Lesson Video: The Electric Potential Difference Provided by Cells Science

In this video, we will learn how to calculate the potential difference provided by a cell based on the amount of work it does to separate charge.

14:26

Video Transcript

In this lesson, we will learn how the electric potential difference of a cell is caused by the separation of charges inside the cell. We will then learn how to calculate this electric potential difference based on the amount of work done to separate those charges.

Let’s start by recalling that when it comes to electric charge, two objects with the same sign of electric charge, both positive or both negative, will repel each other, while two objects with opposite charges, one negative and one positive, will attract each other. In terms of forces, we would say that the electric force pushes apart like charges and pulls together unlike charges.

Now let’s think about what would happen if we wanted to move these charged objects. In particular, let’s think about what would happen if we wanted to move together two objects with like charge. Since there is already an electric force pushing these objects apart, trying to move them together would be moving them against this force. And doing that requires energy. This is similar to a ball sitting on the surface of the earth. The force of gravity pulls the ball downward. So lifting the ball up off the surface of the earth requires energy because we’re moving it against the force of gravity.

On the other hand, if we were to drop a ball above the surface of the earth, the ball would naturally fall straight down. In fact, this situation of lifting the ball off the surface of the earth is exactly analogous to two objects with unlike charge. These two objects are attracted to each other, so trying to move them apart is moving them against the direction of the electric force and therefore requires energy. What we see is that in both of these cases, moving the objects against the direction of the electric force requires us to put energy into the system to oppose that force.

This energy is called work. In particular, if there’s some force acting on an object, then the amount of work done is the amount of energy spent moving the object in the opposite direction to the force or gained moving the object in the same direction as the force. For the rest of this lesson, we will primarily focus on separating objects of opposite charge. So the fact that we need is that separating charges takes work.

Not only does it take work to separate a positive and a negative charge because of the attractive forces between them, separating these charges creates a potential difference. Now it turns out that potential difference is closely related to the energy of a system. And as we know, separating charges requires work. And work is another way of thinking about the change in the energy of a system. So because separating charges both requires work and creates a potential difference, we might expect that there is a relationship between work and potential difference.

And indeed there is such a relationship. The potential difference created by separating charges is exactly equal to the work done to separate the charges divided by the total amount of charge that was separated. As a formula, we can write 𝑉, the potential difference, is equal to 𝑊, the work done to separate the charges, divided by 𝑄, the total charge that was separated. Appropriate units for these quantities are volts for potential difference, joules for work, and coulombs for charge.

We are now ready to understand how cells get their potential difference from a separation of charges and how this separation of charges drives current in a circuit. We’ll start with a simplified scenario and build up to a full circuit.

We have two identical boxes. And inside of each box are several atoms. The positively charged nuclei of the atoms are represented by large red dots, and the negatively charged electrons are represented by small blue dots. Initially, both boxes have the same number of atoms and therefore the same amount of positive and negative charge. Since the net charge in each box is the same, there is no separation of charges and therefore no potential difference.

Let’s now move some electrons from the box on the left to the box on the right. If the net charge inside of both boxes was initially zero, then moving some electrons from the left to the right would result in a net negative charge on the right side and a net positive charge on the left side. In other words, we have created a charge separation between the two boxes and therefore created a potential difference between them. Let’s now open a path so that electrons can flow freely between these two boxes.

Now that electrons can flow freely between these two boxes, the net negative charge inside the right-hand box will tend to push out electrons, while the net positive charge inside the left-hand box will tend to pull in electrons. So let’s watch what happens. Look what’s happening. The separation of charges is resulting in electric forces that are pulling electrons from the side with a net negative charge towards the side with a net positive charge. Now remember, whenever there is a separation of charges, there is also a potential difference. And because this potential difference results in forces that cause the electrons to move, we often call potential difference electromotive force. We often abbreviate electromotive force as emf. And it is a term that we will most commonly use when talking about potential difference in circuits.

Returning to our moving electrons, if we wait long enough, eventually all of the extra electrons will move from the area with a net negative charge to the area with a net positive charge. When this happens, the electrons will stop moving between the two sides because the charge will be balanced. In other words, there is no longer a separation of charge between these two boxes.

Now in electronic circuits, the electron path that we talked about is often a simple metal wire, which is a conductor and therefore allows charge to flow freely. So what we have learned is that when charges can be exchanged between the two sides of a separation of charge, for example, if those two sides are connected by a conductor, then eventually the charge separation will be reduced to zero and there will be no more charges moving. We now have everything we need to understand how cells and batteries provide electromotive force in electronic circuits.

In a cell or a battery, there are extra negative charges at the negative terminal and extra positive charges at the positive terminal. In other words, inside of a cell, there is a separation of charges. And we can see this visually in our real-life diagram of a cell on the left and the circuit symbol for a cell that we’ve drawn on the right. And as we’ve seen, this separation of charges results in an emf which can be calculated from the work required to separate the charge divided by the total amount of charge that was separated.

Now initially, the charged particles are kept separated because they cannot move within the cell itself. However, when we connect the two sides of the charge separation with a series of conductors, either wires or other circuit components, it doesn’t matter how roundabout this path is; the charge can move from one side of the cell to the other. Remember that current is a collection of moving charges. So the current in a circuit is the charges from one side of the charge separation inside of the cell moving to the other side of the charge separation.

Now when one of these charges, say a negative charge, makes it to the positive side of the cell, some of the positive charge combines with this negative charge to form an electrically neutral unit. And the result is a smaller charge separation overall in the cell. But a smaller charge separation overall means a decrease in electric potential difference. So whenever there’s current in the circuit, over time the charge separation inside the cell is reduced, and the cell’s emf decreases.

Finally, we know that when charge flows from one terminal of the cell through the bulb to the other terminal of the cell, the bulb will light up. We are now in a position to understand the source of the energy required to light this bulb. Remember that to create the initial potential difference inside the cell, we had to separate charges, which took work, because we had to spend energy to move the charges against the attractive electronic force. But because work was done on the charges initially to separate them, when the charges come back together, they can do work on other things.

And this is exactly what happens in our circuit. The work done by the charges coming back together provides the energy that lights our light bulb. In fact, we can think about electronic circuits as recycling the work used to initially create the potential difference of the cell into the work needed to perform other useful tasks.

Now that we know how the potential difference provided by a cell is related to the charge separation inside the cell, let’s work through some examples.

The picture shows electrons and atomic nuclei in a piece of material. The electrons cannot flow along the material. The blue circles represent the electrons and the red circles represent the atomic nuclei. Part one, at which end of the material is there a build up of electrons. Part two, fill in the blank. The buildup of electrons at one end of the material creates a blank along the piece of material. (a) Electric current, (b) electric potential difference.

We are told that in this picture here, the red circles represent atomic nuclei and the blue circles represent electrons. Our first task is to determine which end of this material has a buildup of electrons. That is, which end of the material has more electrons than the other. Looking at the picture, we can see that there are many more blue circles at the right-hand end of the material than there are at the left-hand end. But since blue circles represent electrons, we can see that there is a build up of electrons at the right-hand end.

To address the second question, recall that a separation of charges creates a potential difference. Looking back at the picture, since there are more electrons than there are nuclei at the right-hand end, there is a net negative charge at this end. And at the left-hand end, there are more nuclei than there are electrons. So there is a net positive charge. So the build up of electrons result in a charge separation, which creates a potential difference. And electric potential difference is the answer that we’re looking for.

We also know that our other choice, electric current, cannot be correct because, as we are told, the electrons cannot flow along this material. And by definition, an electric current is a flow of charges. So since charges cannot flow, electric current cannot be the correct answer.

In this example, we used our qualitative understanding of the relationship between potential difference and charge separation. In our next example, we will use our quantitative understanding of this relationship.

A cell does 20 joules of work to separate four coulombs of charge. What potential difference does this create across the terminals of the cell?

This question asks us to calculate a potential difference. The information we are given is how much work it took to separate an amount of charge. Given what we are looking for and what we have to work with, we can recall a formula that relates all three of these quantities. The formula we need tells us that the potential difference across the terminals of a cell is equal to the work done to separate the charge divided by the total amount of charge that was separated.

When we substitute 20 joules for the work and four coulombs for the charge, we have that the potential difference is 20 joules divided by four coulombs. Now, to figure out what value this is as a potential difference, we first divide 20 by four, which is five. And then we notice that the units in the numerator are joules and the units in the denominator are coulombs. Whenever we have a numerator with units of joules divided by a denominator with units of coulombs, the units of the final quantity are volts. So the potential difference that we are looking for is five volts.

Alright, now that we’ve worked through some examples, let’s review what we’ve learned in this lesson. We first learned that a separation of charges creates a potential difference. And when this is the potential difference of a cell, we often call it an electromotive force or emf.

We also learned that as charges move freely along conductors, they eventually balance out all charge separations and reduce them to zero. This also explains why cells eventually stopped working. The current in a circuit powered by a cell is the flow of charge along the circuit from one terminal of the cell to the other. And this flow of charge eventually reduces the charge separation inside the cell to zero. And when there is no charge separation inside the cell, there is also no emf to provide to the circuit.

Finally, we learned how to use the formula 𝑉 equals 𝑊 divided by 𝑄 to calculate the potential difference across the terminals of a cell from the work done to separate the charge inside the cell and the total amount of charge that was separated.

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