Welcome back. 
Again, I'm Nathan Parrish and this is 
Linear Circuits. 
Today we're going to be talking about 
voltage. 
The aims of this class are to allow us to 
modify voltages to reflect voltage 
references, to describe how a chemical 
battery works, and then to identify if a 
battery is charging or discharging. 
From our previous class, we talked a 
little bit about charge and current as 
well as electric fields, the way that 
these charges interact with each other. 
We've also looked at current as being the 
flow of charge. 
And so the way that this, kind of, fits 
in is we've already talked about charge 
and current, today we talk about voltage 
which does have some impact on charge and 
current. 
Next time we'll talk about power and 
energy and then we go on and we'll 
actually look at some actual diagrams. 
The lesson objectives today, first of 
all, we want to calculate voltage from 
the energy gained or consumed as a charge 
moves through an electric field. 
We want to be able to correctly specify 
voltages as reference directions change. 
We want to describe the operation of a 
chemical battery. 
And identify battery is charging or 
discharging based upon the direction that 
the current is flowing and the references 
on the battery. 
So, first of all let's kind of describe 
what voltage is and give a definition for 
it. 
If I take a charge and I move it through 
an electric field, like this, there is a 
voltage. 
And the way that we measure that voltage 
is by calculating the amount of energy, 
that is either gained or lost as the 
charge moves through the electric field, 
and then taking that as the ratio of the 
amount of charge that was moving. 
So if this is one coulomb of charge, that 
is going from the top to the bottom, and 
in so doing it consumed one joule of 
energy then we take 1 joule divided by 1 
coulomb , giving us 1 volt. 
And the variable you're going to use for 
voltage is a v. 
It's measured in units of volts, which is 
named after Alessandro Volta, who was one 
of the first people to study batteries. 
It also turns out that you can do this 
the opposite way, if we have a charge 
that is going backwards through and 
electric field, what it's going to be 
doing is generating energy. 
And so now it's generating one joule of 
energy, and if it's one coulomb of charge 
that is doing it, again one volt from the 
bottom to the top. 
But where does this voltage come from? 
What is the origin of it. 
Voltage is essentially coming from these 
electric fields that we talked about. 
And these electric fields are established 
because of a difference in density of 
charge. 
So, if we look at this example, we have a 
whole bunch of negative charges all 
clumped up together, and when we do that, 
they have a tendency to try and pull all 
positive charges towards them. 
So if I introduce a positive charge to 
the system, this positive charge is going 
to be sucked up by that big collection of 
negative charges. 
Now, if we instead take all of these 
negative charges and distribute them 
evenly throughout the material, our 
electric field goes away. 
It's only by a difference in the charge 
density that we establish this voltage. 
Now, we're going to back and shove them 
all back together and reestablish our 
electric field again. 
Now when we're talking about voltage, 
reference is very important. 
If somebody says oh, well it's at 1,000 
volts. 
Well, 1,000 volts with reference to what? 
Could be anything. 
It's kind of similar to if you wanted to 
measure how tall a man was. 
Now you might say this man is six feet 
tall. 
But generally what we're going to be 
doing is measuring from the bottoms of 
his feet to the top of his head. 
But if he happened to be a mountain 
climber you could just as easily say that 
this man is 10,000 feet tall, if we were 
measuring from the sea, sea floor to the 
top of his head we might get a very 
different value. 
So keep the reference instructions is 
very important, anytime you see a voltage 
you should be asking yourself. 
With reference to what? 
And so, if we flip the reference 
direction. 
If we decided, instead, to measure a man 
from the top of his head to the bottom of 
his feet. 
We might get negative six feet. 
And that's just fine. 
But the important thing is, we're 
consistent. 
We know what our reference is with 
reference to. 
And so the way we do that in si-, in our 
diagrams, is, we'll use a minus sign. 
To say what the bottom is, and the plus 
sign to say where the top is. 
Now if I flip the bottom and the top 
signs, so the plus is now at the bottom 
and minus is now at the top, you take 
whatever voltage you have and you flip 
its direction. 
Because the field inside of the device 
hasn't changed, just what we're 
referencing, and our direction. 
So let's actually do a problem, to 
practice this. 
In this problem, we have, four points. 
And we want to know, the value, of the 
voltage v. 
And it has its references labeled as 
well. 
Here, we have a minus here, same where 
the bottom is, and a plus here, where the 
top is. 
So to do this, we have, some, identified 
voltages here, here, and here. 
This is, this is three volts, this 
negative six volts, and this is negative 
four volts. 
So let's work our way around. 
This is a minus and this is a plus, and 
this is three volts. 
So from this point to this point, we've 
gone up three volts. 
This is a minus and this is a plus. 
This is a minus 6 volts. 
So from this point to this point we've 
gone down 6 volts. 
So up three and down six means overall 
we've gone down three. 
Now here's a plus and here's a minus, and 
this is minus four volts. 
And this is the same thing as if this 
were a minus, and this were a plus, and 
this was a positive four volts. 
So from here to here, we've actually gone 
up four volts. 
So we go up three, down six and up four. 
Which means from here to here, we've 
actually gone up one. 
And so this is a way that we can find 
voltages, by taking a look at other 
voltages and just adding them together. 
So now we've specified our reference 
directions, and we've combined them in a 
way that makes sense. 
Now let's look at an actual application 
of voltage being generated, and see how 
it works in an actual application. 
And this is an application that is still 
used today, lead-acid battery, you might 
be familiar with the way that these 
batteries operate in your vehicles, in 
your cars. 
For lead-acid battery, we have what's 
called a cathode here, and an anode here, 
when we are discharging current. 
So this arrow here is indicating that we 
see current flowing this direction. 
There's a kind of mnemonic device, acid, 
where anode, we have current into device, 
ACID, anode, current into device, so here 
we see the current flowing into the 
device. 
So that means this is going to be our 
anode. 
The battery is going to be labeled plus 
and minus, to let us know what the 
reference directions for the battery 
happen to be. 
And anytime you look at a battery you'll 
see that they're labeled appropriately. 
In lead-acid battery this negative 
terminal is just a pure lead bar, and 
then in this other terminal, the positive 
terminal, it's lead oxide. 
Inside of this middle area there is 
hydro-, or there's sulfuric acid and 
water. 
And what happens is the sulfuric acid in 
the water is spread out. 
So, we get these ions, that are kind of 
swimming in a soup. 
Now, when we're discharging a battery, 
what happens is we have some ions here, 
sulphide ion that's going to come over 
here to this lead bar. 
And it's going to combine, and this is in 
a reduction. 
Type of chemical reaction, and then in a 
reduction electrons are generated. 
And so these electrons are now able to 
flow. 
Well, they get pushed through, and 
remember the current's flowing this 
direction, so these electrons are going 
to be flowing against our traditional 
current flow. 
But when electrons hit this side it now 
makes an oxidation reaction possible. 
Because an oxidation reaction wants extra 
electrons for it to occur. 
So these two electrons are going to mix, 
then, with this lead oxide, some 
hydrogen, and some sulphate. 
And all together, we get two water atoms, 
or two water molecules. 
As well as some lead sulphate, that, is 
over here. 
So you notice that we now have lead 
sulphate on both sides. 
And this is what happens as the battery 
discharges. 
Now, if the battery continues to 
discharge, what will happen is these two 
plates are then going to be coated with 
this lead sulfate, and the battery dies. 
But what we're going to make sure is that 
we don't completely kill our battery. 
You might be aware, lead-acid batteries 
can recharge, and so we're going to take 
a look at that reaction next. 
But because of the electrons that are 
being generated over here and pushed over 
here, that's what's causing this 
displacement, this difference in charge 
density. 
And that's why a battery has a voltage. 
Well, let's learn what happens if we do 
it the other direction, if we're actually 
charging the battery. 
In this case, we still see that we have 
the lead sulfate on both plates. 
That are kind of coating the outsides. 
We have our water molecules still here. 
And then this soup of sulfuric acid and 
water. 
But if we take these two water out 
molecules and mix them over here, again 
we're going to be doing another oxidation 
or, another reduction reaction. 
Electrons are provided, and they go this 
way. 
And notice that our current is now 
flowing the opposite direction because 
electrons are going this way, from the 
anode to the cathode. 
And notice our anode and cathode have 
flipped places. 
Because current is going into the anode. 
And now the anode is going to be the plus 
terminal instead of the minus terminal of 
the battery. 
Now, these electrons that have come over 
here. 
We see the same reaction happening where 
we get a sulfate coming back into the 
soup this becomes pure lead again, and 
the battery goes back to its original 
configuration. 
And so that's how a battery work. 
So to emphasize some points, if we have 
our current going from the minus to the 
plus that means the battery is charging. 
If we have the current going from the 
plus to the minus, the battery is 
discharging. 
Now we can see that it's actually these 
chemical reactions that are happening 
within the battery to make this voltage 
happen and make batteries work. 
To summarize, charges create electric 
fields, and voltage is the amount of 
energy that's gained or released as 
charges move through an electric field. 
We also described how voltage originates 
from differences in charge density. 
And, we did a case study by looking at 
how lead-acid batteries work, and we 
emphasized that the direction of the 
current flow with reference to the two 
terminals let us know if the battery is 
charging or if the battery is 
discharging. 
So, for next class, we will take a closer 
look at this way that current and voltage 
interact. 
And we'll take a look at electric power 
and electric energy. 
And we'll do our first circuit analysis. 
Now I want to remind you about the 
forums, if you have any questions on the 
material that was covered in this class, 
please go to the forums and post there, 
it's the quickest way that you'll be able 
to get answers to your questions. 
And also go and help the other students. 
That they're taking this class and answer 
their questions if there is something 
that you understand. 
And so, we look forward to seeing you on 
the forums, as well as seeing you in the 
class next time. 
And until then, cheers.