Video Transcript
In this video, we will learn what
electric potential difference is and how an electric potential difference across a
component in a circuit creates a current in that component. We’re going to see that electric
potential difference involves doing work on electric charges.
Say that we start out with these
two objects. They could be anything. They could be marbles or Ping-Pong
balls or balloons. But the important thing about these
objects is that each one has an electric charge. Remember that there are two types
of electric charge. There’s positive charge and
negative charge. And what we’re going to say is this
object on the left has a positive charge, and the one on the right has a negative
electric charge.
Any time an object has an electric
charge, that means it exerts a force on any other object that also has an electric
charge. This means that each of our objects
will exert a force on the other object. We can tell what sort of force this
will be because these two objects have different or opposite electric charges. Objects with opposite electric
charge attract one another. The red object will be pulled to
the right and the blue object to the left. So the objects will get closer
together. And in fact, they’ll continue
moving toward one another until they meet. In order to stop this from
happening, to keep the charges in place or even to move them farther apart from one
another, we would need to exert a force on these charges. That force would need to be at
least as strong as the force that pulls the charges together.
Now, say that we did that, say that
we push on each one of these objects with a force, we’ll call 𝐹, that is strong
enough so that the objects do move apart. By doing this, we’ve done what is
called work on these two objects. In physics, this word work has a
very specific meaning. It’s equal to the force we exert on
some object multiplied by the displacement or movement of that object. Because we exerted a force on both
our positively charged and negatively charged objects and we made those objects move
because of that force, we did work on them. This all relates closely to
electric potential difference. Any time we do work, where that
work is spread over some amount of electric charge, then we have created electric
potential difference.
Electric potential difference is a
long-sounding phrase, but now we know what it means physically. Given a group of objects with
electric charge, say, these two objects here, we create electric potential
difference when we do work on those charges. This equation shows us how we can
get more or less electric potential difference. Working with these two objects, we
can increase their electric potential difference by doing more work on them. That could mean applying this force
𝐹 for a longer time so that the charges move farther and farther apart. This means if we wanted to decrease
the electric potential difference of these charges, we could of course do less work
on them. In that case, they would end up
closer together rather than farther apart.
We see though that something else
that affects electric potential difference is the amount of charge involved. If we, say, increased the amount of
charge on each of these two objects while we kept the work done on the charges the
same as it was before, then overall we would decrease their electric potential
difference. This idea of electric charges being
separated by work is actually behind what makes charges flow in an electric
circuit.
Imagine that we have a chunk of
metal sitting on our desk. If we looked very, very closely at
this metal block, we could see the atoms that make it up. Here, each red dot represents the
nucleus of an atom. This nucleus has an overall
positive charge, and each little blue dot represents an electron. These have negative electric
charge. So all throughout this metal block,
we’ve got a bunch of objects with positive and negative electric charges. Just like before, when we only had
two charged objects, we can do work on these charges. Now, there’s a bit of a special
condition here. Because we’re working with a piece
of metal, that means the positively charged nuclei are fixed in place. They can’t move. The electrons, on the other hand,
can move. They’re free to move all throughout
this block of material.
So if we start to do work on these
charges to push them apart, farther apart than they would naturally be, the red
dots, the nuclei, will stay fixed in place. But the blue dots, the electrons,
will start to move toward one end of this metal block. The charges in the metal will start
to look something like this. Notice that now there are many more
electrons near this end of the block and far fewer electrons over here. And again, this happened because
we’ve done work on these charges. Since we’ve done work over this
group of charges, that means there’s an electric potential difference from one end
of this block to the other. The way we got this separation of
charge so that mostly negative charge was over here and mostly positive charge was
here was by exerting a force on these charges.
If we stopped exerting that force,
then all these negative charges would go back to the way they were before, evenly
spread out throughout this block. But, say, instead we maintain this
electric potential difference. That is, we keep pushing on the
negative charges toward the right side of the block. Even though they’re attracted to
the overall positive side on the left, we don’t let them move that way because of
the forces we exert. Set up this way, this block of
material is like a cell or a battery. The purpose of a cell in an
electric circuit is to supply an electric potential difference. We’ve said that the negative
charges at this end of our cell are naturally attracted to the positive charges at
this end but that they can’t move that way so long as we maintain this electric
potential difference.
Now, say that we take a bit of wire
attached to a light bulb and we fasten the ends of the wire to the ends of our cell
like this. The negative charges at this end of
our cell, which all repel one another, now have a pathway to travel to get towards
the positive end of the cell. The negative electrons will flow
out this way. The wire itself already has
electrons in it. And the movement of electrons from
the cell will push them along the wire, causing the bulb to light up and charge to
flow all through the circuit as it moves toward the positive end of the cell. This flow of electrons is called
electric current.
Any time there’s an electric
potential difference across an electric circuit, charge will flow. There will be current. The amount of current depends, in
part, on the amount of electric potential difference. Electric potential difference is
measured in units called volts. A small cell or battery, for
example, might provide 1.5 volts of potential difference. The way our cell here is set up,
we’ve seen that the end of the cell with an overall negative charge is here. This is called the negative
terminal of the cell. Likewise, this end here, which has
mostly positive charges, is called the positive terminal.
We can represent a cell using
something called a circuit symbol. A cell with its positive terminal
on the left and its negative terminal on the right would be symbolized this way. Notice that the shorter line
corresponds to that negative terminal. Likewise, there’s a circuit symbol
for a bulb. That looks like this. It’s a circle with two diagonal
lines making a cross. When we connect these circuit
symbols using straight lines, we’re saying they’re all joined in one continuous
circuit. So here is our cell with its
positive terminal on the left, here is our bulb, and here is wire connecting the
cell and bulb. Because the cell creates an
electric potential difference across the bulb, electric charge flows through it.
Knowing all this, let’s look now at
a few examples.
The picture shows an electron that
is near to an atomic nucleus. Do the atomic nucleus and the
electron attract or repel one another?
In our picture, we have two
objects: an atomic nucleus and an electron. Our question is asking whether the
nucleus and electron attract or repel one another. This implies that there’s some
force between them. These two objects will have a force
between them if they both have an electric charge. Indeed, that’s the case. An electron has a negative electric
charge, while an atomic nucleus overall has a positive electric charge. Since both objects are charged,
there will be a force between them. What’s more, we know that these
objects have opposite electric charges. Whenever two objects have opposite
electric charges, they attract one another. There will be a force on the
nucleus toward the electron and a force on the electron toward the nucleus. In answer to this question then, we
write that the nucleus and the electron attract each other.
Let’s look now at part two of this
example.
Which of the following statements
is true? (A) The electron can be moved
farther away from the nucleus without doing any work. (B) In order to move the electron
farther away from the nucleus, work must be done on the electron.
We’ve seen from the first part of
this question that there’s an attractive force between the nucleus and the
electron. This force will tend to make the
electron and nucleus move closer together. In this part of our question,
though, we’re imagining moving the electron farther away from the nucleus. To do that, we would need to exert
some force that would overcome this attractive force, drawing the electron and
nucleus together. So we need to exert a force on the
electron, and this force is what would cause it to move farther away. Since we’re exerting a force on the
electron over some distance, that means we’re doing work on it. If we didn’t do any work on the
electron, there’s no way it could move farther from the nucleus. And so we choose answer option
(B). In order to move the electron
farther away from the nucleus, work must be done on the electron.
Let’s look now at another
example.
A cell does work on the charges
within it to create a separation of charge across its two terminals. Complete the following sentence:
The potential difference provided by the cell is equal to the blank divided by the
blank. (A) Amount of charge that has been
separated, amount of work done. (B) Amount of charge that has been
separated, distance between the terminals. (C) Amount of work done, amount of
charge that has been separated. (D) Amount of work done, distance
between the terminals.
Knowing that we’re working here
with a cell, let’s clear some space at the top of our screen and consider what’s
happening in this cell. This cell contains electric
charges. It has positive charges, we’ve
shown them here in red, arranged in an orderly grid. And it also has negative charges
here in blue. These charges are able to move
throughout the cell. We’re told that the cell does work
on these charges to separate them. This means it exerts forces on the
charges and causes them to move. We mentioned that the red charges,
the positive ones, are fixed in place, but the blue negative charges can move. So this force will make the blue
negative charges concentrate at one end of the cell.
For that reason, this end of the
cell is called its negative terminal. And that means the other end, where
there are more positive than negative charges, is the positive terminal. So the cell has done work on the
charges within it to create a charge separation. This separation of charges means
there’s now a potential difference across the cell.
We want to know which of our four
answer options best describes this potential difference by filling in the gaps in
our sentence. The first thing we can say about
this potential difference is that it depends on the amount of work that was done to
separate the charges in the cell. The greater the amount of work, the
more negative charges would tend toward the negative terminal, and therefore the
larger the potential difference would be. Now, notice that our sentence is
describing a fraction. Whatever goes in the first blank is
being divided by whatever goes in the second blank. We can think of this sentence in
fact as being similar to a mathematical equation for potential difference.
Clearing just a bit more space
still, we can write that that equation would go like this. The potential difference provided
by the cell, we’ll call it PD, is equal to whatever goes in the first blank of our
sentence divided by whatever goes in the second blank. A moment ago, we noted that the
more work was done on the charges in the cell, the greater the potential difference
across the cell would be. And that tells us what must go in
the first blank in our sentence. The amount of work done by the cell
must be in the numerator of this fraction. Looking over our answer options, we
see that only options (C) and (D) have the amount of work done going in that first
blank.
Right away then, we can eliminate
options (A) and (B) from consideration. Options (C) and (D) are different
in what they suggest for completing the second blank. Choice (C) gives the amount of
charge that has been separated. Option (D), on the other hand,
describes the distance between the terminals, that is, the physical distance between
the positive and negative terminals of our cell.
Now, let’s think for a moment about
work as it applies in physical situations. The work done on an object, say,
one of these charges in the cell, is equal to the force exerted on that charge
multiplied by the distance the charge travels. In other words, the distance these
charges move is already included in this idea of work. We don’t need to take that distance
into account again, as option (D) suggests. If, instead of distance, we put
charge in the denominator of this fraction, then we see that for some fixed amount
of work done on the charges, more charge having to be separated means that fixed
amount of work doesn’t separate the charge very much. And that means that the potential
difference is not so great.
On the other hand, for a smaller
amount of charge, a fixed amount of work can push those charges relatively farther
apart from one another. Fewer charges to separate then
means a greater potential difference again for a given amount of work done. It does make sense then that work
would go in the numerator of this fraction and charge in the denominator. For our answer then, we choose
option (C). The potential difference provided
by the cell is equal to the amount of work done divided by the amount of charge that
has been separated.
Let’s finish this lesson by
reviewing a few key points. In this video, we learned that
electric potential difference, sometimes called potential difference for short,
equals the work done to separate electric charges divided by the amount of charge
that is separated. And we saw also that electric
potential difference across a component in a circuit creates current in that
component. Lastly, we learned that electric
potential difference is measured in units of volts, abbreviated capital V. This is a summary of electric
potential difference.
