# Lesson Explainer: Cells in Parallel Science

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

A cell can be used to transfer energy to an electric circuit. A cell connects to a circuit at its terminals. There are two terminals.

The figure shows the symbol used to represent a cell in a circuit diagram.

We see that the symbol consists of two vertical, parallel lines. Each line represents a terminal.

One terminal is the positive terminal. The longer, thinner line always represents the positive terminal. The shorter, thicker line always represents the negative terminal.

The positive terminal of a cell is positively charged, and the negative terminal of a cell is negatively charged.

The difference in charge of the terminals of a cell produces a potential difference across a circuit connected to the cell. The potential difference across a circuit due to a cell is also known as an electromotive force. Electromotive force can be written as emf.

A circuit contains many electrons. Electrons are negatively charged, and so they are repelled from the negatively charged terminal and attracted toward the positively charged terminal. The motion of the electrons is an electric current. A potential difference across a circuit therefore produces an electric current in the circuit.

A circuit in which there is only a single path between the terminals of a cell is called a series circuit. This is shown in the following figure.

A circuit can have multiple paths between the terminals of a cell. This is shown in the figure below.

The different paths from one terminal to the other terminal are the parallel branches of the circuit.

There can be a current between the terminals of the cell through either of the parallel branches.

Wires can be connected in parallel with each other. Cells can also be connected in parallel with each other.

Let us now look at an example of cells connected in parallel.

### Example 1: Identifying Cells Connected in Parallel

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

### Answer

Both diagrams show three cells that are connected together.

For the cells to be connected in parallel, there must be multiple paths from a terminal of one of the cells to the opposite terminal.

For option B, for each cell, there are no paths that connect one terminal of a cell to the opposite terminal of the same cell. These cells are not then connected in parallel.

For option A, the figure below shows that for any of the three cells, there are two paths that can be taken to connect the opposite terminals of that cell.

We see then that option A shows the cells connected in parallel.

The potential difference across a circuit connected to one cell is equal to the potential difference of that cell.

Cells connected in parallel across a circuit also produce a potential difference across the circuit.

The following figure shows three cells connected in parallel across a circuit.

The figure below shows how, for each cell, the circuit can connect the opposite terminals of each cell to each other.

Let us suppose that each cell has a potential difference of 1 volt, as shown in the following figure.

We can then see the potential difference across each path that connects the opposite terminals of a cell, as shown in the figure below.

We see that for each path, the potential difference across the path is 1 volt.

This means that for any path across the circuit, the potential difference across the path is 1 volt.

It is important to understand the potential differences of the cells are not added to each other.

Let us now look at some examples of the potential difference across a circuit connected to cells that are connected in parallel.

### Example 2: Determining the Total emf of Cells Connected in Parallel

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

### Answer

There are three paths through the circuit. Each path connects the opposite terminals of one of the cells. This is shown in the figure below.

We see that the potential difference across each path is 4 volts. This is the same as the emf of each cell.

This means that for any path across the circuit, the potential difference across the path is 4 volts, and the emf provided across the path is 4 volts.

This means that the total emf across the circuit that the cells provide is 4 volts.

### Example 3: Determining the emfs of Cells Connected in Parallel

The diagram shows three identical cells connected in parallel. The total emf provided by the cells is 6 V. What is the emf provided by each cell?

### Answer

There are three paths through the circuit. Each path connects the opposite terminals of one of the cells.

The total emf across the circuit is 6 volts. This is shown in the following figure.

The total emf across the circuit is 6 volts, and so the emf across any path through the circuit must also be 6 volts.

This means that the potential difference across each cell must be 6 volts. Each cell must provide an emf of 6 volts.

When a potential difference is connected across a circuit, the path from one terminal of a cell to the opposite terminal is not the same path if the positions of the terminals are reversed. This is shown in the figure below.

We can see that the path between opposite terminals can be clockwise or counterclockwise, depending on which end of the circuit connects to the positive terminal and which to the negative terminal.

The direction of the path from the positive terminal to the negative terminal is the direction of the current between the terminals.

Let us consider two cells in parallel that have equal emfs. These cells are connected to a circuit. This is shown in the figure below.

We can consider a path that connects the positive terminals of the cells to each other. We can also consider a path that connects the negative terminals of the cells. These paths are shown in the following figure.

For both of these paths, the charge is equal at both ends of the path. This means that there is zero potential difference across these paths, which means that there will be no current along them.

There will be currents along the paths connecting the opposite terminals of the cells. These paths are shown in the following figure.

For all these paths, the potential difference across the path is the same, 6 volts. The direction of the current along all the paths is clockwise.

It is very important to notice that for both cells, the positive terminals are facing clockwise, the same direction as that of the current in the circuit.

This means that for any wire that is connected to a cell terminal, the current direction is away from the positive terminal and toward the negative terminal.

Cells could instead be connected in parallel, with one cell’s positive terminal facing clockwise and the other cell’s positive terminal facing counterclockwise, as shown in the following figure.

A circuit connected like this would carry four possible currents.

Two of these currents are shown in the figure below.

These currents are each between the opposite terminals of one cell.

Two of these currents that are not as simple are shown in the following figure.

We see that each of these currents is along a path that passes through multiple cells.

When a circuit is connected in this way, the current along this path becomes very high. If it continues, it increases the temperature of the wires greatly.

Let us now look at an example in which cells are connected in parallel in such a way.

### Example 4: Describing How to Correctly Align Cells Connected in Parallel

A student sets up the circuit shown in the diagram. After a short while, the wires connecting the cells start to melt, and eventually they become unusable. Explain what the student should have done differently to avoid this problem.

### Answer

The problem with the circuit is caused by the directions of the terminals of the cells.

The figure below shows the currents through a path that passes through the resistor due to the cells.

It is important to notice that these currents are in opposite directions.

The following figure shows the current through a path that does not pass through the resistor due to the cells.

This current is very high, which melts the wires in this part of the circuit.

The circuit can be set up with the positive terminals of the cells both facing clockwise as shown in the figure below.

Assuming that the cells have equal emfs, there will be no current between the positive terminals of the two cells nor between their negative terminals. The current will be along the path that contains the resistor, as shown in the figure below.

We could just as well have set both cell’s positive terminals to face counterclockwise. This would have produced a current in the opposite direction.

We have seen that connecting cells in parallel can produce very high currents that can damage the circuit if the cells are connected with their positive terminals facing in opposite directions.

Very high currents that cause damage can also be produced by cells that have their positive terminals facing in the same direction.

Consider the circuit shown in the figure below.

It is important to notice that the emfs of the cells are not equal.

When a circuit is connected this way, the current along the path through the cell with the lower emf becomes very high. If it continues, it damages this cell.

Let us now look at an example in which cells are connected in parallel in such a way.

### Example 5: Identifying the Change Required to a Cell That is Connected in Parallel with Other Cells

A student sets up the circuit shown in the diagram. After a while, the 3 V cell breaks and is no longer usable. Explain what the student should have done differently to avoid this problem.

### Answer

The problem with the circuit is caused by using one cell that has a different emf to the other cells.

Either the 3-volt cell should be replaced by a 9-volt cell or the 9-volt cells should be replaced by 3-volt cells.

Let us now summarize what we have learned in this explainer.

### Key Points

• To be safely connected in parallel with the circuit, cells must have equal values of emf.
• To be safely connected in parallel with the circuit, cells must have their positive terminals facing in the same direction as each other.
• When cells are safely connected in parallel with the circuit, the total emf supplied to the circuit is equal to the emf of any one of the cells.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.