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.