# EMF Formula

## What is EMF ?

Electromotive force is one of the important concepts that help us understand the process of electromagnetism. The electromotive force is abbreviated as the EMF and it is closely associated with the more common concept of voltage. The electromotive force is the total energy provided by a battery or a cell per coulomb q of charge crossing through it.

The magnitude of EMF is equal to the potential difference across the cell terminals when there is no current flowing through the given electrical circuit and the formula used is known as the EMF formula. In this article, we will learn in detail the electromotive force formula, the idea of EMF physics and by the end with the help of the EMF equation with a few solved examples.

### EMF Physics

The electromotive force can be defined as the total voltage or the potential difference across the terminals of the battery in an open circuit or in other words when no current is flowing through it. This might not appear like this as it would make a variance, but every battery will be built with some particular internal resistance. It is related to the regular resistance that reduces the flow of current in an electrical circuit, but it is enclosed only within the battery itself.

We know that when the circuit is open, no current will be flowing through the cell, this implies that the internal resistance of the battery will not change anything because there is no current for it to reduce or slow down. Thus, the electromotive force can be considered as the maximum potential difference or the voltage across the two terminals in an idealized condition. This explains the EMF physics and we can understand from this that the electromotive force is a special case of the voltage difference.

Now, the question that arose was even though the electromotive force is not a form of force at all, then why is it referred to as the electromotive force, what is the difference between the EMF and regular potential difference, and what will be the source of EMF? To answer these doubts, consider a simple electrical circuit of a lamp connected to a battery.

We know that any electro voltaic device can be expressed as a two-terminal device that keeps one terminal at a higher potential and another terminal at a lower potential. The higher electric potential is commonly known as the positive terminal and it is generally designated with a plus sign. The lower-potential terminal is known as the negative terminal and designated with a minus sign. This is called the source of the EMF.

When the source of the electromotive force is disconnected from the lamp i.e., when the circuit is open, then there is no net movement of charges within the given EMF source. Once the circuit is closed then or reconnected to the lamp, charges will move from one terminal of the battery, through the lamp and this further will result in the lamp glowing and back to the other terminal of the battery.

If we consider the conventional flow of electric current i.e., positive current, positive charges tend to leave the positive terminal, drive through the lamp, and enter the negative end of the EMF source. This is how an EMF source is arranged. At the same time, the electromotive force of a battery is the potential difference developed at both ends of the given battery.

Therefore, EMF physics explains that the electromotive force is the total energy supplied by a battery or a cell per coulomb of charge passing through it. The total magnitude of EMF is equal to the voltage or the potential difference across the terminals of the battery when there is no current moving through the given electrical circuit.

### EMF Equation

We know that the charges circulate in the electric circuit, for the motion of the charges in a given electric circuit we need to apply an external force to it. We say that an external electric source such as a battery uses such force which will give acceleration to the charges and it is kenned as the electromotive force. Despite its name, it's not a form of force but a potential difference, in fact, it is a special case of potential difference and it is generally denoted by the symbol .

Now, let us have a look at the EMF equation:

According to the definition of EMF and EMF physics, the EMF formula is given by:

$\Rightarrow EMF=\varepsilon =\frac{E}{Q}$…..(1)

Where,

E - The total energy of the battery

Q - The total charge flowing through the given circuit

Equation (1) can be used if we know the total energy of the battery used in the circuit. The electromotive force is also the potential difference developed in the circuit, thus, the EMF formula can also be found using the ohm’s law. Hence we write:

ε = IR…..(2)

Where,

I - The total current flowing in the circuit

R - The total resistance used in the circuit

Since we know that the EMF depends upon the internal resistance of the battery, we should replace the resistance with the sum of the resistance and the internal resistance. Thus equation (2) becomes:

ε = I (r + R)

ε = Ir + IR

ε = V + Ir…….(3)

Where,

V - The total potential difference developed in the circuit

I - The total current flowing in the circuit

r - The internal resistance of the battery

Therefore, equation (1) and equation (3) are known as the EMF formula or the EMF equation. Let us understand the EMF formula and how to find EMF or how to calculate EMF with a few solved examples.

### Examples:

1. Consider an electrical circuit with a potential difference of 5V, with a current of1 A. If the internal resistance of the battery used is 0.8 ohms. Then, determine the EMF of the circuit using the EMF formula.

Sol:

Given,

The potential difference of the electric circuit = V = 5 volts

The total current flowing through the circuit = I = 1 A

The internal resistance of the battery = r = 0.8 ohms

We are asked to determine the EMF of the circuit using the EMF equation. We know that the EMF of the circuit can be calculated using the formula given below:

ε = V + Ir…….(1)

Where,

V - The total potential difference developed in the circuit

I - The total current flowing in the circuit

r - The internal resistance of the battery

Substituting the value of potential difference, current and the internal resistance in equation (1) we get:

ε = V + Ir

ε = 5 + (10.8)

ε = 5.8 volts

Therefore, the EMF of the circuit using the EMF formula is 5.8 Volts.

2. Calculate the terminal potential difference of a battery when it is connected to a 10 ohm load with battery EMF, ε = 3 volts and the internal resistance of the battery is 2 ohm.

Sol:

Given,

The total EMF of the battery = ε = 3 volts

The external load applied to the battery = RL = 10 ohms

The internal resistance of the battery = r = 2 ohms

Now, we are asked to determine the terminal potential difference of the battery. Before that let us calculate the current flowing through the given circuit. according to ohm’s law, we know that:

$\Rightarrow I=\frac{V}{R}=\frac{\varepsilon }{r+R_{L}}$….(1)

I = 3/12 = 0.25 amp

Now, let us determine the terminal potential difference of the battery. The EMF formula is given by:

ε = V + Ir…….(2)

Where,

V - The total potential difference developed in the circuit

I - The total current flowing in the circuit

r - The internal resistance of the battery

Substituting the value of EMF, current and the internal resistance in equation (2) we get:

3 = V + (0.252)

V =3 - 0.5

V = 2.5 Volts

Therefore, the terminal potential difference of the battery is 2.5 volts.