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# EMF Formula

Electromotive force i.e EMF is an unfamiliar concept to most of the students. But it is closely linked to the more familiar concept of voltage. Understanding the difference between these two and what EMF means gives us the tools we need to solve many problems in physics as well as in electronics. It will also introduce the concept of the internal resistance of a battery. EMF tells about the voltage of the battery without the internal resistance reducing the value. This topic will explain the emf formula with examples. Let us learn it!

## What is EMF?

The electromotive force is defined as the potential difference across the terminals of the battery when no current is flowing through it. This might not seem like this as it would make a difference, but every battery has internal resistance. It is similar to the ordinary resistance that reduces the current in a circuit, but it exists within the battery itself.

When no current is flowing through the cell, then this internal resistance will not change anything because there is no current for it to slow down. In this way, the EMF can be thought of as the maximum potential difference across the terminals in an idealized situation.

The EMF or electromotive force is the energy supplied by a battery or a cell per coulomb (Q) of charge passing through it. The magnitude of emf is equal to V (potential difference) across the cell terminals when there is no current flowing through the circuit.

Source: en.wikipedia.org

### Difference between EMF and Potential Difference?

The amount of energy changed into electrical energy per coulomb of charge is referred to as EMF. On the other hand, the potential difference is the amount of electrical energy that is changed into other forms of energy per coulomb of charge. Cell, solar cell, battery, generator, thermocouple, dynamo, etc are examples of sources of emf.

## The Formula for Calculating the EMF

There are two main equations used to calculate EMF. The fundamental definition is the number of joules of energy each coulomb of charge picks up as it passes through the cell.

$$\varepsilon = \frac {E}{Q}$$

 $$\varepsilon$$ electromotive force E the energy in the circuit Q Charge of the circuit.

If we know the resulting energy and the amount of charge passing through the cell. It is the simplest way to calculate the EMF.

Instead, we may use the definition more like the Ohm’s law i.e V = IR. So the formula is,

$$\varepsilon = I (R+r)$$

 I Current $$\varepsilon$$ The electromotive force of cell. R Resistance in the circuit. r Internal resistance of a cell. V Voltage

Now, expanding this:

$$\varepsilon = IR + Ir$$

$$\varepsilon = V + Ir$$

This shows that we can calculate the EMF if we know the voltage across the terminals, the current flowing and the internal resistance of the cell.

## Solved Examples for EMF Formula

Q.1: Consider that we have a circuit with a potential difference of 3.2 V, with a current of 0.6 A. The internal resistance of the battery at 0.5 ohms. Use EMF Formula.

Solution: Given,

• V = 3.2 V
• I = 0.6 A
• r = 0.5 ohm

Using the formula: $$\varepsilon = V + Ir$$

$$\varepsilon = 3.2 + 0.6 \times 0.5$$

= 3.2 V + 0.3 V

= 3.5 V

So the EMF of the circuit is 3.5 V.

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