Biogeochemical cycles

WEBVTT
Kind: captions
Language: en

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- [Instructor] Talk a little bit about

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biogeochemical cycles.

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And the term biogeochemical
sounds very fancy.

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But really these are
just cycles that involve

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different molecules that
are essential for life

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and how they circulate
through and an ecosystem

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and really how they
circulate through the entire,

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through an entire biosphere.

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And the molecules that we care about,

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and molecules that could
consist of one element

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or multiple elements.

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They are things like

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well, water molecules.

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H2O.

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Oxygen and hydrogen
make up a lot of living,

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a lot of living creatures,
a lot of biomass.

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And water is just an essential element

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that is involved in life as we know it.

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We're also gonna be talking about carbon.

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And carbon takes on may forms

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when we think about biogeochemical cycles.

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There's carbon dioxide in the air.

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There's a lot of carbon
in organic molecules

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that form up most of the
mass of life as we know it.

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And there is actors that maybe
don't get as much attention.

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There are things like nitrogen

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and of course, you have characters like,

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characters like phosphorus.

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And you might say, "Okay, I
get that most organic molecules

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"are made up of a bunch
of carbons and hydrogens

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"and every now and then, oxygens.

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"But what about nitrogens?

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"And what about phosphorus?"

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And remember, your DNA,
deoxyribonucleic acid.

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We're talking about nitrogenous bases.

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Your adenines and guanines
and all these things

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that we talk about in DNA,

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they involve nitrogen.

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And there's other biomolecules.

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Amino acids, proteins, amino
acids which make up proteins

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that involve nitrogen.

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Phosphorus, ATP.

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The adenosine triphosphate.

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It's essential.

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It's in that core biomolecule.

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It's also in the backbone of DNA.

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So these are all essential
elements for life.

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And the key thing is,

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is that they all get recycled
through biogeochemical cycles.

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So they are all recycled.

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We talked about how an
ecosystem energy flows.

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It might start with
light energy from the sun

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and then over time as it's
transferred from one form

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to another as it flows
from one form to another,

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it gets dissipated as heat.

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But the matter, the
elements, the molecules here.

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This is recycled.

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It was a originally formed.

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I mean there's a few meteorites
that hit every now and then.

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But the most part,

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most of the matter around
us was here at the dawn of,

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when the earth was first formed.

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It was first created in the
inside due to fusion reactions

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of stars billions and billions
and billions of years ago.

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So all of life, everything
that we've seen so far

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in the history of earth,

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for the most part,

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it's the same elements
and the same molecules

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that have been recycled over
and over and over again.

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And so when we think about
biogeochemical cycles,

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we will think about things like,
if we're talking about H20,

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we're gonna think about the water cycle.

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Water cycle.

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And we have a whole video on that

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but in (stutters) the short version of it

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is you could have water actually stored

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in a multiple different ways.

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Some of it can evaporate

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as water vapor.

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Eventually it condenses
in the form of clouds

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and then it can rain back down

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and along the way, you could have animals

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that get access especially
to the fresh water

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and make that part of the
actual living organisms.

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You actually, I also have living organisms

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that view the water as
part of their ecosystem

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but we go into some
depth in another video.

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You'll also hear people talk about,

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if we're talking about carbon,

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the carbon cycle.

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The carbon cycle.

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And just as a very high level of overview

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of the carbon cycle.

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So let's say that's the ground.

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Let's say that this is
a plant right over here.

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Take primary producer and autotroph.

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We talk about that in our ecosystem video.

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So let me draw a leaf here.

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This is a plant that is growing.

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What it's doing while
it takes light energy,

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so it gets light energy from the sun.

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So that's the light
energy right over there

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and it uses that light
energy to fix carbon.

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The carbon that is making up this plant.

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It's just not emerging out of nowhere,

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it's being recycled.

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It's being recycled from carbon molecules

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that are in the air.

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So the carbon molecules in the air,

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they're going to be, or
the carbon in the air,

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it's gonna be in molecular form in terms

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it's going to be carbon dioxide.

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So that over there is CO2.

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And so the plant uses that light energy

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and that gaseous, that CO2 gas,

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and it's able to fix the
carbon to construct it.

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So it's looks like that
plant is just growing.

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It's not clear where all
that mass is coming from.

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But it literally is coming from the air.

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And it might be able to get,

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it might get a few of the nutrients.

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Especially things like nitrogen phosphorus

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from the ground and that's
where we could go into the whole

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nitrogen and phosphorus cycles.

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But then once these plants
fix all of this carbon,

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some of it gets stored in the biomass,

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sometimes the plant dies
and then it gets buried

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and if there was enough pressure,

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it can turn into a hydrocarbons.

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So a hydrocarbons, when you
fuel your car, it's a really

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it's really energy stored by dead plants

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a long long time ago that got
buried and put into that form

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but it was essentially
plants through photosynthesis

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that first stored that energy.

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But then of course, and
we've talked about this,

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you can have animals
that eat those plants.

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So let me draw an animal
that is eating it.

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So that looks like an animal.

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Well that one looks like something

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that likes to eat more than just plants.

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So this is, you draw it like

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it's like an alligator
chicken looking thing.

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Well, that's close enough.

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Well you get the idea.

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When it eats that plant, it's
using some of that carbon

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that was fixed originally by
that plant for it's own biomass

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but it'll also as it metabolizes
the some of it (stutters)

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it will use that the bond,

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the energy stored in those chemical bonds,

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to live and grow and move about.

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And as it does that,

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it will exhale the CO2.

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So that the CO2 goes back
into the environment.

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Now this is a huge oversimplification
of the carbon cycle

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but this is the general idea.

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And eventually this thing might die

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or might get eaten by other consumers.

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And then you have the
decomposers down here

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who could further make use
of those chemical bonds

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that the primary producer first created

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using that light energy.

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Decom, decomposers right over here.

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And they might also, as they consume that,

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release more CO2 which will
eventually then get fixed again

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by a primary producer.

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And there's similar cycles
for nitrogen and phosphorus.

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These often involving bacteria

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to fix the nitrogen and
the phosphorus from the air

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to make it available as
nutrients in the soil

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for some of the primary producers in say,

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the carbon cycle.

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And nitrogen doesn't
get a lot of attention,

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but this is actually the
most gas in our atmosphere.

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So it's all around you right now

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even while we're breathing,

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we are breathing a lot of nitrogen.

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Although it doesn't play as
strong of a role as say oxygen

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and the oxygen in the air is
going to be molecular oxygen.

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So I could also write O2 right over here.

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Or as we breathe out,

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carbon dioxide.

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So I could write C

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CO2.

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CO2 right over there.

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But hopefully this gives you a sense

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of how matter is recycled.

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Energy is flowing through ecosystems

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including the largest ecosystems on earth

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which is earth is biosphere.

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You have matter being constantly recycled.

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And the cycle of that matter,

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we call biogeochemical cycles.

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I think I just said the word cycle a lot.


The water cycle

WEBVTT
Kind: captions
Language: en

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- [Voiceover] Let's talk a little bit

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about the water cycle, which
we're all familiar with.

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In fact, we're all part
of the water cycle,

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every moment of our lives.

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We might not fully appreciate it.

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So let's just jump in the cycle.

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I'll start with evaporation.

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So we could start with the
surface of the ocean here,

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or this river, or this lake.

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And at any given moment,

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there's going to be water
evaporating off of that surface.

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Water molecules that were
in their liquid state,

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liquid state, they just have
enough energy to bounce away

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and go into the gas state.

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And water in a gaseous state
we call vapor, water vapor.

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Water, water vapor.

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And so that water vapor,
it is going to rise,

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likely with the air that has
been heated on the surface,

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due to the sun, and there's
other more complex dynamics

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at play, but as it rises, and
as the overall temperature

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cools, that water vapor will
condense into little droplets.

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It'll condense around
little, tiny air particles,

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little particles of dust
that you can't even see

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with your eye, and
that's what forms clouds.

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So this is little droplets,
so the water's actually back

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to the liquid form, they're
not individual water molecules

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anymore, they're now able
to interact with each other,

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and they're condensing
around these little,

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microscopic dust particles
to form these water droplets.

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And if it's cold enough,
they might also form

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small ice crystals, and
that's what clouds are.

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And we see here, they're
talking about transportation,

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you can have these clouds, we
obviously, if you look outside

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and you see clouds, those
clouds are moving with the wind.

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And so they could be moving
all of those droplets

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with the overall wind.

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And when those droplets get heavy enough,

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they will precipitate,
they will precipitate down.

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Now they could precipitate
back into where we started,

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they could go back to the ocean there.

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Or you could go onto a mountain here,

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and since if the air is cold enough,

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and if you have the right conditions,

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that precipitation might be snow,

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and it might stay snow right over there.

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Or ice, but then eventually
things might warm up,

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or they might not warm up,
but if they do warm up,

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well, then, they would melt,

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and there would be snow melt run-off.

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And that's what you're seeing there.

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If that rain is falling in this area,

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so let's say it's not cold
enough for it to be snow,

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we are talking about rain.

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Well, most of that water
is actually going to

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percolate down into the soil.

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So most of it goes down.

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We look around us and we
see these rivers and lakes,

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and we say wow, there's
a lot of water there.

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But it turns out, there's
actually a lot more water

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inside the ground and
obviously, in the ocean.

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And we'll talk about that in a little bit.

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So you have all of this water that forms

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in these underground aquifers here.

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But some of it also ends up in these lakes

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and these lakes are usually
in a situation where

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the ground is either already
saturated with water,

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or there's the right types of rocks,

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so it can contain the water up here,

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and similarly, rivers
are formed by runoff,

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it's snow melt run-off
can famously form rivers.

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And in general, if you
see a creek or a river

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near your house, especially
when it rains it fills up,

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that's a good indication
that the ground water's

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already saturated and so
things are running off

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into that river.

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And so that in general is the water cycle.

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You have evaporation, it
condenses into clouds,

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it eventually precipitates,
and it keeps going,

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round and round and round.

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Now of course, there's
others actors at play.

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You have things like plants.

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Plants will take up water
from the upper soil,

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as far as the plant's roots go.

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And it will use that water
to transport nutrients

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down from the soil up into the leaves.

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It also uses that water as part of

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the photosynthesis
process that we've studied

00:04:03.759 --> 00:04:05.625
in many videos.

00:04:05.625 --> 00:04:09.843
And a lot of that water
gets transpired out.

00:04:09.843 --> 00:04:12.861
So once again, this is
transpiration, essentially,

00:04:12.861 --> 00:04:15.503
evaporation out the leaves of the water.

00:04:15.503 --> 00:04:18.836
Over here you see this word sublimation.

00:04:19.711 --> 00:04:22.885
That's going straight from
the solid form of water, ice,

00:04:22.885 --> 00:04:27.097
into the gas form of
water, or water vapor.

00:04:27.097 --> 00:04:29.745
And this will happen in
situations where it's cold

00:04:29.745 --> 00:04:32.218
and it's very, very, very, very dry.

00:04:32.218 --> 00:04:35.501
And you have, in general, low pressure.

00:04:35.501 --> 00:04:38.649
So instead of going into the liquid state,

00:04:38.649 --> 00:04:40.856
right then the water
molecules start just leaving

00:04:40.856 --> 00:04:42.106
as water vapor.

00:04:44.423 --> 00:04:46.149
And of course, I said, we're part of it.

00:04:46.149 --> 00:04:47.297
Well, how are we part of it?

00:04:47.297 --> 00:04:49.760
We will drink some of this fresh water,

00:04:49.760 --> 00:04:52.108
our bodies are actually mostly water.

00:04:52.108 --> 00:04:54.632
The cells in our bodies are 70% water.

00:04:54.632 --> 00:04:58.540
Everything we study in biology,
water is a key environment

00:04:58.540 --> 00:05:01.837
for all of these things to occur.

00:05:01.837 --> 00:05:03.587
And then we use that water,

00:05:03.587 --> 00:05:07.271
and then we will get that
water out of our body,

00:05:07.271 --> 00:05:11.749
and then it continues on as
part of this water cycle.

00:05:11.749 --> 00:05:13.717
Now one thing that I
find really interesting,

00:05:13.717 --> 00:05:17.576
as an organism that is
dependent on fresh water,

00:05:17.576 --> 00:05:18.576
when people say fresh water,

00:05:18.576 --> 00:05:19.935
we're talking about water without salt,

00:05:19.935 --> 00:05:21.768
as opposed to salt water.

00:05:21.768 --> 00:05:24.532
So we really need the
fresh water in this lake,

00:05:24.532 --> 00:05:27.490
or in this river, or we might dig wells,

00:05:27.490 --> 00:05:30.762
so that we can get the water
out of these aquifers.

00:05:30.762 --> 00:05:33.448
It actually turns out that
very little of the overall

00:05:33.448 --> 00:05:36.281
water in the world is fresh water.

00:05:37.767 --> 00:05:41.140
And so let me show you
this chart over here.

00:05:41.140 --> 00:05:43.370
I always knew that, but
I didn't fully appreciate

00:05:43.370 --> 00:05:45.583
how little was fresh water.

00:05:45.583 --> 00:05:47.987
So of all the water on our planet,

00:05:47.987 --> 00:05:52.740
97.5% is salt water, for the
most part, in our oceans.

00:05:52.740 --> 00:05:55.061
Only 2-1/2% is fresh water.

00:05:55.061 --> 00:05:58.822
And even of that 2-1/2% fresh water,

00:05:58.822 --> 00:06:01.428
very little of it is what
we traditionally associate

00:06:01.428 --> 00:06:03.303
fresh water, the lakes and the rivers.

00:06:03.303 --> 00:06:05.150
When I think of fresh
water, I'm gonna say oh,

00:06:05.150 --> 00:06:06.749
let me go to a lake or a river,

00:06:06.749 --> 00:06:08.633
that's stuff that we
could potentially drink.

00:06:08.633 --> 00:06:11.520
But most of it is actually in glaciers

00:06:11.520 --> 00:06:13.827
and permanent snow cover.

00:06:13.827 --> 00:06:17.494
So it's ice, snow, that
is just not melting.

00:06:18.899 --> 00:06:20.466
And it makes you think
about what would happen

00:06:20.466 --> 00:06:22.292
if this stuff were to melt.

00:06:22.292 --> 00:06:24.083
And then you also have ground water,

00:06:24.083 --> 00:06:25.456
which we could have access to.

00:06:25.456 --> 00:06:28.967
That's why people dig wells,
so we're talking about,

00:06:28.967 --> 00:06:31.724
well, ground water includes soil moisture,

00:06:31.724 --> 00:06:33.813
swamp water, and permafrost.

00:06:33.813 --> 00:06:37.637
Very little of the water is
actually in lakes and rivers,

00:06:37.637 --> 00:06:39.615
which I personally find fascinating.

00:06:39.615 --> 00:06:43.299
It wasn't obvious to me before
I, frankly, saw this chart.

00:06:43.299 --> 00:06:45.178
Now another really interesting thing is,

00:06:45.178 --> 00:06:48.294
how long, on average,
water molecules might stay

00:06:48.294 --> 00:06:50.747
in different parts of this water cycle.

00:06:50.747 --> 00:06:53.891
Going back here, you can
imagine that a water molecule

00:06:53.891 --> 00:06:56.862
can stay for a very
long time in the ocean,

00:06:56.862 --> 00:06:58.967
especially, you know it's
going to be moving around,

00:06:58.967 --> 00:07:01.744
depending on ocean
currents and temperature

00:07:01.744 --> 00:07:03.205
and all of that, but you can imagine,

00:07:03.205 --> 00:07:05.500
it could stay in that
liquid form in that ocean

00:07:05.500 --> 00:07:06.907
for a very long time.

00:07:06.907 --> 00:07:09.237
And maybe it spends a shorter
amount of time in a cloud.

00:07:09.237 --> 00:07:11.338
And people have actually studied this,

00:07:11.338 --> 00:07:12.631
which I find fascinating.

00:07:12.631 --> 00:07:14.643
I'd be curious to figure
out how they actually

00:07:14.643 --> 00:07:16.252
got this data.

00:07:16.252 --> 00:07:20.601
But this is the average residence
time for water molecules.

00:07:20.601 --> 00:07:24.896
And you can see here that
water can stay in glaciers

00:07:24.896 --> 00:07:27.266
and permafrost for a very long time,

00:07:27.266 --> 00:07:29.649
we're talking it could
be up to 10,000 years,

00:07:29.649 --> 00:07:31.002
and these are all rough numbers.

00:07:31.002 --> 00:07:33.560
It can stay as ground water
anywhere from two weeks,

00:07:33.560 --> 00:07:35.906
to 10,000 years, I guess,
depending on how isolated

00:07:35.906 --> 00:07:37.983
that ground water is.

00:07:37.983 --> 00:07:40.591
It could be in the oceans
and seas as salt water

00:07:40.591 --> 00:07:43.387
for 4,000 years, and we
can look at all of these,

00:07:43.387 --> 00:07:46.470
all the way, within living organisms,

00:07:47.374 --> 00:07:50.353
it'll stay about, on
average, a water molecule

00:07:50.353 --> 00:07:52.968
will last about a week in the atmosphere,

00:07:52.968 --> 00:07:55.860
so that's getting water
vapor, turning into a cloud,

00:07:55.860 --> 00:07:59.169
precipitating down, on
average, one and a half weeks.

00:07:59.169 --> 00:08:00.407
And once again, these are averages.

00:08:00.407 --> 00:08:01.946
It doesn't mean that every
water molecule will stay

00:08:01.946 --> 00:08:04.523
exactly one and half
weeks in the atmosphere,

00:08:04.523 --> 00:08:06.637
but it's a pretty interesting
thing to think about,

00:08:06.637 --> 00:08:08.578
and it gives you a
little bit more sense of,

00:08:08.578 --> 00:08:10.118
well, one, where all the water is,

00:08:10.118 --> 00:08:12.863
and how it all works together
with the water cycle.


Impedance of simple networks

WEBVTT
Kind: captions
Language: en

00:00:01.372 --> 00:00:02.582
- [Voiceover] Let's talk about the idea

00:00:02.582 --> 00:00:05.171
of the impedance of some simple networks.

00:00:05.171 --> 00:00:07.926
Now, what I've shown here
is a very simple network.

00:00:07.926 --> 00:00:11.571
It has two impedances
in it, Z one and Z two.

00:00:11.571 --> 00:00:13.648
And inside these boxes

00:00:13.648 --> 00:00:16.735
are one of our favorite
passive components,

00:00:16.735 --> 00:00:18.859
either an R, an L, or a C.

00:00:18.859 --> 00:00:20.587
That's what's in both of these things.

00:00:20.587 --> 00:00:21.420
We're gonna look at combinations of this

00:00:21.420 --> 00:00:23.543
and figure out what the impedance

00:00:23.543 --> 00:00:26.541
of simple combinations are.

00:00:26.541 --> 00:00:27.880
When we talk about impedance,

00:00:27.880 --> 00:00:29.456
what we mean is we take
sinusoidal signals.

00:00:29.456 --> 00:00:31.894
We take a sinusoidal voltage,

00:00:31.894 --> 00:00:35.582
and divide it by a sinusoidal current.

00:00:35.582 --> 00:00:39.104
And that is, that ratio is impedance.

00:00:39.104 --> 00:00:40.655
And so the voltage is impressed

00:00:40.655 --> 00:00:43.580
across the two terminals here,

00:00:43.580 --> 00:00:46.747
and then the current I flows this way.

00:00:48.290 --> 00:00:51.779
So this will be I, and this
will be plus or minus V

00:00:51.779 --> 00:00:53.612
between here and here.

00:00:55.437 --> 00:00:57.142
And the relationship
between those two things

00:00:57.142 --> 00:00:58.809
is called impedance.

00:01:02.568 --> 00:01:04.670
So now we have a circuit here

00:01:04.670 --> 00:01:07.701
with two impedances in it in series.

00:01:07.701 --> 00:01:10.353
They're connected in series
because they're head to tail.

00:01:10.353 --> 00:01:15.021
Now, if both of these
impedances were resistors,

00:01:15.021 --> 00:01:18.521
like this, if we just make them resistors,

00:01:20.754 --> 00:01:23.771
when we write down the
impedance of a resistor,

00:01:23.771 --> 00:01:27.673
we just write down R, the
impedance of a resistor is R.

00:01:27.673 --> 00:01:30.002
And the impedance of this one is R.

00:01:30.002 --> 00:01:33.568
So we'll call that one R two, and R one.

00:01:33.568 --> 00:01:36.372
And the overall, the effect of
impedance of the whole thing

00:01:36.372 --> 00:01:40.539
is resistors in series, we
know this, is R one plus R two.

00:01:41.980 --> 00:01:44.052
So nothing new here yet.

00:01:44.052 --> 00:01:47.496
Now let's make a little
change, let's do this.

00:01:47.496 --> 00:01:49.020
Let's make a network that looks

00:01:49.020 --> 00:01:51.687
like a resistor and a capacitor.

00:01:57.004 --> 00:01:59.216
And I want to know the
voltage to current ratio,

00:01:59.216 --> 00:02:00.707
or I want to know the impedance,

00:02:00.707 --> 00:02:02.915
the effective impedance of this.

00:02:02.915 --> 00:02:04.653
So we transform the circuit,

00:02:04.653 --> 00:02:06.845
we write down, this value is R.

00:02:06.845 --> 00:02:11.012
And the impedance of a
capacitor is one over J Omega C.

00:02:15.592 --> 00:02:18.581
And if I want to, I can write
it exactly the same way,

00:02:18.581 --> 00:02:22.748
I could say that is equal to
minus J times one over Omega C.

00:02:24.613 --> 00:02:28.303
Remember, one over J
is the same as minus J.

00:02:28.303 --> 00:02:32.470
So, if I want to know the
impedance of this network here,

00:02:35.239 --> 00:02:37.830
Z is, now, this is the great trick

00:02:37.830 --> 00:02:39.771
of doing this transformation.

00:02:39.771 --> 00:02:42.873
We can use the same laws
that we know for resistors

00:02:42.873 --> 00:02:44.779
on this transformed circuit.

00:02:44.779 --> 00:02:48.145
We transformed it into
the frequency domain.

00:02:48.145 --> 00:02:50.692
So this series combination
of two impedances

00:02:50.692 --> 00:02:53.160
is the sum of the impedances.

00:02:53.160 --> 00:02:55.327
R plus one over J Omega C.

00:03:00.241 --> 00:03:03.824
This is the impedance
of this network here.

00:03:07.185 --> 00:03:09.712
Let's do another one, let's
do an inductor combination.

00:03:09.712 --> 00:03:13.045
So, we'll do a resistor and an inductor.

00:03:18.522 --> 00:03:21.721
Like that, so the impedance
of a resistor is R,

00:03:21.721 --> 00:03:25.221
the impedance of an inductor is J Omega L.

00:03:27.756 --> 00:03:29.687
And I can write the
combined impedance of this,

00:03:29.687 --> 00:03:32.310
the same thing, it's a series impedance.

00:03:32.310 --> 00:03:34.727
So I can do R plus J Omega L.

00:03:40.288 --> 00:03:43.675
Now what I want to do next is
introduce some new terminology

00:03:43.675 --> 00:03:46.144
that we talk about impedances with.

00:03:46.144 --> 00:03:48.094
So let's look at these
two examples down here,

00:03:48.094 --> 00:03:50.103
for the capacitor and the inductor.

00:03:50.103 --> 00:03:53.270
R's a real number, one over J Omega C,

00:03:54.689 --> 00:03:57.185
that's a imaginary number,

00:03:57.185 --> 00:03:59.993
and together they make a complex number.

00:03:59.993 --> 00:04:02.157
And over here with the
inductor, we see the same thing,

00:04:02.157 --> 00:04:04.595
a real part and an imaginary part.

00:04:04.595 --> 00:04:06.806
So the way we write an
impedance in general,

00:04:06.806 --> 00:04:09.027
as a rectangular complex number,

00:04:09.027 --> 00:04:11.194
is we say Z equals R plus,

00:04:15.634 --> 00:04:18.361
and the letter we use is X.

00:04:18.361 --> 00:04:20.444
Now, R is the resistance,

00:04:25.003 --> 00:04:28.836
and X, the name for X
in general is reactance.

00:04:34.939 --> 00:04:36.998
X is the imaginary part of an impedance,

00:04:36.998 --> 00:04:39.771
and that's referred to as the reactance.

00:04:39.771 --> 00:04:43.489
We also talked about the
inverse of a resistance.

00:04:43.489 --> 00:04:46.989
One over resistance is called conductance.

00:04:53.163 --> 00:04:54.663
That's one over R.

00:04:58.788 --> 00:05:02.538
And one over X is referred
to as susceptance.

00:05:13.539 --> 00:05:14.665
Now these are all just words that,

00:05:14.665 --> 00:05:16.980
they all sound like they
sort of mean the same thing,

00:05:16.980 --> 00:05:19.281
but engineers wanted to have,
sort of, different words

00:05:19.281 --> 00:05:21.767
for different parts of the impedance.

00:05:21.767 --> 00:05:24.114
And these are the words that we use.

00:05:24.114 --> 00:05:26.461
And finally, we have
another word for the inverse

00:05:26.461 --> 00:05:30.192
of impedance, the general
idea of one over Z,

00:05:30.192 --> 00:05:33.118
and that's referred to as admittance.

00:05:33.118 --> 00:05:34.785
Ad, mit, admittance.

00:05:40.023 --> 00:05:41.285
This is our little vocabulary,

00:05:41.285 --> 00:05:44.088
we have admittance is the
opposite of impedance,

00:05:44.088 --> 00:05:46.008
or the inverse of impedance.

00:05:46.008 --> 00:05:49.984
Susceptance is the inverse of reactance.

00:05:49.984 --> 00:05:53.384
And conductance is the
inverse of resistance.

00:05:53.384 --> 00:05:56.493
These are all just, sort of,
every word we can think of

00:05:56.493 --> 00:05:59.326
that meant resist and let through.

00:06:04.068 --> 00:06:05.625
So now I'm gonna roll
up here a little bit,

00:06:05.625 --> 00:06:07.027
and we'll do some plots.

00:06:07.027 --> 00:06:11.194
We'll look more carefully at
these impedance expressions.

00:06:13.990 --> 00:06:16.109
So if these are all complex numbers,

00:06:16.109 --> 00:06:19.387
that means I can plot
them on a complex plane.

00:06:19.387 --> 00:06:22.356
So let's do that and see what it tells us,

00:06:22.356 --> 00:06:24.976
see if we can learn anything.

00:06:24.976 --> 00:06:29.059
Okay, this is the real
and this is the imaginary.

00:06:30.004 --> 00:06:32.338
Now, for resistance to resistors,

00:06:32.338 --> 00:06:33.801
we just have two real parts.

00:06:33.801 --> 00:06:36.454
So there's some Z that's
the sum of two R's,

00:06:36.454 --> 00:06:38.008
and that's a real number.

00:06:38.008 --> 00:06:40.429
So I would just get a,

00:06:40.429 --> 00:06:43.762
some sort of value like here, like that.

00:06:45.139 --> 00:06:47.225
I'd add those two vectors together,

00:06:47.225 --> 00:06:48.892
and that would be Z.

00:06:51.430 --> 00:06:54.356
So let's do that for
the other circuit now.

00:06:54.356 --> 00:06:57.606
If I do it for capacitance, RC circuit,

00:06:59.629 --> 00:07:02.879
the one resistor is out here like this,

00:07:04.035 --> 00:07:05.702
that's a value of R.

00:07:06.577 --> 00:07:08.484
And C, how do we plot C?

00:07:08.484 --> 00:07:11.776
Well, C, remember, is one over J Omega C

00:07:11.776 --> 00:07:15.859
is the same as negative
J times one over Omega C.

00:07:17.183 --> 00:07:20.796
So that's gonna give us a negative J.

00:07:20.796 --> 00:07:23.753
It's gonna give us a line
on the negative J axis.

00:07:23.753 --> 00:07:26.086
Here it is, real, imaginary.

00:07:27.562 --> 00:07:32.164
And Z is gonna be, this
value here, right there,

00:07:32.164 --> 00:07:35.664
has a magnitude of one over J Omega, oops.

00:07:38.930 --> 00:07:40.941
This point right here has a magnitude.

00:07:40.941 --> 00:07:45.005
The length of that vector
is one over Omega C.

00:07:45.005 --> 00:07:48.817
And that point right there,
when we do the vector add,

00:07:48.817 --> 00:07:50.585
that'll be Z right there.

00:07:50.585 --> 00:07:53.085
Dat, dat, dat, dah, like that.

00:07:54.393 --> 00:07:55.976
And let's do the L.

00:07:56.921 --> 00:08:01.048
Let's plot the circuit
that has an L in it.

00:08:01.048 --> 00:08:03.977
Okay, again we have an R,
so we go out some distance.

00:08:03.977 --> 00:08:05.144
R right there.

00:08:09.126 --> 00:08:11.657
And now J Omega L, we
have a positive J here,

00:08:11.657 --> 00:08:13.668
so it goes up by Omega L.

00:08:13.668 --> 00:08:16.093
So let's say L was kind of small.

00:08:16.093 --> 00:08:17.404
Let's say it goes right there.

00:08:17.404 --> 00:08:21.571
So that has a magnitude of
Omega L on the imaginary axis.

00:08:25.143 --> 00:08:29.310
And that'll give us a point,
that'll be Z for that network.

00:08:33.106 --> 00:08:36.310
Now you notice as, let's
say we change Omega.

00:08:36.310 --> 00:08:38.017
Let's say Omega is varying.

00:08:38.017 --> 00:08:41.478
Omega goes up, in this
case here, Omega goes up.

00:08:41.478 --> 00:08:43.703
This point will travel up.

00:08:43.703 --> 00:08:47.678
It'll move in the complex
plain if Omega changes.

00:08:47.678 --> 00:08:49.502
This one, if Omega changes,

00:08:49.502 --> 00:08:52.328
if Omega gets bigger for a capacitor,

00:08:52.328 --> 00:08:54.675
if Omega gets bigger for a capacitor,

00:08:54.675 --> 00:08:57.143
that means this number gets smaller,

00:08:57.143 --> 00:09:00.226
and this will move in this direction.

00:09:02.501 --> 00:09:05.303
And on the resistor
side, if Omega changes,

00:09:05.303 --> 00:09:07.233
well, there's no Omega term here.

00:09:07.233 --> 00:09:09.857
So nothing changes when Omega changes

00:09:09.857 --> 00:09:11.989
in this resistor picture.

00:09:11.989 --> 00:09:15.237
So, this shows us what
happens in a graphical way

00:09:15.237 --> 00:09:20.099
when we change the frequency
of a complex impedance.

00:09:20.099 --> 00:09:22.266
Now I want to do one more.

00:09:23.194 --> 00:09:25.236
Let's do a circuit that looks like this,

00:09:25.236 --> 00:09:27.200
let's do three things.

00:09:27.200 --> 00:09:28.033
Let's do

00:09:31.009 --> 00:09:35.176
an inductor, a resistor, and
a capacitor, all in series.

00:09:38.585 --> 00:09:39.752
And what is C?

00:09:42.468 --> 00:09:44.053
So, we label it as we did before,

00:09:44.053 --> 00:09:46.803
J Omega L, R, one over J Omega C.

00:09:50.257 --> 00:09:52.707
So let's now work out
the impedance of this.

00:09:52.707 --> 00:09:55.299
It's a series circuit,
so the impedances add.

00:09:55.299 --> 00:09:58.966
So we can say that Z
equals J Omega L plus R

00:10:04.185 --> 00:10:06.185
plus one over J Omega C.

00:10:09.517 --> 00:10:12.657
So we can try a plot of these things.

00:10:12.657 --> 00:10:15.824
Here's the real, here's the imaginary.

00:10:18.086 --> 00:10:19.074
Let's do R first.

00:10:19.074 --> 00:10:23.241
R is always on the real
axis, some value like that.

00:10:25.553 --> 00:10:28.220
J Omega L goes up by some value.

00:10:29.332 --> 00:10:32.999
Here's the inductor
represented as a vector.

00:10:34.770 --> 00:10:36.688
And here's one over J Omega C

00:10:36.688 --> 00:10:39.237
that goes down on the axis like that,

00:10:39.237 --> 00:10:42.132
so it's gonna come down
here somehow like this.

00:10:42.132 --> 00:10:44.460
Let's make the capacitor small,

00:10:44.460 --> 00:10:47.872
which makes it's impedance large.

00:10:47.872 --> 00:10:51.372
The magnitude of that is one over Omega C,

00:10:52.340 --> 00:10:54.610
and when we put all these together,

00:10:54.610 --> 00:10:58.267
we do, basically, we do a
vector add of these guys here.

00:10:58.267 --> 00:11:01.253
So I can, let's move
the L over here, let's,

00:11:01.253 --> 00:11:05.033
L goes up like that,
there's a vector add of L.

00:11:05.033 --> 00:11:07.823
And then I have a vector
add of this vector here,

00:11:07.823 --> 00:11:10.823
adds onto that, back down like that,

00:11:11.724 --> 00:11:15.391
and the final answer
is this guy right here.

00:11:19.679 --> 00:11:23.031
And this is Z for this network right here,

00:11:23.031 --> 00:11:26.274
is that complex number right there.

00:11:26.274 --> 00:11:31.255
And you see, as we change
Omega, different things happen,

00:11:31.255 --> 00:11:34.242
and we can basically
move this point around.

00:11:34.242 --> 00:11:36.501
Moving this point around with frequency

00:11:36.501 --> 00:11:40.616
is basically the essence of AC analysis.

00:11:40.616 --> 00:11:42.616
We'll see you next time.


KVL in the frequency domain

WEBVTT
Kind: captions
Language: en

00:00:00.206 --> 00:00:01.518
- [Voiceover] As we do AC analysis,

00:00:01.518 --> 00:00:04.223
and we do operations in
the frequency domain,

00:00:04.223 --> 00:00:06.453
we need to bring along Kirchhoff's Laws

00:00:06.453 --> 00:00:08.995
so that we can make sense of circuits.

00:00:08.995 --> 00:00:11.120
So, in this video, I'm
gonna basically show

00:00:11.120 --> 00:00:13.453
that Kirchhoff's Voltage Law works

00:00:13.453 --> 00:00:15.590
in the frequency domain.

00:00:15.590 --> 00:00:16.820
And what I have here is a circuit

00:00:16.820 --> 00:00:19.728
that has some voltage
source, an AC voltage source,

00:00:19.728 --> 00:00:22.394
let's put AC on it like that,

00:00:22.394 --> 00:00:25.005
and it has three impedances connected.

00:00:25.005 --> 00:00:29.313
Inside each of these boxes
is an R, an L, or a C,

00:00:29.313 --> 00:00:30.710
and we're not gonna show which

00:00:30.710 --> 00:00:32.278
because we're gonna carry these along

00:00:32.278 --> 00:00:35.350
just as general impedances.

00:00:35.350 --> 00:00:39.820
So, in AC analysis, the
voltages are all cosine waves.

00:00:39.820 --> 00:00:41.070
So, v-in equals

00:00:44.173 --> 00:00:46.840
some voltage amplitude times cos

00:00:48.562 --> 00:00:49.812
of omega-t plus

00:00:52.091 --> 00:00:54.008
we'll call it phi-zero,

00:00:56.042 --> 00:00:58.187
some starting phase shift.

00:00:58.187 --> 00:00:59.512
So, this is our input signal.

00:00:59.512 --> 00:01:01.464
Now let me label the
voltages on everything else.

00:01:01.464 --> 00:01:03.297
We'll call this v-one,

00:01:04.227 --> 00:01:07.643
and I'm gonna label it this way, here,

00:01:07.643 --> 00:01:09.560
and this will be v-two,

00:01:10.996 --> 00:01:13.980
and I'll put it upside-down
like that, the plus,

00:01:13.980 --> 00:01:15.860
and this will be v-three,

00:01:15.860 --> 00:01:17.610
minus, plus, v-three.

00:01:20.621 --> 00:01:23.198
And, oh, now that I have v-one here,

00:01:23.198 --> 00:01:25.160
let's change the name of this to v-zero

00:01:25.160 --> 00:01:27.645
just so I don't get i and one mixed up.

00:01:27.645 --> 00:01:29.316
So, we'll change that to zero.

00:01:29.316 --> 00:01:31.789
So, the input source is v-zero,

00:01:31.789 --> 00:01:34.367
and that's that voltage.

00:01:34.367 --> 00:01:38.419
Now, when we apply KVL to
this, Kirchhoff's Voltage Law,

00:01:38.419 --> 00:01:40.253
what it says is if we start in a corner,

00:01:40.253 --> 00:01:41.344
if we start somewhere in the circuit,

00:01:41.344 --> 00:01:42.981
let's start right here,

00:01:42.981 --> 00:01:46.012
and go around the loop,
it should add up to

00:01:46.012 --> 00:01:46.958
zero volts.

00:01:46.958 --> 00:01:49.785
That's KVL for normal DC circuits,

00:01:49.785 --> 00:01:53.025
and we're gonna see how that
applies to AC circuits, here.

00:01:53.025 --> 00:01:56.100
So in time domain, we say that v-zero

00:01:56.100 --> 00:01:57.850
plus v-one plus v-two

00:02:00.416 --> 00:02:02.499
plus v-three equals zero.

00:02:04.297 --> 00:02:06.108
So, let's talk about how
this is gonna turn out.

00:02:06.108 --> 00:02:07.873
Well, what do we know right now?

00:02:07.873 --> 00:02:10.822
Well, we know that v-zero is a cosine wave

00:02:10.822 --> 00:02:12.877
at some phase angle.

00:02:12.877 --> 00:02:16.952
Now, what do we know about
the other voltages in this?

00:02:16.952 --> 00:02:18.682
In AC analysis, what we're
doing is we're looking

00:02:18.682 --> 00:02:20.157
for a forced response.

00:02:20.157 --> 00:02:23.059
So, we've let the natural
responses to die out.

00:02:23.059 --> 00:02:24.522
There's no switch in this circuit,

00:02:24.522 --> 00:02:26.298
and we just assume this circuit has been

00:02:26.298 --> 00:02:28.237
in this state forever.

00:02:28.237 --> 00:02:30.320
So, the natural response,

00:02:33.160 --> 00:02:35.993
the natural response has died out,

00:02:39.406 --> 00:02:43.573
and that means we're looking
for the forced response.

00:02:47.208 --> 00:02:49.251
So, what we know is,
we have three voltages.

00:02:49.251 --> 00:02:51.168
We have three voltages.

00:02:56.089 --> 00:02:58.295
We know that all these voltages

00:02:58.295 --> 00:03:01.128
are gonna resemble the input voltage.

00:03:01.128 --> 00:03:04.045
So, they're all gonna be sinusoids.

00:03:09.812 --> 00:03:12.959
All the voltages here
are gonna be AC sinusoids

00:03:12.959 --> 00:03:16.976
because the forcing
function is a sinusoid.

00:03:16.976 --> 00:03:20.154
The other thing we know, they're gonna all

00:03:20.154 --> 00:03:21.821
have the same omega.

00:03:25.614 --> 00:03:27.761
The frequency of this
voltage, and this voltage,

00:03:27.761 --> 00:03:31.337
and this voltage is gonna
be identical to omega, here.

00:03:31.337 --> 00:03:34.333
I'm gonna put a big bang there.

00:03:34.333 --> 00:03:35.946
That's really important.

00:03:35.946 --> 00:03:37.711
In an AC circuit, when you're driving it

00:03:37.711 --> 00:03:41.322
from a frequency, every
other frequency in the system

00:03:41.322 --> 00:03:43.155
is the same frequency.

00:03:44.433 --> 00:03:47.487
This is a linear system
and linear components.

00:03:47.487 --> 00:03:49.933
All the analysis we've done,

00:03:49.933 --> 00:03:52.967
linear components don't
create new frequencies.

00:03:52.967 --> 00:03:55.242
They're all omega.

00:03:55.242 --> 00:03:57.123
Now, some other things we know.

00:03:57.123 --> 00:03:58.806
There's gonna be phase
shifts involved here.

00:03:58.806 --> 00:04:00.037
Remember when we do impedance,

00:04:00.037 --> 00:04:04.516
we are multiplying by j and
rotating things by 90 degrees.

00:04:04.516 --> 00:04:07.099
So, we're gonna have different,

00:04:09.557 --> 00:04:11.890
different phi, for each one.

00:04:13.783 --> 00:04:15.095
And, the other thing we're gonna have,

00:04:15.095 --> 00:04:17.762
is we're gonna have different...

00:04:20.517 --> 00:04:22.433
The amplitude of our sinusoids
are gonna be different.

00:04:22.433 --> 00:04:25.022
The amplitude of v-one could be different

00:04:25.022 --> 00:04:27.077
than the amplitude of v-two.

00:04:27.077 --> 00:04:29.631
So, this is what an AC
solution is going to look like.

00:04:29.631 --> 00:04:31.997
Let's move on a little farther here.

00:04:31.997 --> 00:04:33.660
What I'm gonna do now is we're gonna take

00:04:33.660 --> 00:04:36.980
this input voltage plus these
things that we know, here,

00:04:36.980 --> 00:04:39.689
and we're gonna see how
Kirchhoff's Voltage Law works

00:04:39.689 --> 00:04:40.881
in the frequency domain,

00:04:40.881 --> 00:04:45.026
when we worked with these
transformed z's, these impedances.

00:04:45.026 --> 00:04:47.776
Okay, let's go ahead and do that.

00:04:49.287 --> 00:04:53.287
Okay, let's do a little
more in the time domain.

00:04:56.880 --> 00:04:58.935
And we'll write out
our KVL equation again.

00:04:58.935 --> 00:05:01.768
So, the KVL equation was v-naught,

00:05:02.836 --> 00:05:05.169
cosine omega-t plus phi-zero

00:05:08.524 --> 00:05:12.024
plus v-one, that's the amplitude of v-one,

00:05:13.610 --> 00:05:14.777
cosine omega-t

00:05:16.675 --> 00:05:19.426
plus some different phase angle.

00:05:19.426 --> 00:05:21.539
We don't know what that is yet.

00:05:21.539 --> 00:05:24.206
Plus, v-two, amplitude of v-two,

00:05:27.216 --> 00:05:28.383
cosine omega-t

00:05:30.525 --> 00:05:31.692
plus phi-three

00:05:34.426 --> 00:05:37.676
plus v-three, the amplitude of v-three,

00:05:39.291 --> 00:05:41.708
cosine omega-t plus phi-three

00:05:44.562 --> 00:05:45.895
all equals zero.

00:05:47.174 --> 00:05:50.494
And omega, all these omegas,
are the same exact number,

00:05:50.494 --> 00:05:52.294
the same radian frequency.

00:05:52.294 --> 00:05:53.687
All the phi's are different,

00:05:53.687 --> 00:05:57.054
and all the v-twos and
v-threes are different.

00:05:57.054 --> 00:05:58.947
Okay, now I'm gonna switch

00:05:58.947 --> 00:06:01.614
to complex exponential notation.

00:06:09.860 --> 00:06:11.381
We just changing notation here.

00:06:11.381 --> 00:06:13.308
We can represent this number here

00:06:13.308 --> 00:06:15.308
as this is the real part

00:06:16.315 --> 00:06:17.982
of v-naught, v-zero,

00:06:20.498 --> 00:06:21.331
e to the j

00:06:22.878 --> 00:06:23.961
times omega-t

00:06:25.229 --> 00:06:26.396
plus phi-zero.

00:06:30.605 --> 00:06:31.719
That's exactly the same as this.

00:06:31.719 --> 00:06:33.809
This cosine can be represented

00:06:33.809 --> 00:06:37.652
as the real part of a complex exponential

00:06:37.652 --> 00:06:39.319
with this frequency.

00:06:40.601 --> 00:06:43.851
And, I can write out the rest of these.

00:06:47.416 --> 00:06:48.833
V-one, e to the j

00:06:51.839 --> 00:06:53.506
omega-t plus phi-one

00:06:56.193 --> 00:06:57.943
plus the real part of

00:07:00.791 --> 00:07:02.958
v-two, e to the j-omega-t,

00:07:06.677 --> 00:07:08.844
plus phi-two, parentheses,

00:07:11.045 --> 00:07:12.128
plus v-three,

00:07:15.078 --> 00:07:15.911
oops,

00:07:19.425 --> 00:07:20.425
real part of

00:07:23.546 --> 00:07:24.379
v-three,

00:07:25.746 --> 00:07:27.246
e to the j-omega-t

00:07:29.245 --> 00:07:30.412
plus phi-three

00:07:35.191 --> 00:07:36.191
equals zero.

00:07:41.542 --> 00:07:43.666
All right, now, one thing I can do next,

00:07:43.666 --> 00:07:44.525
we can start to factor this.

00:07:44.525 --> 00:07:47.056
We can start to take
this apart a little bit.

00:07:47.056 --> 00:07:49.924
So, I know that if I have the expression,

00:07:49.924 --> 00:07:50.999
if I have the expression,

00:07:50.999 --> 00:07:52.499
e to the j-omega-t

00:07:56.264 --> 00:07:58.283
plus phi, just in general,

00:07:58.283 --> 00:08:01.035
I can change that just
by exponent properties

00:08:01.035 --> 00:08:05.202
to e to the j-phi, let's get
the parentheses in there,

00:08:06.333 --> 00:08:07.838
like that,

00:08:07.838 --> 00:08:11.171
e to the j-phi times e to the j-omega-t.

00:08:12.889 --> 00:08:14.444
So, I'm gonna do this transformation

00:08:14.444 --> 00:08:16.940
on all four of these terms here.

00:08:16.940 --> 00:08:18.357
Let's keep going.

00:08:22.304 --> 00:08:23.137
So, we're still working on this.

00:08:23.137 --> 00:08:25.625
Let's go real part...

00:08:25.625 --> 00:08:28.330
Now I'm gonna take apart omega-t

00:08:28.330 --> 00:08:30.385
and phi-zero, here,

00:08:30.385 --> 00:08:31.885
and I get v-naught

00:08:33.868 --> 00:08:35.535
e to the j-phi-zero,

00:08:38.152 --> 00:08:39.735
e to the j-omega-t,

00:08:41.879 --> 00:08:43.129
plus real part,

00:08:46.378 --> 00:08:47.422
v-one,

00:08:47.422 --> 00:08:49.005
e to the j-phi-one,

00:08:51.844 --> 00:08:53.427
e to the j-omega-t,

00:08:55.121 --> 00:08:56.954
plus real part, v-two,

00:08:59.985 --> 00:09:01.568
e to the j-phi-two,

00:09:04.734 --> 00:09:06.817
times e to the j-omega-t,

00:09:09.724 --> 00:09:10.891
plus real part

00:09:14.153 --> 00:09:16.653
v-three, e to the j-phi-three,

00:09:19.964 --> 00:09:21.464
e to the j-omega-t

00:09:23.180 --> 00:09:24.513
all equals zero.

00:09:28.242 --> 00:09:31.203
And here's a nice simplification,

00:09:31.203 --> 00:09:32.921
we take out this common term.

00:09:32.921 --> 00:09:35.649
We're gonna factor out this common term

00:09:35.649 --> 00:09:38.714
across the entire equation.

00:09:38.714 --> 00:09:39.655
And what do we come up with?

00:09:39.655 --> 00:09:41.155
We come up with...

00:09:42.464 --> 00:09:44.964
The result is the real part of

00:09:46.783 --> 00:09:47.616
v-zero,

00:09:48.524 --> 00:09:50.191
e to the j-phi-zero,

00:09:52.832 --> 00:09:53.665
plus v-one

00:09:57.012 --> 00:09:58.512
e to the j-phi-one

00:10:00.123 --> 00:10:02.706
plus v-two, e to the j-phi-two.

00:10:06.265 --> 00:10:07.598
See the pattern.

00:10:13.636 --> 00:10:14.803
All that times

00:10:18.019 --> 00:10:19.602
e to the j-omega-t.

00:10:21.741 --> 00:10:24.609
And we close that and that equals zero.

00:10:24.609 --> 00:10:25.514
Now, we're getting close.

00:10:25.514 --> 00:10:27.523
We're getting close.

00:10:27.523 --> 00:10:30.808
All right, how do we
make this equation zero?

00:10:30.808 --> 00:10:34.317
Does e to the j-omega-t ever become zero?

00:10:34.317 --> 00:10:36.317
Well, e to the j-omega-t

00:10:38.877 --> 00:10:41.536
e to the j-omega-t is a rotating vector.

00:10:41.536 --> 00:10:42.869
It's never zero.

00:10:45.716 --> 00:10:46.946
So, that's not gonna do it.

00:10:46.946 --> 00:10:47.779
So, how do we get it?

00:10:47.779 --> 00:10:49.686
Well, that means that
this other term, here,

00:10:49.686 --> 00:10:52.101
has to be equal to zero.

00:10:52.101 --> 00:10:53.611
So, how am I gonna do that?

00:10:53.611 --> 00:10:56.362
I'm gonna make one more notational change.

00:10:56.362 --> 00:10:58.695
This kind of a number, here,

00:10:59.842 --> 00:11:01.425
is called a phasor.

00:11:04.760 --> 00:11:07.309
It's some amplitude times e

00:11:07.309 --> 00:11:09.689
to a complex one angle,

00:11:09.689 --> 00:11:11.163
and there's no time up here.

00:11:11.163 --> 00:11:12.278
There's no time.

00:11:12.278 --> 00:11:14.495
The time is only over here.

00:11:14.495 --> 00:11:17.131
This is the only place that
time appears in the equation,

00:11:17.131 --> 00:11:19.088
and this is the only
place that omega appears

00:11:19.088 --> 00:11:21.758
in the equation, and these
are just phase angles,

00:11:21.758 --> 00:11:23.593
these are starting phase angles.

00:11:23.593 --> 00:11:27.041
So, my notation for a
phasor is gonna be...

00:11:27.041 --> 00:11:28.016
This gonna be called...

00:11:28.016 --> 00:11:31.302
I'm gonna call it v-zero and
I'm gonna put a line over it

00:11:31.302 --> 00:11:33.891
to indicate that it's a complex vector,

00:11:33.891 --> 00:11:35.141
and that equals

00:11:36.951 --> 00:11:38.317
v-naught,

00:11:38.317 --> 00:11:40.150
e to the j-phi-naught.

00:11:42.761 --> 00:11:46.615
So, when you see the vector
symbol and the aught,

00:11:46.615 --> 00:11:48.615
that's that right there.

00:11:56.376 --> 00:11:58.876
And we can write now, finally,

00:12:00.261 --> 00:12:01.594
the real part of

00:12:04.526 --> 00:12:05.950
V-naught

00:12:05.950 --> 00:12:07.367
plus V-one phasor

00:12:10.377 --> 00:12:11.794
plus V-two phasor

00:12:13.605 --> 00:12:15.188
plus V-three phasor

00:12:18.504 --> 00:12:19.504
equals zero.

00:12:21.744 --> 00:12:25.077
So, this is KVL in the frequency domain.

00:12:34.548 --> 00:12:36.848
And fortunately, it looks like...

00:12:36.848 --> 00:12:39.302
It looks exactly like KVL that we remember

00:12:39.302 --> 00:12:41.028
from our DC analysis.

00:12:41.028 --> 00:12:43.826
The sum of the voltages,
going around the loop,

00:12:43.826 --> 00:12:45.869
is equal to zero, and, in this case,

00:12:45.869 --> 00:12:48.586
it's the sum of the phasors
going around the loop

00:12:48.586 --> 00:12:50.003
is equal to zero.

00:12:51.121 --> 00:12:55.288
Let's try to give a graphical
interpretation to this.

00:13:01.659 --> 00:13:05.914
Here's our real and imaginary
plane, the complex plane,

00:13:05.914 --> 00:13:09.112
and what it says is that these phasors...

00:13:09.112 --> 00:13:10.201
So, let's say that v-naught,

00:13:10.201 --> 00:13:13.745
let's say that v-naught look like that.

00:13:13.745 --> 00:13:15.869
That was our voltage source, okay.

00:13:15.869 --> 00:13:17.544
This represents a vector spinning around

00:13:17.544 --> 00:13:19.860
at the frequency, omega,

00:13:19.860 --> 00:13:24.484
and it's offset phase is
this angle right here.

00:13:24.484 --> 00:13:26.234
So, this is phi-zero.

00:13:29.360 --> 00:13:31.664
Each of these other
components is gonna have

00:13:31.664 --> 00:13:34.422
an AC voltage, a sinusoidal voltage on it,

00:13:34.422 --> 00:13:36.918
with some phase and some magnitude,

00:13:36.918 --> 00:13:38.691
and what KVL tells us,

00:13:38.691 --> 00:13:42.444
it puts a constraint on
what those voltages can be.

00:13:42.444 --> 00:13:43.919
So, we have three impedances here.

00:13:43.919 --> 00:13:44.894
I don't know what they are

00:13:44.894 --> 00:13:46.415
because we didn't fill in the circuit,

00:13:46.415 --> 00:13:48.737
but there's gonna be some vector

00:13:48.737 --> 00:13:50.258
associated with each one of those.

00:13:50.258 --> 00:13:52.789
Let's say that's vector-one,

00:13:52.789 --> 00:13:55.956
and let's say that this is vector-two,

00:13:58.420 --> 00:14:00.707
and what it says is that vector-three,

00:14:00.707 --> 00:14:02.709
by the time we get done,

00:14:02.709 --> 00:14:05.792
vector-three has to sum back to zero.

00:14:09.519 --> 00:14:10.831
So, this kind of a constraint

00:14:10.831 --> 00:14:14.476
where voltage is going around in a circle,

00:14:14.476 --> 00:14:15.997
have to come back to zero,

00:14:15.997 --> 00:14:18.459
that's KVL and the frequency domain.

00:14:18.459 --> 00:14:20.711
That's what that means.

00:14:20.711 --> 00:14:23.335
So, we've shown that KVL
works in the frequency domain.

00:14:23.335 --> 00:14:24.322
I could do a similar analysis

00:14:24.322 --> 00:14:27.352
and show that KCL,
Kirchhoff's Current Law,

00:14:27.352 --> 00:14:29.964
also works in the frequency domain,

00:14:29.964 --> 00:14:32.135
and that means, fantastically,

00:14:32.135 --> 00:14:34.144
that all the tools that we developed

00:14:34.144 --> 00:14:37.490
for DC analysis of just resistor circuits,

00:14:37.490 --> 00:14:41.412
all those tools work
for AC analysis as well.

00:14:41.412 --> 00:14:42.563
Thanks for listening.


Flow of energy and matter through ecosystem

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:03.779
- [Voiceover] Let's think a
little bit how energy flows,

00:00:03.779 --> 00:00:07.362
and how matter is
recycled in an ecosystem.

00:00:08.342 --> 00:00:11.099
And so the whole time that
we go through this video,

00:00:11.099 --> 00:00:12.829
think about these two ideas.

00:00:12.829 --> 00:00:14.268
And even after watching this video,

00:00:14.268 --> 00:00:15.789
look at ecosystems around yourself,

00:00:15.789 --> 00:00:17.182
even ones that you're a part of

00:00:17.182 --> 00:00:20.967
and think about how energy
flows and how matter's recycled.

00:00:20.967 --> 00:00:23.394
Let's first think about energy.

00:00:23.394 --> 00:00:26.180
The energy for most ecosystems

00:00:26.180 --> 00:00:28.282
originally comes from the Sun.

00:00:28.282 --> 00:00:29.559
There are other sources of energy,

00:00:29.559 --> 00:00:31.579
you could think about even moonlight,

00:00:31.579 --> 00:00:34.133
but that essentially comes from the Sun.

00:00:34.133 --> 00:00:36.245
But there's also geothermal energy,

00:00:36.245 --> 00:00:39.740
but the Sun is a source of
most energy for most ecosystems

00:00:39.740 --> 00:00:41.145
we could think of.

00:00:41.145 --> 00:00:43.618
And how does the ecosystem
make use of that energy?

00:00:43.618 --> 00:00:45.057
How does it get into,

00:00:45.057 --> 00:00:47.077
how does it that get
stored within the ecosystem

00:00:47.077 --> 00:00:49.040
especially as biomass?

00:00:49.040 --> 00:00:51.303
Well, it starts with primary producers

00:00:51.303 --> 00:00:52.952
which are usually going to be plants.

00:00:52.952 --> 00:00:57.119
They can also be bacteria that
are able to photosynthesize,

00:00:58.752 --> 00:01:01.735
or that are able to take that
energy and create biomolecules

00:01:01.735 --> 00:01:03.743
that store energy from it.

00:01:03.743 --> 00:01:06.660
And so these are primary producers,

00:01:07.943 --> 00:01:10.857
these plants in this diagram.

00:01:10.857 --> 00:01:13.980
Sometimes you'll see them
referred to as autotrophs.

00:01:13.980 --> 00:01:18.160
They are getting their
own food from the Sun,

00:01:18.160 --> 00:01:19.577
from this energy.

00:01:20.424 --> 00:01:23.094
And once again, how is that energy stored?

00:01:23.094 --> 00:01:25.637
Well, it's stored in these
biological molecules.

00:01:25.637 --> 00:01:28.806
If you were to zoom in into
the molecules in this plant,

00:01:28.806 --> 00:01:30.490
and this is a huge oversimplification,

00:01:30.490 --> 00:01:34.321
you'll see all these bonds
between these carbons.

00:01:34.321 --> 00:01:37.072
And to make those bonds requires energy

00:01:37.072 --> 00:01:39.174
and if you were to break those bonds

00:01:39.174 --> 00:01:41.473
it could release energy.

00:01:41.473 --> 00:01:42.306
And you might say, well,

00:01:42.306 --> 00:01:45.919
where did all these carbons
come from that are in this tree?

00:01:45.919 --> 00:01:48.137
Well, the carbon is coming from the air.

00:01:48.137 --> 00:01:50.644
Our air has carbon dioxide in it.

00:01:50.644 --> 00:01:53.561
It has carbon dioxide,
so those are the carbons,

00:01:53.561 --> 00:01:55.213
maybe let me draw some oxygens.

00:01:55.213 --> 00:01:57.880
So two oxygens for every carbon.

00:01:58.916 --> 00:02:01.749
And the whole process of photosynthesis

00:02:01.749 --> 00:02:03.932
is all about fixing that carbon.

00:02:03.932 --> 00:02:05.453
Let me write that word down.

00:02:05.453 --> 00:02:07.536
We are fixing that carbon

00:02:11.246 --> 00:02:14.857
from a gaseous form when
it's part of carbon dioxide,

00:02:14.857 --> 00:02:16.703
into the structure of the plant,

00:02:16.703 --> 00:02:19.779
into the biological
molecules of the plant.

00:02:19.779 --> 00:02:21.498
So it's storing that energy.

00:02:21.498 --> 00:02:23.715
Now it's not a perfectly
efficient process.

00:02:23.715 --> 00:02:26.223
Not all of the energy from the Sun

00:02:26.223 --> 00:02:28.487
is going to be able to be stored.

00:02:28.487 --> 00:02:30.333
Some of it is being reflected.

00:02:30.333 --> 00:02:33.166
Even the plant itself as it lives,

00:02:34.721 --> 00:02:38.390
as it reproduces, as its cells divide,

00:02:38.390 --> 00:02:39.992
some of that energy is used.

00:02:39.992 --> 00:02:43.034
And eventually, that
energy is released as heat.

00:02:43.034 --> 00:02:44.509
And you're gonna see this trend a lot

00:02:44.509 --> 00:02:46.111
in thermodynamic systems,

00:02:46.111 --> 00:02:48.897
that you're going from one energy,

00:02:48.897 --> 00:02:51.196
you're using energy to do some work,

00:02:51.196 --> 00:02:55.178
but in the process, you are
going to be producing heat.

00:02:55.178 --> 00:02:58.951
But this is just the
beginning of our energy flow.

00:02:58.951 --> 00:03:01.506
Now we could think about
how that energy now flows

00:03:01.506 --> 00:03:03.978
to the other actors in the ecosystem.

00:03:03.978 --> 00:03:07.136
So the next phase, and this
is a very simplified diagram

00:03:07.136 --> 00:03:08.750
or ecosystem that we're thinking about.

00:03:08.750 --> 00:03:12.152
Most ecosystems are far,
far, far more complex.

00:03:12.152 --> 00:03:15.321
Let's think about the characters
that would eat the plants,

00:03:15.321 --> 00:03:18.328
the characters that would
eat the primary producers,

00:03:18.328 --> 00:03:20.876
and we call the folks that
eat the primary producers,

00:03:20.876 --> 00:03:23.965
we call them primary consumers.

00:03:23.965 --> 00:03:27.877
So this bunny, or this
squirrel right over here,

00:03:27.877 --> 00:03:30.127
they are primary consumers.

00:03:31.987 --> 00:03:35.157
They consume the primary producers.

00:03:35.157 --> 00:03:36.678
And why do they consume them?

00:03:36.678 --> 00:03:39.499
Why does a bunny eat the grass?

00:03:39.499 --> 00:03:43.119
Well, because it gets
energy from those bonds

00:03:43.119 --> 00:03:46.521
in the biological molecules,
from those carbon bonds,

00:03:46.521 --> 00:03:48.483
and other bonds.

00:03:48.483 --> 00:03:52.546
And it's able to use that
energy to grow itself,

00:03:52.546 --> 00:03:55.629
to reproduce, to live, to run around,

00:03:56.494 --> 00:04:00.720
and it also stores some of
that energy in its own biomass.

00:04:00.720 --> 00:04:03.773
And once again, this process
is not very efficient.

00:04:03.773 --> 00:04:08.603
Going from one layer of trophic
to another layer of trophic,

00:04:08.603 --> 00:04:10.484
you only have about 10%,

00:04:10.484 --> 00:04:14.416
10% of the energy gets transferred

00:04:14.416 --> 00:04:17.166
or gets stored in the next layer.

00:04:18.526 --> 00:04:20.128
Why only 10%?

00:04:20.128 --> 00:04:24.250
Well, because not all
of the plants get eaten.

00:04:24.250 --> 00:04:28.577
The whole process of eating
plants, digesting plants,

00:04:28.577 --> 00:04:31.993
some of the energy gets pooped out,

00:04:31.993 --> 00:04:33.357
gets pooped out

00:04:33.357 --> 00:04:36.858
because the primary consumer
here, or the consumer

00:04:36.858 --> 00:04:39.284
isn't able to get all of it out

00:04:39.284 --> 00:04:41.885
of the actual biological molecules.

00:04:41.885 --> 00:04:44.834
And so overall, it's
an inefficient process.

00:04:44.834 --> 00:04:46.645
Now, we're not done yet.

00:04:46.645 --> 00:04:49.315
We still have energy stored
in the biological molecules

00:04:49.315 --> 00:04:51.208
of this primary consumer that someone

00:04:51.208 --> 00:04:52.531
might be interested in.

00:04:52.531 --> 00:04:54.389
And we know that in many ecosystems

00:04:54.389 --> 00:04:57.501
there are things that like to
eat rabbits or even squirrels.

00:04:57.501 --> 00:05:00.333
And in this drawing it will be this fox.

00:05:00.333 --> 00:05:03.422
And this fox because it
eats primary consumers,

00:05:03.422 --> 00:05:06.870
we would call it a secondary consumer.

00:05:06.870 --> 00:05:09.459
The secondary consumer.

00:05:09.459 --> 00:05:11.850
And you could keep going on with this

00:05:11.850 --> 00:05:14.022
if there were some character out here.

00:05:14.022 --> 00:05:17.644
Let's say there's some guy
who likes to eat foxes.

00:05:17.644 --> 00:05:19.490
That's a knife in his hand that he uses

00:05:19.490 --> 00:05:21.138
to go after the foxes with.

00:05:21.138 --> 00:05:24.006
Well, so the fox could go to him,

00:05:24.006 --> 00:05:25.933
and once again, why is he eating foxes?

00:05:25.933 --> 00:05:28.650
Well, he wants that energy in that fox,

00:05:28.650 --> 00:05:31.657
and actually it's not
just about molecules.

00:05:31.657 --> 00:05:33.224
We'll talk about matter in a second.

00:05:33.224 --> 00:05:35.442
He wants the energy and
the matter from the fox

00:05:35.442 --> 00:05:38.077
to grow and live himself.

00:05:38.077 --> 00:05:41.978
And so this character would
be called a tertiary consumer.

00:05:41.978 --> 00:05:43.478
Tertiary consumer.

00:05:45.485 --> 00:05:47.493
And if there's no one
who wants to eat him,

00:05:47.493 --> 00:05:50.988
well then he would be
considered an apex consumer,

00:05:50.988 --> 00:05:52.718
or an apex predator.

00:05:52.718 --> 00:05:54.738
And these characters
that eat other animals,

00:05:54.738 --> 00:05:57.245
we've talked about it before,
they're called carnivores.

00:05:57.245 --> 00:05:59.138
But let me just say, he's the apex.

00:05:59.138 --> 00:06:01.019
And apex, we're really thinking

00:06:01.019 --> 00:06:02.574
about the top of the food chain.

00:06:02.574 --> 00:06:03.979
That's why they're called,

00:06:03.979 --> 00:06:08.008
that would be called an apex
consumer, or an apex predator.

00:06:08.008 --> 00:06:10.713
But we're not done yet
because at some point

00:06:10.713 --> 00:06:12.931
all of these characters,
whether we're talking

00:06:12.931 --> 00:06:15.102
about the trees, the bunnies, the fox,

00:06:15.102 --> 00:06:18.886
this character who likes to eat foxes,

00:06:18.886 --> 00:06:20.895
they're going to die.

00:06:20.895 --> 00:06:23.449
And that energy just doesn't disappear.

00:06:23.449 --> 00:06:24.390
In general, you're going to see,

00:06:24.390 --> 00:06:27.513
energy is conserved and it
flows from one place to another.

00:06:27.513 --> 00:06:31.680
That energy is then going to
be used by these characters

00:06:33.328 --> 00:06:36.410
right over here, which
we call decomposers.

00:06:36.410 --> 00:06:40.020
They can take all that leftover
energy and that dead carcass

00:06:40.020 --> 00:06:43.109
or even in the poop, and
they can make use of it,

00:06:43.109 --> 00:06:46.812
once again, for them to
live, for them to reproduce.

00:06:46.812 --> 00:06:49.395
And then by breaking that down,

00:06:50.252 --> 00:06:52.687
they can release a lot of those nutrients

00:06:52.687 --> 00:06:53.918
and the matter that's used.

00:06:53.918 --> 00:06:55.524
And once again, the matter's recycled,

00:06:55.524 --> 00:06:58.607
once again, to be used by the plants.

00:07:00.202 --> 00:07:02.466
So it creates this really nice cycle.

00:07:02.466 --> 00:07:04.069
And the important thing to realize is

00:07:04.069 --> 00:07:06.321
that it comes in as light
that energy gets transferred

00:07:06.321 --> 00:07:10.802
as we go through the
different layers of trophic.

00:07:10.802 --> 00:07:14.169
And it's not a completely
efficient process,

00:07:14.169 --> 00:07:15.203
and a lot of that energy,

00:07:15.203 --> 00:07:18.314
especially as these organisms
live, and reproduce,

00:07:18.314 --> 00:07:21.397
and run around gets released as heat.

00:07:22.389 --> 00:07:24.038
Now we've focused a lot on the energy,

00:07:24.038 --> 00:07:25.965
let's think a little about the matter.

00:07:25.965 --> 00:07:29.088
I've already touched on it,
but the matter is recycled.

00:07:29.088 --> 00:07:31.886
There isn't, at least the
way that we've set this up,

00:07:31.886 --> 00:07:34.347
there isn't new matter that is entering

00:07:34.347 --> 00:07:37.842
or leaving these ecosystems
or being magically created

00:07:37.842 --> 00:07:39.781
or magically destroyed.

00:07:39.781 --> 00:07:42.033
As I mentioned, when you look at a leaf

00:07:42.033 --> 00:07:44.541
on a plant growing, or a tree growing,

00:07:44.541 --> 00:07:46.793
or a leave of grass growing,

00:07:46.793 --> 00:07:49.212
that matter isn't just
coming out of nowhere,

00:07:49.212 --> 00:07:51.454
it's coming out of,

00:07:51.454 --> 00:07:52.918
it's just a different form,

00:07:52.918 --> 00:07:54.764
or maybe the best way to put it,

00:07:54.764 --> 00:07:58.143
that matter was always there
in the form of carbon dioxide.

00:07:58.143 --> 00:08:00.767
The plant is just using
that energy from the Sun

00:08:00.767 --> 00:08:04.934
to fix that carbon from a
gas form into a solid form.

00:08:06.328 --> 00:08:10.570
And it's able to use
that energy to form bonds

00:08:10.570 --> 00:08:13.445
between the carbons in
these biological molecules

00:08:13.445 --> 00:08:15.209
that actually store energy.

00:08:15.209 --> 00:08:17.555
And the plant can use that energy to grow

00:08:17.555 --> 00:08:19.726
and as we've talked about,
things that eat the plants,

00:08:19.726 --> 00:08:21.827
or things that eat the
things that eat the plants

00:08:21.827 --> 00:08:23.847
can use that energy.

00:08:23.847 --> 00:08:27.052
And as we talked before,
the carbon dioxide

00:08:27.052 --> 00:08:29.432
comes in these plants.

00:08:29.432 --> 00:08:32.021
And maybe this arrow might
be a little bit misleading,

00:08:32.021 --> 00:08:34.438
so let me erase that for now.

00:08:36.386 --> 00:08:38.553
But we release oxygen, O2.

00:08:40.658 --> 00:08:43.162
That oxygen, and we've seen that as part

00:08:43.162 --> 00:08:44.777
of the photosynthesis process,

00:08:44.777 --> 00:08:48.777
that oxygen is used by
the animals to metabolize

00:08:51.221 --> 00:08:53.039
these biological molecules.

00:08:53.039 --> 00:08:56.675
We studied that in biology in respiration.

00:08:56.675 --> 00:08:58.783
And the matter itself, as we say,

00:08:58.783 --> 00:09:00.413
we have this carbon right over here.

00:09:00.413 --> 00:09:02.341
When it gets eaten, well
then that becomes part

00:09:02.341 --> 00:09:05.841
of the bio molecules inside of this bunny,

00:09:08.529 --> 00:09:12.186
and when the bunny uses any
of these biological molecules

00:09:12.186 --> 00:09:15.205
as a source of energy so it's
able to break those bonds

00:09:15.205 --> 00:09:16.389
through respiration.

00:09:16.389 --> 00:09:19.848
Well, then that carbon
gets released in the form

00:09:19.848 --> 00:09:23.931
of carbon dioxide, so
maybe this is a better way.

00:09:25.033 --> 00:09:28.620
Oh, actually it was already
drawn right over here.

00:09:28.620 --> 00:09:31.093
And so the important thing
to realize is that energy

00:09:31.093 --> 00:09:33.637
is flowing, light from the
Sun comes in, it's slow,

00:09:33.637 --> 00:09:35.528
you know all this action goes on,

00:09:35.528 --> 00:09:37.267
and then it gets released as heat

00:09:37.267 --> 00:09:40.518
on almost every step,
but the matter itself,

00:09:40.518 --> 00:09:41.830
it's always been there.

00:09:41.830 --> 00:09:44.384
All of the atoms in our body, on Earth,

00:09:44.384 --> 00:09:46.450
it's just constantly being recycled.

00:09:46.450 --> 00:09:49.655
It's actually was
generated inside of stars

00:09:49.655 --> 00:09:52.081
many, many billions of years ago,

00:09:52.081 --> 00:09:54.998
and we just keep reusing it
over, and over, and over again.

00:09:54.998 --> 00:09:58.362
It gets recycled from one form to another,

00:09:58.362 --> 00:10:01.279
even after all of these actors die,

00:10:02.995 --> 00:10:04.515
the decomposers break them down

00:10:04.515 --> 00:10:06.199
into simple inorganic molecules.

00:10:06.199 --> 00:10:08.207
As we talked about before,

00:10:08.207 --> 00:10:11.087
that can then be used as
the plants in conjunction

00:10:11.087 --> 00:10:14.988
with the carbon from the air
and the light from the Sun

00:10:14.988 --> 00:10:18.923
and water that it gets through its roots

00:10:18.923 --> 00:10:22.840
to start that process
all over, all over again.


Ecosystems and biomes

WEBVTT
Kind: captions
Language: en

00:00:00.160 --> 00:00:01.216
- [Voiceover] So, just as a bit of review.

00:00:01.216 --> 00:00:04.235
If we take the members
of a certain species

00:00:04.235 --> 00:00:06.487
that share the same area,

00:00:06.487 --> 00:00:08.654
we call that a population.

00:00:10.203 --> 00:00:11.189
Population.

00:00:11.189 --> 00:00:13.558
All of the organisms in
this particular population

00:00:13.558 --> 00:00:15.404
will be members of the same species.

00:00:15.404 --> 00:00:16.669
There could be other
members of that species

00:00:16.669 --> 00:00:18.132
that aren't in that same area,

00:00:18.132 --> 00:00:21.406
and they wouldn't be a member
of this particular population.

00:00:21.406 --> 00:00:22.997
And a certain area won't have just one,

00:00:22.997 --> 00:00:25.377
or it doesn't tend to have
just one species in it.

00:00:25.377 --> 00:00:27.629
So, we could call this population one.

00:00:27.629 --> 00:00:29.545
You might have other populations there

00:00:29.545 --> 00:00:30.927
of a different species.

00:00:30.927 --> 00:00:33.562
So, this is another
species right over here.

00:00:33.562 --> 00:00:35.783
All of them combined in the same area,

00:00:35.783 --> 00:00:38.833
we could call this population,

00:00:38.833 --> 00:00:40.616
population two.

00:00:40.616 --> 00:00:41.677
And if you take...

00:00:41.677 --> 00:00:43.988
And we could, obviously have
many more populations there.

00:00:43.988 --> 00:00:45.555
And if you take all of the populations

00:00:45.555 --> 00:00:47.680
in a given area,

00:00:47.680 --> 00:00:49.781
there's flexibility on
how you define that area

00:00:49.781 --> 00:00:51.255
or define that region,

00:00:51.255 --> 00:00:52.145
you take those together,

00:00:52.145 --> 00:00:54.846
so you're really taking
all of the living things

00:00:54.846 --> 00:00:58.513
in a certain area, we
call that a community.

00:00:59.464 --> 00:01:02.358
A community of populations.

00:01:02.358 --> 00:01:05.040
Now, the community only
consists of living things,

00:01:05.040 --> 00:01:06.840
the biotic factors.

00:01:06.840 --> 00:01:08.314
So, let me write that down.

00:01:08.314 --> 00:01:12.110
Biotic referring to the living
things in a certain area.

00:01:12.110 --> 00:01:14.305
But if we want to think about
not just the living things,

00:01:14.305 --> 00:01:16.883
but also the non-living
things in that region.

00:01:16.883 --> 00:01:19.481
So, I'll write abiotic.

00:01:19.481 --> 00:01:21.933
Let me do that in another color.

00:01:21.933 --> 00:01:25.227
So, let's take the abiotic factors,

00:01:25.227 --> 00:01:27.477
or the abiotic environment.

00:01:28.423 --> 00:01:31.558
And, once again, we're
sharing the same region,

00:01:31.558 --> 00:01:34.379
and that is flexible on
how you define that region.

00:01:34.379 --> 00:01:36.678
You put all of these things together,

00:01:36.678 --> 00:01:39.127
and then you get your ecosystem.

00:01:39.127 --> 00:01:41.101
Your ecosystem, once again,

00:01:41.101 --> 00:01:42.610
it could be a very small region,

00:01:42.610 --> 00:01:44.178
it could be a very large region,

00:01:44.178 --> 00:01:45.687
but it's made up of all living things,

00:01:45.687 --> 00:01:48.613
the biotic factors, and
the non-living things,

00:01:48.613 --> 00:01:50.540
the abiotic factors.

00:01:50.540 --> 00:01:51.887
Now, what we're gonna
think about in this video

00:01:51.887 --> 00:01:54.336
is just the types of
ecosystems that you might have.

00:01:54.336 --> 00:01:55.973
Think a little bit about it,

00:01:55.973 --> 00:02:00.146
and also begin to think about
how the different factors

00:02:00.146 --> 00:02:01.639
interact with each other.

00:02:01.639 --> 00:02:03.497
How there's conservation of matter

00:02:03.497 --> 00:02:06.135
where, within an ecosystem,
matter tends to go

00:02:06.135 --> 00:02:07.607
from one form to another.

00:02:07.607 --> 00:02:10.196
You also have a flow of energy.

00:02:10.196 --> 00:02:13.175
Energy tends to enter an ecosystem

00:02:13.175 --> 00:02:15.710
in form of light, and that
energy gets transferred

00:02:15.710 --> 00:02:17.591
from one organism to another,

00:02:17.591 --> 00:02:19.356
and, sometimes, even involving
the non-living things,

00:02:19.356 --> 00:02:21.523
eventually, getting turned

00:02:22.606 --> 00:02:24.847
into actual heat.

00:02:24.847 --> 00:02:26.531
Now, in terms of the types of ecosystems.

00:02:26.531 --> 00:02:28.899
I already mentioned there's
a lot of variety there.

00:02:28.899 --> 00:02:31.117
This, right here, is a
picture of a tide pool

00:02:31.117 --> 00:02:33.450
at Half Moon Bay, not too
far from where I live.

00:02:33.450 --> 00:02:36.364
I've actually been to the
tide pools at Half Moon Bay.

00:02:36.364 --> 00:02:39.766
And you could consider
one particular tide pool,

00:02:39.766 --> 00:02:42.460
both the abiotic factors, the water,

00:02:42.460 --> 00:02:44.043
and the rock there,

00:02:45.009 --> 00:02:46.686
as well as the biotic factors,

00:02:46.686 --> 00:02:49.344
the starfish, the sea anemones,

00:02:49.344 --> 00:02:51.782
and whatever else might be living there.

00:02:51.782 --> 00:02:54.731
Those combined, that
could be an ecosystem.

00:02:54.731 --> 00:02:57.158
You might say that the
entire beach is an ecosystem.

00:02:57.158 --> 00:02:59.747
You might say that the entire
region is an ecosystem.

00:02:59.747 --> 00:03:02.557
Once again, it depends
on how much you want

00:03:02.557 --> 00:03:04.948
to zoom in or how much
you want to zoom out,

00:03:04.948 --> 00:03:06.411
and you can zoom out a good bit.

00:03:06.411 --> 00:03:08.436
This rain forest, right over here,

00:03:08.436 --> 00:03:10.080
this is the Amazon rain forest.

00:03:10.080 --> 00:03:12.762
You can consider the whole
rain forest an ecosystem,

00:03:12.762 --> 00:03:14.329
or maybe you just want to study,

00:03:14.329 --> 00:03:15.966
maybe you just want to study

00:03:15.966 --> 00:03:18.996
what's happening in this exact
region, right over there.

00:03:18.996 --> 00:03:21.051
You can also consider that an ecosystem.

00:03:21.051 --> 00:03:23.129
You can consider what's
happening in the river, itself,

00:03:23.129 --> 00:03:26.705
an ecosystem, or, maybe,
one part of that river.

00:03:26.705 --> 00:03:29.039
And, as you notice, I'm
talking about some ecosystems

00:03:29.039 --> 00:03:31.465
that are on land, and
some that are in water,

00:03:31.465 --> 00:03:34.937
and that is a general way,
one way of classifying them.

00:03:34.937 --> 00:03:37.886
So an ecosystem, you
could have it on land.

00:03:37.886 --> 00:03:41.044
You could have it on, near, in the water.

00:03:41.044 --> 00:03:43.389
So, you could say it's aquatic.

00:03:43.389 --> 00:03:44.585
And then, if within aquatic,

00:03:44.585 --> 00:03:46.012
you could have ones that...

00:03:46.012 --> 00:03:48.892
You have salt water, or
partially salty water,

00:03:48.892 --> 00:03:50.657
and these are called marine,

00:03:50.657 --> 00:03:52.085
and the main marine ecosystem,

00:03:52.085 --> 00:03:56.160
we're thinking about the
oceans and things like that.

00:03:56.160 --> 00:03:57.971
And then, you have freshwater ecosystems.

00:03:57.971 --> 00:04:00.096
Like if you are in the upper-Amazon,

00:04:00.096 --> 00:04:02.232
that is freshwater that is flowing.

00:04:02.232 --> 00:04:05.030
So we could say fresh, freshwater,

00:04:05.030 --> 00:04:06.363
non-salty water.

00:04:08.176 --> 00:04:10.208
And even though it looks
like rivers are big

00:04:10.208 --> 00:04:11.531
and there's a lot of freshwater around us.

00:04:11.531 --> 00:04:13.459
Obviously we need freshwater to live,

00:04:13.459 --> 00:04:16.895
most of the aquatic ecosystems are marine,

00:04:16.895 --> 00:04:18.288
are not involved freshwater.

00:04:18.288 --> 00:04:21.028
Freshwater is a very small subset.

00:04:21.028 --> 00:04:23.327
Now, this is just a few examples.

00:04:23.327 --> 00:04:25.742
Even your body, you could view your body

00:04:25.742 --> 00:04:26.926
as a whole ecosystem.

00:04:26.926 --> 00:04:29.109
You could view parts of
your body as an ecosystem.

00:04:29.109 --> 00:04:30.583
You could look at just...

00:04:30.583 --> 00:04:32.429
You could look at just a fraction of...

00:04:32.429 --> 00:04:35.599
If this is my hand right over here,

00:04:35.599 --> 00:04:37.213
you could take just a
little square, there,

00:04:37.213 --> 00:04:39.198
and you could consider that an ecosystem.

00:04:39.198 --> 00:04:41.404
You can think about the different bacteria

00:04:41.404 --> 00:04:43.529
that are there, other
types of microorganisms

00:04:43.529 --> 00:04:45.340
that are there, and
how they're interacting

00:04:45.340 --> 00:04:48.173
with the non-living things, the air.

00:04:48.173 --> 00:04:51.830
How they're interacting
with the oil on your skin,

00:04:51.830 --> 00:04:53.676
with the dead skin cells, and also,

00:04:53.676 --> 00:04:55.649
how they're interacting
with the living skin cells,

00:04:55.649 --> 00:04:57.577
and you, yourself.

00:04:57.577 --> 00:05:01.536
Now, since we're in
the, since we're focused

00:05:01.536 --> 00:05:03.628
on how we can classify ecosystems,

00:05:03.628 --> 00:05:05.030
one thing that's often done

00:05:05.030 --> 00:05:09.732
is classifying land ecosystems
into various categories.

00:05:09.732 --> 00:05:12.899
And, right over here, we have depicted

00:05:13.889 --> 00:05:16.060
the major types of land ecosystems

00:05:16.060 --> 00:05:17.143
on our planet

00:05:18.668 --> 00:05:20.274
and where you might find them.

00:05:20.274 --> 00:05:22.991
And these different
types of land ecosystems,

00:05:22.991 --> 00:05:25.510
these are called biomes.

00:05:25.510 --> 00:05:26.613
Biomes.

00:05:26.613 --> 00:05:28.506
And as you can see from this diagram,

00:05:28.506 --> 00:05:31.060
tropical forests, you can
find it right over here.

00:05:31.060 --> 00:05:32.778
This is the Amazon rain forest.

00:05:32.778 --> 00:05:33.893
You can find it in Africa.

00:05:33.893 --> 00:05:36.064
You can find it in Southeast Asia.

00:05:36.064 --> 00:05:39.405
You can find it in
Central and even Southern

00:05:39.405 --> 00:05:41.046
or North America.

00:05:41.046 --> 00:05:43.030
You have boreal forests which you'll find

00:05:43.030 --> 00:05:44.423
in more northern latitudes.

00:05:44.423 --> 00:05:47.383
Savanna, desert, tundra,
chaparral, polar ice,

00:05:47.383 --> 00:05:49.856
temperate forest, temperate grasslands,

00:05:49.856 --> 00:05:50.797
and these are just helpful

00:05:50.797 --> 00:05:54.326
for thinking about roughly
the types of ecosystem,

00:05:54.326 --> 00:05:57.948
or ecosystems we would
find in those regions.

00:05:57.948 --> 00:06:01.199
And it's typically most determined by

00:06:01.199 --> 00:06:04.116
temperature, moisture, the climate.

00:06:05.253 --> 00:06:07.480
Actually, the climate and the terrain

00:06:07.480 --> 00:06:09.489
and the types of minerals
that you would find there,

00:06:09.489 --> 00:06:12.107
that tends to be a pretty good indicator

00:06:12.107 --> 00:06:14.992
for what it will be like,
what the life would be like.

00:06:14.992 --> 00:06:16.385
But even with that said, there could

00:06:16.385 --> 00:06:18.289
still be a lot of variety.

00:06:18.289 --> 00:06:22.532
For example, the Sonoran
Desert, that is right over here

00:06:22.532 --> 00:06:23.792
in the southwest United States,

00:06:23.792 --> 00:06:26.207
in the northwest Mexico.

00:06:26.207 --> 00:06:29.290
This is a desert, and there's deserts

00:06:30.150 --> 00:06:32.244
all over the rest of the planet,

00:06:32.244 --> 00:06:33.556
but they won't have...

00:06:33.556 --> 00:06:34.996
They might be similar in a lot of ways,

00:06:34.996 --> 00:06:37.260
but they won't have
the exact same climate,

00:06:37.260 --> 00:06:40.046
or the exact same abiotic factors,

00:06:40.046 --> 00:06:42.391
or the exact same biotic factors.

00:06:42.391 --> 00:06:44.284
So, for example, right now
I'm gonna show you a picture,

00:06:44.284 --> 00:06:46.792
pictures of the Sonoran
Desert and the Rock Desert

00:06:46.792 --> 00:06:48.347
that's on the island of Boa Vista.

00:06:48.347 --> 00:06:49.484
Boa Vista is right over there.

00:06:49.484 --> 00:06:50.317
You really can't see it.

00:06:50.317 --> 00:06:53.073
It's a very small island
off the coast of Africa.

00:06:53.073 --> 00:06:57.125
And, as we see in these
diagrams, or in this picture,

00:06:57.125 --> 00:06:58.990
you don't have to be an
expert to recognize that,

00:06:58.990 --> 00:07:00.457
okay, these are both deserts.

00:07:00.457 --> 00:07:01.687
They both look dry.

00:07:01.687 --> 00:07:03.278
There's not a lot of water here,

00:07:03.278 --> 00:07:05.611
but they are also very different.

00:07:05.611 --> 00:07:07.841
The Sonoran Desert looks to have

00:07:07.841 --> 00:07:09.814
at least a lot more life,

00:07:09.814 --> 00:07:11.660
than the Rock Desert have here.

00:07:11.660 --> 00:07:13.785
It's appropriately named the Rock Desert

00:07:13.785 --> 00:07:15.375
because it seems, at
least to the naked eye,

00:07:15.375 --> 00:07:17.691
it looks like all you can see is rock.

00:07:17.691 --> 00:07:20.147
So biomes, once again, it's a very rough,

00:07:20.147 --> 00:07:23.351
high-level way to
classifying land ecosystems.

00:07:23.351 --> 00:07:27.018
But even the same biome
can be very, very...

00:07:28.011 --> 00:07:30.271
Two things that are
categorizing in the same biome

00:07:30.271 --> 00:07:31.879
could be very different.


Khan Academy Welcomes Duck Duck Moose

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:03.002
- Hi, I'm Salman Khan,
founder of the Khan Academy.

00:00:03.002 --> 00:00:06.260
- And I'm Caroline Hu Flexer,
founder of Duck Duck Moose.

00:00:06.260 --> 00:00:08.719
- And we have a very
exciting announcement today.

00:00:08.719 --> 00:00:11.425
As you probably know, Khan
Academy is a not-for-profit

00:00:11.425 --> 00:00:13.606
with a mission of a free
world-class education

00:00:13.606 --> 00:00:14.975
for anyone anywhere.

00:00:14.975 --> 00:00:17.064
And we've always viewed
core to our mission

00:00:17.064 --> 00:00:18.771
of how do we, how do we meet the needs

00:00:18.771 --> 00:00:21.400
of our youngest learners,
of kids in preschool

00:00:21.400 --> 00:00:23.235
or who might be in kindergarten.

00:00:23.235 --> 00:00:25.144
And whenever we thought
about this in the past,

00:00:25.144 --> 00:00:26.983
we always looked to Duck Duck Moose

00:00:26.983 --> 00:00:29.382
as really the best company out there.

00:00:29.382 --> 00:00:31.557
I'm a father of young children,

00:00:31.557 --> 00:00:33.435
and they, to some degree,

00:00:33.435 --> 00:00:35.218
grew up on these apps.

00:00:35.218 --> 00:00:38.241
And so it was very exciting
when Caroline and her team

00:00:38.241 --> 00:00:42.088
reached out to us and
propose that we join forces.

00:00:42.088 --> 00:00:44.482
- We're thrilled to be
joining Khan Academy.

00:00:44.482 --> 00:00:47.402
Duck Duck Moose is an indie
developer, and originally,

00:00:47.402 --> 00:00:49.520
we started designing
apps for our own children

00:00:49.520 --> 00:00:52.666
and now we have 21 early-learning apps.

00:00:52.666 --> 00:00:56.128
And we've always been a
mission-driven company

00:00:56.128 --> 00:00:58.238
concerned about kids and education,

00:00:58.238 --> 00:00:59.506
trying to make the biggest impact,

00:00:59.506 --> 00:01:02.009
and I think this is why
this is so exciting for us.

00:01:02.009 --> 00:01:04.005
Being part of a larger nonprofit

00:01:04.005 --> 00:01:06.020
where we can really make an impact

00:01:06.020 --> 00:01:07.872
on kids all around the world.

00:01:07.872 --> 00:01:11.375
- And you already have an
incredible suite of 21 apps

00:01:11.375 --> 00:01:13.305
which now are going to be

00:01:13.305 --> 00:01:14.188
- Free!

00:01:14.188 --> 00:01:15.751
- [Khan] Free. And really free.

00:01:15.751 --> 00:01:18.710
Not download and then try, truly free

00:01:18.710 --> 00:01:22.456
because we want young
children all over the world

00:01:22.456 --> 00:01:25.293
to be able to have
access to this learning.

00:01:25.293 --> 00:01:27.138
And as a reminder to you,

00:01:27.138 --> 00:01:28.642
the only way we're able to do this

00:01:28.642 --> 00:01:30.587
is with philanthropic support.

00:01:30.587 --> 00:01:33.025
So, if you're a big
supporter of this vision,

00:01:33.025 --> 00:01:35.577
please think about donating.

00:01:35.577 --> 00:01:37.170
So, as you can imagine,

00:01:37.170 --> 00:01:39.234
we're all very excited
that now Duck Duck Moose,

00:01:39.234 --> 00:01:40.189
the Duck Duck Moose team,

00:01:40.189 --> 00:01:42.664
is now part of the
not-for-profit Khan Academy.

00:01:42.664 --> 00:01:45.003
And keep a lookout for what's to come

00:01:45.003 --> 00:01:48.273
because these 21 apps
are just the beginning.

00:01:48.273 --> 00:01:50.156
We have some fun plans ahead of us.

00:01:50.156 --> 00:01:51.239
- Absolutely.