Lec 09 Currents, Resistivity and Ohm's Law8.02 Electricity and Magnetism (Walter Lewin)

When positive charges move in
this direction, then per definition,
we say the current goes in this direction.
When negative charges go in this direction,
we also say the current goes in that direction,
that's just our convention. If I apply a potential
difference over a conductor, then I'm going to create an
electric field in that conductor.
And the electrons -- there are free electrons in a conductor --
they can move, but the ions cannot move,
because they are frozen into the solid, into the crystal.
And so when a current flows in a conductor, it's always the
electrons that are responsible for the current.
The electrons fuel the electric fields, and then the electrons
try to make the electric field zero, but they can't succeed,
because we keep the potential difference over the conductor.
Often, there is a linear relationship between current and
the potential, in which case,
we talk about Ohm's Law. Now, I will try to derive Ohm's
Law in a very crude way,
a poor man's version, and not really one hundred
percent kosher, it requires quantum mechanics,
which is beyond the course -- beyond this course -- but I will
do a job that still gives us some interesting insight into
Ohm's Law. If I start off with a
conductor, for instance, copper, at room temperature,
three hundred degrees Kelvin, the free electrons in copper
have a speed, an average speed of about a
million meters per second.

So this is the average speed of
those free electrons, about a million meters per
second. This in all directions.
It's a chaotic motion. It's a thermal motion,
it's due to the temperature. The time between collisions --
time  between the collisions -- and this is a collision of the
free electron with the atoms -- is approximately -- I call it
tau -- is about three times ten to the
minus fourteen seconds.

No surprise,
because the speed is enormously high.
And the number of free electrons in copper per cubic
meter, I call that number N, is about ten to the
twenty-nine. There's about one free electron
for every atom. So we get twen- ten to the
twenty-nine free electrons per cubic meter.
So now imagine that I apply a potential difference  piece of
copper -- or any conductor, for that matter -- then the
electrons will experience a force which is the charge of the
electron, that's my little E. Times the electric field that
I'm creating, because I apply a potential
difference.

I realize that the force and
the electric field are in opposite directions for
electrons, but that's a detail, I'm interested
in the magnitudes only. And so now these electrons will
experience an acceleration, which is the force divided by
the mass of the electron, and so they will pick up,
eh, speed, between these colli- collisions, which we call the
drift velocity, which is A times tau,
it's just eight oh one. And so A equals F divided by M.
E F is in the A, so we get E times E divided by
the mass of the electrons, times tau.
And that is the the drift velocity.
When the electric field goes up, the drift velocity goes up,
so the electrons move faster in the direction opposite to the
current. If the time between collisions
gets larger, they -- the acceleration lasts longer,
so also, they pick up a larger speed, so that's intuitively
pleasing.

If we take a specific case,
and I take, for instance, copper,
and I apply over the -- over a wire -- let's say the wire has a
length of 10 meters -- I apply a potential difference I call
delta V, but I could have said just V -- I apply there a
potential difference of ten volts, then the electric field
-- inside the conductor, now -- is about one volt per
meter. And so I can calculate,
now, for that specific case, I can calculate what the drift
velocity would be. So the drift velocity of those
free electrons would be the charge of the electron,
which is one point six times ten to the minus nineteen
Coulombs. The E field is one,
so I can forget about that.

Tau is three times ten to the
minus fourteen, as long as I'm room
temperature, and the mass of the electron is about ten to the
minus thirty kilograms. And so, if I didn't slip up,
I found that this is five times ten to the minus three meters
per second, which is half a centimeter per second.
So imagine, due to the thermal motion, these free electrons
move with a million meters per second.
But due to this electric field, they only advance along the
wire slowly, like a snail, with a speed on average of half
a centimeter per second. And that goes very much against
your and my own intuition, but this is the way it is.
I mean, a turtle would go faster than these electrons.
To go along a ten-meter wire would take half hour.
Something that you never thought of.
That it would take a half hour for these electrons to go along
the wire if you apply potential difference of ten volts,
copper ten meters long. Now, I want to massage this
further, and see whether we can somehow
squeeze out Ohm's Law, which is the linear relation
between the potential and the current.
So let me start off with a wire which has a cross-section A,
and it has a length L, and I put a potential
difference over the wire,
plus here, and minus there, potential V,
so I would get a current in this direction,
that's our definition of current, going from plus to
minus.

The electrons,
of course, are moving in this direction, with the drift
velocity. And so the electric field in
here, which is in this direction, that electric field
is approximately V divided by L, potential difference divided by
distance. In one second,
these free electrons will move from left to right over a
distance V D meters. So if I make any cross-section
through this wire, anywhere, I can calculate how
many electrons pass through that cross-section in one second.
In one second, the volume that passes through
here, the volume is V D times A.

But the number of free
electrons per cubic meter is called N, so this is now the
number of free electrons that passes, per second,
through any cross-section. And each electron has a charge
E, and so this is the current that will flow.
The current, of course, is in this
direction, but that's a detail. If I now substitute the drift
velocity, which we have here, I substitute that in there,
but then I find that the current -- I get a E squared,
the charge squared, I get N, I get tau,
I get downstairs, the mass of the electron,
and then I get A times the electric field E.
Because I have here, is electric field E.
When you look at this here, that really depends only on the
properties of by substance, for a given temperature.
And we give that a name. We call this sigma,
which is called conductivity.

Conductivity.
If I calculate, for copper, the conductivity,
at room temperature, that's very easy,
because I've given you what N. Is, on the blackboard there,
ten to the twenty-nine, you know what tau is at room
temperature, three times ten to the minus fourteen,
so for copper, at room temperature,
you will find about ten to the eighth.
You will see more values fro sigma later on during this
course. This is in SI units.
I can massage this a little further, because E is V divided
by L, and so I can write now that the
current is that sigma times A. Times V divided by L.
I can write it down a little bit differently,
I can say V, therefore, equals L divided by
sigma A, times I.

And now, you're staring at
Ohm's Law, whether you like it or not,
because this is what we call the resistance,
capital R. We often write down rho for one
over sigma, and rho is called the resistivity.
So either one will do. So you can also write down --
you can write down V equals I R, and this R, then,
is either L divided by sigma A, or L times rho -- let me make
it a nicer rho -- divided by A. That's the same thing.
The units for resistance R is volts per ampere,
but we call that ohm.

And so the unit for R is ohm.
And so if you want to know what the
unit for rho and sigma is, that follows immediately from
the equations. The unit for rho is then
ohm-meters. So we have derived the
resistance here in terms of the dimensions -- namely,
the length and the cross-section -- but also in
terms of the physics on an atomic scale,
which, all by itself, is interesting.
If you look at the resistance, you see it is proportional with
the length of your wire through
which you drive a current. Think of this as water trying
to go through a pipe.

If you make the pipe longer,
the resistance goes up, so that's very intuitively
pleasing. Notice that you have A
downstairs. That means if the pipe is
wider, larger cross-section, it's also easier for the
current to flow, it's easier for the water to
flow. So that's also quite pleasing.
Ohm's Law, also, often holds for insulators,
which are not conductors, even though I have derived it
here for conductors, which have these free
electrons.

And so now, I want to make a
comparison between very good conductors, and very good
insulators. So I'll start off with a -- a
chunk of material , cross-sectional area A -- let's
take it one millimeter by one millimeter -- so A is ten to
the minus six square meters. So here I have a chunk of
material, and the length of that material L is one meter.
Put a potential difference over there, plus here,
and minus here. Current will start to flow in
this direction, electrons will flow in this
direction.

The question now is,
what is the resistance of this chunk of material?
Well, very easy. You take these equations,
you know L and A, so if I tell you what sigma is,
then you can immediately calculate what the resistance
is. So let's take,
first, a good conductor. Silver and gold and copper are
very good conductors.
They would have values of sigma, ten to the eight,
we just calculated for copper, you've seen in front of your
own eyes.

So that means rho would be ten
to the minus eight, it's one over sigma.
And so in this particular case, since A is ten to the minus
six, the resistance R is simply ten to
the sixth times rho. Because L is one meter.
So it's very easy -- resistance here, R, is ten to the minus two
ohms. One-hundredth of an ohm.
For this material if it were copper.
Let's now take a very good insulator.
Glass is an example. Quartz, porcelain,
very good insulators.

Now, sigma, the conductivity,
is extremely low. They vary somewhere from ten to
the minus twelve through ten to the minus sixteen.
So rho, now, the resistivity,
is something like ten to the twelve to twelve to the plus
sixteens, and if I take ten to the fourteen,
just I grab -- I have to grab a number -- then you'll find that
R, now, is ten to the twenty ohms.
A one with twenty zeros. That's an enormous resistance.
So you see the difference -- twenty-two orders of magnitude
difference between a good conductor and a good insulator.
And if I make this potential difference over the wire,
if I make that one volt, and if I apply Ohm's Law,
V equals I R, then I can also calculate the
current that is going to flow. If I R is one,
then the current here is hundred amperes,
and the current here is ten to the minus twenty amperes,
an insignificant  current, ten to the minus twenty
amperes.

I first want to demonstrate to
you that Ohm's Law sometimes holds, I will do a
demonstration, whereby you have a voltage
supply  -- put a V in here -- and we change the voltage in a
matter of a few seconds from zero to four volts.
This is the plus side, this is the minus side,
I have connected it here to a resistor which is fifty ohms --
we use this symbol for a resistor -- and here is a
current meter. And the current meter has
negligible resistance, so you can ignore that.
And I'm going to show you on an oscilloscope -- we've never
discussed an oscilloscope, but maybe we will in the future
-- I'm going to show you, they are projected -- the
voltage unintelligible go from zero to four,
versus the current. And so it will start here,
and by the time we reach four volts, then we would have
reached a current of four divided by fifty,
according to Ohm's Law, I will write down just four
divided by fifty amperes, which is point
oh eight amperes. And if Ohm's Law holds,
then you would find a straight line.
That's the whole idea about Ohm's Law, that the potential
difference, linearly proportional to the current.
You double the potential difference, your current
doubles.

So let's do that,
let's take a look at that, you're going to see that there
-- and I have to change my lights so
that you get a good shot at it -- oh, it's already going.
So you see, horizontally, we have the current,
and vertically, we have the voltage.
And so it takes about a second to go from zero to four -- so
this goes from zero to four volts -- and you'll see that the
current is beautifully linear. Yes, I'm blocking it -- oh,
no, it's my reflection, that's interesting.
Ohm's Law doesn't allow for that.
So you see how beautifully linear it is.
So now, you may have great confidence in Ohm's Law.
Don't have any confidence in Ohm's Law.
The conductivity sigma is a strong function of the
temperature. If you increase the
temperature, then the time tau between collisions goes down,
because the speed of these free electrons goes up.
It's a very strong function of temperature.
And so if tau goes down, then clearly,
what will happen is that the conductivity will go down.
And that means rho will go up. And so you get more resistance.
And so when you heat up a substance, the resistance goes
up.

A higher temperature,
higher resistance. So the moment that the
resistance R becomes a function of the
temperature, I call that a total breakdown
of V equals I R, a total breakdown of Ohm's Law.
If you look in your book, they say, "Oh,
no, no, no, that's not a breakdown.
You just have to adjust the re- the resistance for a different
temperature." Well, yes, that's an incredible poor
man's way of saving a law that is a very bad law.
Because the temperature itself is a function of current,
the higher the current the higher the temperature.
And so now, you get a ratio, V divided by I,
which is no longer constant. It becomes a function of the
current. That's the end of Ohm's Law.
And so I want to show you that if I do the same experiment that
I did here, but if I replace this by a light bulb of fifty
ohms -- it's a very small light bulb, resistance when it is hot
is fifty ohms, when it is cold,
it is seven ohms.

So R cold of the light bulb is
roughly seven ohms, I believe, but I know that when
it is hot, it's very close to the fifty ohms.
Think it's a little lower. What do you expect now?
Well, you expect now, that when the resistance is low
in the beginning, you get this,
and then when the resistance goes up, you're going to get
this. I may end up a little higher
current, because I think the resistance is a
little lower than fifty ohms. And if you see a curve like
this, that's not linear anymore.

So that's the end of Ohm's Law.
And that's what I want to show you now.
So, all I do is, here I have this little light
bulb -- for those of you who sit close, they can actually see
that light bulb  start glowing, but that's not important,
I really want you to see that V. Versus I is no longer linear,
there you go. And you see,
every time you see this light bulb go on, it heats up,
and during the heating up, it, um, the resistance
increases. And it's the end of Ohm's Law,
for this light bulb, at least.
It was fine for the other resistor, but it was not fine
for this light bulb.

There is another way that I can
That is the resistivity, show you that Ohm's Law is not
always doing so well. I have a hundred twenty-five
volt power supply, so V is hundred and twenty-five
volts -- this is the potential difference -- and I have a light
bulb, you see it here, that's the light bulb -- the
resistance of the light bulb, cold, I believe,
is twenty-five ohms, and hot, is about two hundred
and fifty ohms. A huge difference.
So if the  resistance -- if I. Take the cold resistance,
then I would get five amperes, but by the time that the bulb
is hot, I would only get half an ampere.
It's a huge difference.

And what I want to show you,
again with the oscilloscope, is the current as a function of
time. When you switch on a light
bulb, you would expect, if Ohm's Law holds,
that when you switch on the current -- or switch on the
voltage, I should say -- that you see this.
This is then your five amperes. And that it would stay there.
That's the whole idea. Namely, that the voltage
divided by the current remains a constant.
However, what you're going to see is like this.
Current goes up, but then the resistance goes
down, then the resistance goes up, when the current goes up,
the resistance goes up, and then therefore the current
will go down, and will level off at a level
which is substantially below this.
So you're looking there -- you're staring at the breakdown
of Ohm's Law.

And so that's what I want to
show you now. So, here we need a hundred and
twenty five volts -- and there is the light bulb,
and when I throw this switch, you will see the pattern of the
current versus time -- you will only see it once,
and then we freeze it with the oscilloscope -- turn this off --
so look closely, now.
There it is. Forget these little ripple that
you see on it, it has to do with the way that
we produce the hundred and twenty five volts.
And so you see here, horizontally,
time, the time between two adjacent vertical lines is
twenty milliseconds. And so, indeed,
very early on, the current surged toward -- to
a very high value, and then the filament heats up,
and so the resistance goes up, the light bulb,
and the current just goes back again.
From the far left to the far right on the screen is about two
hundred milliseconds.

That's about two tenths of a
second. And here you get a current
level which is way lower than what you get there.
That's a breakdown of Ohm's Law.
It is actually very nice that resistances go up with light
bulbs when the temperature goes up.
Because, suppose it were the other way around.
Suppose you turn on a light bulb, and the resistance would
go down. Light bulb got hot,
resistance goes down, that means the current goes up.
Instead of down, the current goes up.
That means it gets hotter. That means the resistance goes
even further down.

That means the current goes
even further up. And so what it would mean is
that every time you turn on a light bulb, it would,
right in front of your eyes, destruct itself.
That's not happening. It's the other way around.
So, in a way, it's fortunate that the
resistance goes up when the light bulbs get hot.
All right. Let's now be a little bit more
qualitative on some  networks of resistors, and we'll have you do
a few problems like that, whereby we just will assume,
naively, that Ohm's Law holds.

In other words,
we will always assume that the values for the resistances that
we give you will not change. So we will assume that the heat
that is produced will not  play any important role.
So we will just use Ohm's Law, for now, and if you can't use
it, we will be very specific about that.
So suppose I have here, between point A and point B,
suppose I have two resistors, R one and R two.
And suppose I apply a potential difference between A and B,
that this be plus, and this be minus,
and the potential difference is V.
And you know V, this is known,
I give you V, I gave you this resistance,
and I gave you that one. So I could ask you now,
what is the current that is going to flow?
I could also ask you, then, what is the potential
difference over this resistor alone --
which I will call V one -- and what is the potential difference
over the second resistor, which I call V two?
Very straightforward question. Well, you apply,
now, Ohm's Law, and so between A and B,
there are two resistors, in series.
So the current has to go through both,
and so the potential difference V, in Ohm's Law,
is now the total current times R one plus R two.
Suppose these two resistors were the same,
they had the same length, same cross-sectional area.
If you put two in series, you have twice the length.
Well, so, twice the length, remember, resistance is
linearly proportional with the length of a wire,
and so you add them up.

So now you know R one and you
know R two, you know V, so you already know the
current, very simple. You can also apply Ohm's Law,
as long as it holds, for this resistor alone.
So then you get that V one equals I times R one,
so now you have the voltage over this resistor,
and of course, V two must be the current I
times R two. And so you have solved your
problem. All the questions that I asked
you, you have  the answers to.

We could now have a slightly
different problem, whereby point A is here,
but now we have a resistor here,
which is R one, and we have here,
R two. This is point B,
and this is R two. And the potential difference is
V, that is, again, given, and now I could ask you,
what, now, is the current that will flow here?
And then I can also ask you, what is the current that would
go through one -- resistor one, and what is the current that
could go through resistor two?
And I would allow you to use Ohm's Law.
So now you say, "Aha!
The potential difference from A. To B going this route,
that potential difference, is V, that's a given." So V
must now be I one times R one.

That's Ohm's Law,
for this upper branch. But, of course,
you can also go the lower branch.
So the same V is also I two times R two.
But whatever current comes in here must split up between these
two, think of it as water. You cannot get rid of charges.
The number of charges per second that flow into this
juncture continue on, and so I, the total current,
is I one plus I two. And so now,
you see, you have all the ingredients that you need to
solve for the current I -- for the current I one,
and for the current I two.

And you can turn this into an
industry, you can make extremely complicated networks of
resistors -- and if you were in course six, you should love it
-- I don't like it at all, so you don't have to worry
about it, you're not going to get very complicated resistor
net- networks from me -- but in course six,
you're going to see a lot of them.
They're going to throw them -- stuff them down your throat.
The conductivity of a substan- substance goes up if I can
increase the number of charge carriers.
If we have  dry air, and it is cold,
then the resistivity of cold, dry air at
one atmosphere -- so rho for air, cold,  dry,
one atmosphere -- cold means temperature that we have outside
-- it's about four times ten to the thirteen.
That is the resistivity of air. It is  about what it is in
this room, maybe a little lower, because the temperature
is a little higher. If I heat it up -- the air --
then the conductivity will go up.
Resistivity will go down, because now,
I create oxygen and nitrogen ions by heating up the air.
Remember when we had this lightning, the unintelligible
came down, and we created a channel full of ions and
electrons, that had a very low resistivity,
a very high conductivity. And so what I want to
demonstrate to you, that when I create ions in this
room, that I can actually make the conductivity of air go up
tremendously.

Not only will the electrons
move, but also the ions, now, will start to move.
And the way I'm going to do that is, I'm going to put charge
on the electroscope -- oh, that is not so good --
no harm done. I'm going to put charge on the
electroscope, and you will see that the
conductivity of air is so poor that it will stay there for
hours. And then what I will do,
I will create ions in the vicinity of the electroscope.
But let's first put some charge on the electroscope.
I have here a glass rod  and I'll put some charge on it.
OK, that's a lot of charge. And, uh, the r- the air is
quite dry, conductivity is very, very small, and so the charge
cannot go off through the air to the surroundings,
to the earth.

But now I'm going to create
ions there by heating it up, and I decided to do that with a
candle, because a candle is very romantic,
as we all know. So here I have this candle  --
look how well the charge is holding, eh?
-- And here's my candle. And I will bring the candle --
oh, maybe twenty centimeters from the electroscope.
Look at it, look at it, already going.
It's about fifteen centimeters away.
I'll take my candle away, and it stops again.
So it's all due to the fact that I'm ionizing the air there,
creating free electrons as well as ions, and they both
participate now in the current, and the charge can flow away
from the electroscope through the earth, because the
conductivity now is so much higher.
I stop again, and it stops.
You see in front of your eyes how important the temperature
is, in this case, the presence of the ions in the
air. If I have clean,
distilled water -- I mean, clean water.
I don't mean the stuff that you get in Cambridge,
let alone did I mean the stuff that is in the Charles River,
I mean clean water, that has a pH of seven.
That means one out of ten to the seven of the water molecules
is ionized, H plus and O H.

Minus.
The conductivity, by the way, is not the result
of the free electrons,
but is really the result of these H plus and O H minus ions.
It's one of the cases whereby not the -- the electrons are
maj- the major responsibility for the current.
If I have add three percent of salt, in terms of weight,
then all that salt will ionize, so you get sodium plus and C L
minus ions, you increase the number of ions by an enormous
factor. And so the conductivity will
soar up by a factor of three hundred
thousand, or up to a million, because you increase the ions
by that amount. And so it's no surprise then,
for you, that the conductivity of seawater is a million times
higher -- think about it, a million times higher -- than
the conductivity of distilled water.
And I would like to give you the number for water --
so this is distilled water  -- that is about two times ten to
the fifth ohm-meters. There is another way that I can
That is the resistivity, two times ten to the five
oh-meters.

I have here,
a bucket of distilled water. I'll make a drawing for you on
the blackboard there. So here is a bucket of
distilled water, and in there,
is a copper plate, and another copper plate,
and here is a light bulb, and this will go straight  to
the outlet [wssshhht], stick it in,
hundred ten volts. This light bulb has eight
hundred ohm resistance when it is hot.
You see the light bulb here.

You can calculate what this
resistance is between the two plates, that's easy,
you have all the tools now. If you know the distance,
it's about twenty centimeters, and you know the surface area
of the plates, because remember,
the resistance is inversely proportional with A,
so you have to take that into account -- and you take the
resistivity of water into account, it's a trivial
calculation, you can calculate what the resistance is of this
portion here. And I found that this
resistance here is about two megaohms.
Two million ohms. So, when I plug this into a
wall, the current that will flow is extremely low,
because it has to go through the eight hundred ohms,
and through the two megaohms.

So you won't see anything,
the light bulb will not show any
light. But now, if I -- put salt in
here, if I really manage to put three percent in weight salt in
here, then this two megaohm will go down to two ohms,
a million times less. So now, the light bulb will be
happy like a clam at high tide, because two ohms here,
plus the eight hundred, the two is insignificant.
And this is what I want to -- to demonstrate to you now,
the enormous importance of
increasing ions. I increased ions here by
heating the air, now I'm going to increase the
ions by adding salt.

And so the first thing that I
will do is, I will stick this in here.
There's the light bulb. And I make a daring prediction
that you will see nothing. There we go.
Nothing. Isn't that amazing?
You didn't expect that, right?
Physics works.

You see nothing.
If I take the plates out, and touch them with each other,
what will happen? There you go.
But this water has such a huge resistance that the current is
too low. Well, let's add some -- not
pepper -- add some salt. Yes, there's salt in there.
It's about as much as I would put on my eggs in the morning --
stir a little -- ah, hey, look at that.
Isn't that amazing? And when I bring them closer
together, it will become even brighter, because L is now
smaller, the distance is smaller.
I bring them farther apart, it's amazing.
Just a teeny, weeny little bit of salt,
about as much as I use on my egg, let alone -- what the hell,
let's put everything in there -- that's a unintelligible I put
everything, then, of course, you go almost down
to the two ohms, and the light bulb will be just
burning normally. But even with that little bit
of salt, you saw the huge difference.
My body is a fairly good conductor -- yours too,
we all came out of the sea -- so we are almost
all water -- and therefore, when we do experiments with
little charge, like the van der Graf,
being a student, then we have to insulate
ourselves very carefully, putting glass plates under us,
or plastic stools, to prevent that the charge runs
down to the earth.

In fact, the resistance,
my resistance between my body and the earth is largely
dictated by the soles of my shoe,
not by my body, not by my skin.
But if you look at my soles, then you get something like
this, and it has a certain thickness, and this,
maybe one centimeter. This, now, is L in my
calculation for the resistance, because current may flow in
this direction, so that's L.
Well, how large is my foot? Let's say it's one foot long --
no pun implied -- and let's say it's about ten centimeters wide.
So you can calculate what the surface area A is,
you know what L is, and if you know,
now what the resistivity is for my sole, I can make a rough
guess, I looked up the material, and I found that the
resistivity is about ten to the tenth.
So I can now calculate what the resistance is in this
direction. And I found that that
resistance then, putting in the numbers,
is about ten billion ohm. And you will say,
"Wow!" Oh, it's four, actually.
Well, big deal.

Four billion ohm.
So you will say, "That's enormous resistance!"
Well, first of all, I'm walking on two feet,
not on one, so if I would be standing one the whole lecture,
it would probably be four billion, but if I have two feet
on the ground, it's really two billion,
you will say, "Well, that's still extremely
large!" Well, it may look large,
but it really isn't, because all the experiments
that we are doing here in twenty six one hundred,
you're dealing with very small amounts of charge.
Even if you take the van der Graff -- the van der Graff,
say, has two hundred thousand volts -- and let's assume that
my resistance is two times ten to the nine ohms,
two feet on the ground. So when I touch the van der
Graff, the current that would flow,
according to Ohm's Law, would be hundred microamperes.
That means, in one second, I can take hundred
microCoulombs of the van der Graff, but the van der Graff has
only ten microCoulombs on in. So the resistance of four
billion or two billion ohms is way too low for these
experiments that we have been doing in twenty six one hundred,
and that's why we use these plastic stools,
and we use these glass plates in order to make sure that the
current is not draining off the  the
charge that we need for the experiments.
I want to demonstrate that to you, that, indeed,
even with my shoes on -- that means, even with my two billion
ohm resistance to the ground -- that it will be very difficult
for me, for instance, to keep charge on an
electroscope. I'm going to put charge on this
electroscope by scuffing my feet.
But, since I keep my -- I have my shoes on, I'm not standing on
the glass plate, the charge will flow through
me.

You can apply Ohm's Law.
And you will see that as I do this -- I'm scuffing my feet now
-- that I can only keep that electroscope charged as long as
I keep scuffing. But the moment that I stop
scuffing, it's gone. Start scuffing again,
that's fine, but the moment that I
stop scuffing, it goes off again.
Even though this resistance is something like two billion ohms.
Let alone if I take my shoes off.
I apologize for that. If now I scuff,
I can't even get any charge on the electroscope,
because now, the resistance is so
ridiculously low, I don't even have the two
billion ohms, I can't even put any charge on
the electroscope.

It's always very difficult for
us to do these experiments unless we
insulate ourselves very well. And if, somehow,
the weather is a little damp, we can very thin films of water
onto our tools, and then the current can flow
off just through these very thin layers of water.
That's why we always like to do these experiments in winter,
so that the conductivity of the air is very low,
no water anywhere. Here you see a slide of a
robbery. I have scuffed my feet across
the rug, and I am armed with a static charge.
Hand over all your money, or I'll touch your nose.
This person either never took eight oh two,
or he is wearing very, very special shoes.
See you on Wednesday..

Labels: CURRENT

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