What Is The Potential Difference Between The Terminals Of The Battery?

Potential difference is defined as the amount of work it will need to move a single unit of electrical charge from its reference point to another. It is also popularly known as voltage.

It can also be interpreted as the difference in electric potential of two points within an electrical field. This amount of work is measured as voltage, and in it can also be represented as V=IR, where V stands for the potential difference (voltage), I for current (amps), and R for resistance or load (OhmOhm).

What is the potential difference between the terminals of the battery? The potential difference between the two battery terminals without a complete circuit and no current flow is called “electromotive force” or Emf.

In a situation like this, it may seem impossible since there is no circuit for a complete flow of current. However, a battery has its internal resistance that reduces the current flowing on a circuit without any load.

This makes the Emf the maximum quantity of work; a battery’s coulomb of charge needs to move a single unit of electric charge from one of its terminals to the other.

If you take a closer look at the electromotive force definition, we can say that determining its exact value or amount is possible.

This is because all the elements involved in the description, current flow, resistance, voltage, and charge, have their respective mathematical interpretation or equivalent.

Batteries are fascinating devices that work due to the magic of different sciences from within and beyond. Aside from the chemical reactions from within, converting chemical energy to electrical energy also involves physics when it comes to the current flow.

Here I am going to talk about what potential difference is and everything in between. We will discuss its definition, how to calculate its exact value, talk about its significance, and tackle anything related to it. So, keep on reading and have fun learning new things.

How to Calculate the Value of Electromotive Force or Emf

By looking at the fundamental definition of electromotive force, it says that it is the amount of energy (joules) that each coulomb of charge takes as it travels through the cells.

Given the value of the total energy and the amount of charge going through the cell, it will the simplest way to compute for the Emf, and it can be mathematically expressed as:

ε = E / Q


ε = E ÷ Q

Where: ε stands for Emf or electromotive force, E for energy within the circuit, and Q for the charge of the circuit.

Emf or electromotive force can also be defined using Ohm’s law, with a mathematical expression of V=IR. Since the electromotive force is measured in voltage, we can use it in the formula of Ohm’s Ohm’s law.

This will result in:

ε = I (R + r)

Where: ε stands for Emf or electromotive force, I for current, R for resistance or load, and r for the internal resistance that the battery has.

From the major mathematical expression we derived from Ohm’s Ohm’s law, it can be further simplified as:

ε = IR + Ir

Then substitute similar values to derive a more straightforward formula.

ε = V + IR

Where: ε stands for Emf or electromotive force, V for voltage, I for current, and R for resistance.

With the resulting mathematical expression that defines the electromotive force (Emf). It clearly shows that its value can also be computed through Ohm’s law. This will be possible as we know the voltage and current and resistance values in the circuit.

Origin of Potential Difference Between the Battery Terminals

The event happening with a power cell includes the stripping of negatively charged ions, also called as electrons, from the atom. These electrons are stored at the battery’s negative terminal; however, they are also free to move while the positively charged ions or protons are stored on the battery’s positive terminal.

As electrons move along the circuit and pass-through components, work is done. While this happens, the electrons transfer some of its energy to the components. Those causes an energy difference between the terminals.

Since the two terminals are in an electric field, a potential difference is generated between the two points, which are the battery’s positive and negative terminals.

Relating Electromotive Force, Terminal Voltage and Current

We already established earlier that the potential difference is also known as voltage. And any kind of power source needs to generate voltage using the various sources of energy to produce current supplied on the load or resistance.

Once provided, a flow will be generated; thus, the potential difference in the power source becomes the electromotive force (Emf) when no current flow is generated.

To have a better picture of how potential difference, current, Emf, and resistance are related, let us first understand each of them.

1. Electromotive Force or Emf

Defined earlier, the electromotive force or Emf is the potential difference of a power source when there is no current flow. It is also the maximum amount of voltage of the power source, where the only resistance is the internal resistance within the voltage source.

However, the Emf should not be considered as the voltage output of the power supply. This is because the electromotive force is measured between the two endpoints of the voltage source when no current is flowing, while the voltage output is measured between the two endpoints, which is a complete circuit with the current flow.

2. Understanding the Terminal Voltage

Terminal voltage is the output voltage of the power source measured between its two endpoints, and there is a current flow. This means that as the current flow supplying power to the resistance within the circuit, the lower the voltage will become.

The more resistance the circuit has, the more current is needed to flow to accommodate the load. As the current flowing increases, the more potential difference it will need for a smooth flow of energy.

This definition of terminal voltage can be mathematically expressed as:

V = ε – IR

Where: V stands for the Terminal Voltage, I for current, and r for internal resistance.

For defining the value of current that flows within the circuit, we can use Ohm’s Ohm’s law to derive a new mathematical expression, where a load or resistance is connected with the power source.

It will be represented by:

I = ε / R + r


I = ε ÷ R + r

Where: I stands for the current, ε for the electromotive force, R for the resistance, and r for the internal resistance.

As you can see, the electromotive force, terminal voltage, current, and voltage source are correlated. From the perspective where the focus is the electromotive force, you will agree that the Emf is directly related to the source of power since Emf is considered as a special kind of potential difference which is generated by the source.

On the other hand, the terminal voltage clearly shows that it also directly relates to the current and the resistance. The apparent reason is that the terminal voltage is the one that will produce a current which will be distributed to the resistance. I can also say that the electromotive force is related to terminal voltage because they are almost the same.

The Advantage and Disadvantage of Multiple Voltage Sources

Having multiple voltage sources has its advantages and disadvantages. Some people think that with multiple power supplies, a circuit or current flow will be more efficient. This may be true depending on the situation and how the power sources are oriented and setup.

To have a better understanding and visualization with regards to the issue of having multiple sources of voltage, refer to the explanations below.

When it comes to multiple voltage sources, the results will depend on their connection and orientation. In this case, it will be the series connection or parallel connection.

Here’s how they work!

Multiple Voltage Sources in Series

In a case where a battery charger is used while the power cell still acts as a source of voltage, it will have two power sources connected in series. In this case, internal resistances or loads of the voltage sources are summed up, as well as their Emfs.

When multiple sources of voltage are connected in series, the biggest disadvantage is that the internal resistances will be added up, generating more load in ohms. From here, the orientation of the power sources will play a significant role.

Voltage Sources with Opposing Emfs

If the voltage sources are in a series type of connection and oriented with opposing Emfs, the flow of current will be directed toward the power source with greater Emf. However, the amount of current will be limited by the summed up of internal resistances.

This is expressed as:

I = (Emf1 – Emf2) / r1 + r2

It clearly shows that the current that will be flowing within the circuit will be relatively low. You will notice that not only the summed up internal resistance is taking its toll, the opposing Emf also plays a significant role.

Voltage Sources with Linear Emfs

With multiple voltage sources in a series connection with the same orientation of Emfs and connected a resistance or load. The amount of current that will flow through the circuit will be a lot greater than having opposing Emfs, but it will be an adequate amount.

This is expressed as:

I = (Emf1 – Emf2) / r1 + r2 + R

This situation’s mathematical expression clearly shows that the circuit will have an adequate amount of current flow. Enough amount of current that will sustain the circuit’s operation.

Multiple Voltage Sources Connected in Parallel

In the case of multiple power sources with equal amounts of Emf, are parallel with each other and connected to resistance or a load. The summed up amount of Emf will be similar to the individual Emf of both power sources.

However, in a connection like this, the total internal resistance will significantly reduce due to the parallel orientation of the internal resistances.

This allows the circuit to generate a larger amount of current that will flow through the circuit.

This situation is mathematically expressed as:

I = Emf / rtotal + R

Where: rtotal < r1 or r2

The mathematical representation of this kind of connection clearly shows that the current flows through the circuit is greater. This is because the two voltage sources will generate an Emf equal to both individual Emf of the two power sources.

Now the most significant factor is that the overall internal resistance of both sources will be a lot lesser than the individual internal resistance of the two power sources.

This is why parallel connections of multiple voltage sources are commonly used to deliver more current output.