate law,

00:03:00.541 --> 00:03:03.005
So if we just put k on one side

00:03:03.005 --> 00:03:04.953
and everything else on the other side,

00:03:04.953 --> 00:03:07.905
we get that k is equal to rate

00:03:07.905 --> 00:03:11.409
divided by the concentration of A.

00:03:11.409 --> 00:03:13.733
So all I did was divide both sides here

00:03:13.733 --> 00:03:15.913
by the concentration of A.

00:03:15.913 --> 00:03:18.445
And since we know that the units

00:03:18.445 --> 00:03:20.861
on both sides of the equal
sign have to be the same,

00:03:20.861 --> 00:03:23.345
then we can figure out the units of k

00:03:23.345 --> 00:03:25.177
by dividing the units of rate

00:03:25.177 --> 00:03:27.085
by the units of our concentration.

00:03:27.085 --> 00:03:31.261
So that's just molar per
second, for the rate,

00:03:31.261 --> 00:03:33.841
divided by molar,

00:03:33.841 --> 00:03:35.489
for the concentration.

00:03:35.489 --> 00:03:37.161
And then the molar cancels out,

00:03:37.161 --> 00:03:40.413
and we're left with one over seconds.

00:03:40.413 --> 00:03:42.617
So that's an even more
straight-forward way

00:03:42.617 --> 00:03:44.661
to find the units of k.

00:03:44.661 --> 00:03:45.961
But the idea is the same.

00:03:45.961 --> 00:03:48.121
You can treat units the
same way you treat numbers,

00:03:48.121 --> 00:03:49.513
and you just have to make sure they match

00:03:49.513 --> 00:03:51.045
on both sides of your equal sign.

00:03:51.045 --> 00:03:52.741
The last example we're going to go through

00:03:52.741 --> 00:03:56.057
is going to be for second order reactions.

00:03:56.899 --> 00:03:58.998
So second order reactions,

00:04:00.835 --> 00:04:02.264
or second order rate laws

00:04:02.264 --> 00:04:04.004
have the form

00:04:04.004 --> 00:04:06.840
rate is equal to our rate constant k

00:04:06.840 --> 00:04:09.624
times the concentration of our reactant

00:04:09.624 --> 00:04:10.856
to the second power.

00:04:10.856 --> 00:04:13.872
So on one side, we have
molar per second for the rate

00:04:13.872 --> 00:04:15.848
and on the other side, now,

00:04:15.848 --> 00:04:18.820
since our concentration is squared,

00:04:18.820 --> 00:04:20.932
we have molar squared.

00:04:20.932 --> 00:04:23.396
So molar squared times something

00:04:23.396 --> 00:04:25.258
is equal to molar per second.

00:04:27.304 --> 00:04:30.092
We need to add a one over seconds

00:04:30.092 --> 00:04:33.064
in our units for k because
we need to make sure

00:04:33.064 --> 00:04:36.316
when we multiple these, we
get the seconds on the bottom,

00:04:36.316 --> 00:04:39.148
and we need to cancel out one
of these concentration terms,

00:04:39.148 --> 00:04:42.748
so we need to put molar in
the denominator as well.

00:04:42.748 --> 00:04:46.344
So the units of k for
a second order reaction

00:04:46.344 --> 00:04:49.644
are one over molar,

00:04:49.644 --> 00:04:51.756
molar-seconds.

00:04:51.756 --> 00:04:54.960
so these are the three
most common molecularities

00:04:54.960 --> 00:04:57.328
that you might see in a chemistry class.

00:04:57.328 --> 00:04:59.140
And sometimes, you have reactions

00:04:59.140 --> 00:05:02.044
that aren't zeroth,
first, or second order,

00:05:02.044 --> 00:05:03.528
and whenever that happens,

00:05:03.528 --> 00:05:05.340
you can always use the rate law

00:05:05.340 --> 00:05:08.036
to find the units of the rate constant k.