In this explainer, we will learn how to calculate the total emf of a set of cells that are connected in series.

A cell is a power source, which provides electrical energy to a circuit.

The diagram below shows the symbol used to represent a cell in a circuit diagram. The symbol consists of two vertical, parallel lines. One of the lines is shorter and thicker than the other.

Each line represents a terminal of the cell. A terminal is a point where the cell is connected to the rest of the circuit. A cell has two terminals: one positively charged terminal and one negatively charged terminal. The longer, thinner line always represents the positive terminal. The shorter, thicker line always represents the negative terminal.

A cell introduces an electric potential difference to the circuit. The potential
difference across a cell is also known as the **electromotive force** of the
cell. The phrase βelectromotive forceβ is often shortened to
βemfβ. The emf of a cell is equal to the potential difference
across the cell and is measured in units of
volts,
V.

Despite its name, the emf of a cell is not actually a force. The emf is a measure of how much energy the cell transfers per unit of charge passing through it. Cells transfer energy to the charges, allowing them to flow around the circuit. So, the emf of a cell can produce a current in a circuit.

We can connect multiple cells together. One way to do this is to connect them
**in series**. This means that the cells are directly connected, one after
another.

Usually, when cells are connected in series, every cell is aligned the same way. This means that the positive terminal of one cell must be connected to the negative terminal of another cell.

This is shown in the diagram below. The diagram shows two cells, connected in series. The cells are aligned the same way, because the positive terminal of the cell on the left-hand side is connected to the negative terminal of the cell on the right-hand side.

Note that cells can be connected in series, even if they are not aligned the same way. Cells can be connected such that they are aligned in opposite directions, with the positive terminal of one cell connected to the positive terminal of another cell. However, this is less common.

For the rest of this explainer, we will only consider cells that are connected in series and are aligned the same way.

### Example 1: Identifying Cells in Series

Which of the following diagrams shows three cells connected in series?

### Answer

The answer is B.

In diagram B, every cell is aligned the same way, with the positive terminal of one cell connected to the negative terminal of the next. Hence, these cells are connected in series.

Diagram A shows a different way of connecting cells, which is called connecting cells in parallel. Each cell is oriented the same way, with the positive terminal on the right and the negative terminal on the left, so we might think that these cells are aligned with each other. However, the terminals of these cells are not connected in series.

If we follow the wires from one cell to the next, we can see that the positive terminal of one cell is connected to the positive terminal of another. Similarly, the negative terminal of one cell is connected to the negative terminal of another.

This means the cells are not connected in series. For cells to be connected in series, the positive terminal of one cell must be connected to the negative terminal of another cell.

We can connect cells in series to make a battery. A battery is simply two or more cells, connected in series.

The circuit symbol for a battery shows two cells, connected in series. The connection between the cells is represented by a dashed line. Although only two cells are shown in the circuit symbol, a battery can consist of more than two cells.

The diagram below shows the circuit symbol for a battery.

### Example 2: Identifying the Circuit Symbol of a Battery

Which of the following is the correct circuit symbol for a battery?

### Answer

The answer is B.

Diagram B shows a battery. The cells are connected in series, with the positive terminal of the first cell connected to the negative terminal of the next. There is a dashed line representing the connection between the cells. Hence, this is the symbol for a battery.

Diagram A shows a single cell. Diagram C shows a filament bulb. Diagram D shows a switch, and E shows a resistor.

We have already said that a cell provides an emf to a circuit. When cells are connected in series, the emf provided to the circuit is equal to the sum of the emfs of the individual cells. So, if we know the emf of each cell, we simply add them up to find the total emf provided to the circuit.

To understand this, recall that each cell transfers energy to the charges in the circuit. The emf of each cell is a measure of how much energy that cell transfers to each charge. When cells are connected in series, a charge flows around the circuit, and it receives a transfer of energy from each cell in turn. To calculate the energy received by a charge, we add up the energy transferred by each cell.

Hence, to calculate the total emf provided to the circuit, we add up the emfs of each cell.

### Example 3: Calculating the Total emf of Cells in Series

The diagram shows three cells connected in series. What is the total emf provided by the cells?

### Answer

When cells are connected in series, the emf provided to the circuit is equal to the sum of the emfs of each individual cell.

This diagram shows three cells, with emfs of 3 V, 6 V, and 2 V. To find the total emf provided by the cells, we add up the emfs of the three individual cells:

Hence, the total emf provided to the circuit is 11 V.

### Example 4: Calculating the Total emf of Cells in Series

The diagram shows three cells connected in series. The total emf provided by the cells is 8 V. What is the emf provided by the third cell?

### Answer

When cells are connected in series, the emf provided to the circuit is equal to the sum of the emfs of each individual cell.

We know that the total emf provided by these cells is 8 V, and that the first two cells provide emfs of 4 V and 3 V. Let us call the emf provided by the third cell .

Hence, we know that the following equation must be true:

This simplifies to which we can rearrange to find

Hence, the emf provided by the third cell must be equal to 1 V.

### Example 5: Calculating the Total emf of Cells in Series

The diagram shows four identical cells connected in series. The total emf provided by the cells is 8 V. What is the emf provided by one cell?

### Answer

The four cells are identical. This means that each cell provides the same emf to the circuit.

Let us denote the emf of a single cell as .

The total emf provided by the cells is 8 V. We have four cells connected in series; hence,

This simplifies to which we can rearrange to find

Hence, the emf provided by one cell is 2 V.

We already know that a battery is two or more cells connected in series. Hence, the emf provided by a battery is equal to the sum of the emfs provided by the cells in the battery. We can calculate the emf provided by a battery by adding up the emfs of the cells it contains. This is exactly the same as calculating the total emf provided by any set of cells that are connected in series.

Let us now summarize what has been learned in this explainer.

### Key Points

- A cell is a power source, and it provides an electromotive force to a circuit.
- The electromotive force of a cell is not actually a force. It is a measure of how much energy the cell transfers to the charges in the circuit.
- A cell has a positive terminal and a negative terminal.
- Cells can be connected in series. This means that the positive terminal of one cell is connected to the negative terminal of the next.
- When cells are connected in series, the total emf provided to the circuit can be found by adding up the emfs of all the individual cells.
- A battery is two or more cells connected in series.