Electromotive Force (EMF)

A battery or electric cell supplies energy for charge motion in a circuit and maintains a potential difference between its terminals. The idea of electromotive force or EMF tells us how much energy the source can supply per unit charge.

For example, if a dry cell is labelled 1.5 V, it means that ideally the cell can supply 1.5 joules of energy for every 1 coulomb of charge.

Very important: Although the name contains the word “force”, EMF is not a mechanical force. It is a measure of the energy supplied by a source per unit charge.

1. A Simple Idea of EMF

Even though a metallic conductor contains free electrons, their presence alone does not produce a steady current. A source is needed to maintain a potential difference across the circuit.

Inside a cell or battery, chemical reactions separate charges. This process supplies energy to move charge from lower potential to higher potential within the source.

This energy supplied per unit charge is the basic idea of EMF.

2. Definition of Electromotive Force

Qualitative Definition

A source that converts chemical, mechanical or another form of energy into electrical energy and maintains a potential difference in a circuit is described by its EMF, which represents its ability to supply electrical energy.

Quantitative Definition

The energy supplied by a source to move a unit positive charge inside the source from lower potential to higher potential is called the electromotive force or EMF of the source.

If the source supplies energy to move charge , then

where,

= electromotive force or EMF
= energy or work supplied by the source
= charge

3. SI Unit of EMF

The SI unit of EMF is volt (V).

That is,

1 volt = 1 joule/coulomb

Meaning of 1 Volt EMF

If a source supplies 1 joule of energy for every 1 coulomb of charge, its EMF is 1 volt.

4. What Does a 1.5 V Cell Mean?

For a 1.5 V cell,

The energy supplied for 1 C of charge is

Therefore, an ideal 1.5 V cell supplies 1.5 J of energy per coulomb of charge.

5. Why is EMF Not an Actual Force?

The name “Electromotive Force” is historical. Mechanical force is measured in newtons (N), but EMF is measured in volts (V).

A familiar relation for mechanical force is

whereas EMF is

So EMF is not a mechanical force. It represents energy supplied per unit charge.

6. How Does an Electric Cell Produce EMF?

Chemical reactions take place in an electrochemical cell. As a result:

positive and negative charges are separated,
a potential difference develops between the terminals,
energy is supplied to move charge inside the cell from lower potential to higher potential,
chemical energy is converted into electrical energy.

When the circuit is completed, stored chemical energy is supplied to the circuit as electrical energy.

7. Charge Motion Inside and Outside a Cell

To understand the role of a source, think of the circuit in two parts.

Outside the Cell

In the external circuit, conventional current is generally taken as:

higher potential → lower potential

Inside the Cell

Chemical processes inside the cell supply energy to move positive charge:

lower potential → higher potential

This is how a cell or battery can maintain potential difference in the circuit.

8. Open Circuit and EMF

If there is no complete conducting path between the terminals of a cell, the circuit is called an open circuit.

In an open circuit,

so the voltage drop across internal resistance is nearly zero. Therefore, the terminal voltage of a real cell is approximately

Thus, in an open circuit, terminal voltage is approximately equal to EMF.

9. What is Internal Resistance?

Even inside a real cell or battery, there is some opposition to current flow. The resistance caused by the electrolyte, electrodes and internal structure of the cell is called internal resistance.

It is usually represented by and its SI unit is ohm (Ω).

10. Terminal Voltage of a Real Cell

Let

EMF =
internal resistance =
current =
terminal voltage =

When the cell supplies current, the voltage drop across its internal resistance is

Therefore, for a real cell supplying current,

or,

This relation is very important in numerical problems.

11. Why Does Terminal Voltage Decrease When Current Flows?

When no current flows, there is no significant voltage drop across internal resistance. But when current flows,

so part of the total EMF is used inside the cell itself. Therefore, while the cell supplies current,

and generally,

12. Is EMF Always Greater Than Terminal Voltage?

No. The relation depends on the condition of the cell.

Open Circuit

Cell Supplying Current

so generally,

While Charging the Cell

An external source works against the chemical process of the cell. In this condition, terminal voltage can be greater than EMF.

Therefore, it is not correct to say that “EMF is always greater than terminal voltage.”

13. Ideal Cell and Real Cell

Ideal Cell	Real Cell
Internal resistance is taken as zero.	Internal resistance is not zero.
r = 0	r > 0
Terminal voltage = EMF even when current flows.	While supplying current, terminal voltage is usually less than EMF.
It is an idealised concept.	All real cells have some internal resistance.

14. EMF vs Potential Difference

Electromotive Force (EMF)	Potential Difference
Shows how much energy the source supplies per unit charge.	Shows the change in energy per unit charge between two points.
Usually represented by E.	Usually represented by V or ΔV.
Related to energy conversion in the source.	Can be defined between any two points in a circuit.
SI unit is volt.	SI unit is also volt.
In an open circuit, terminal voltage is approximately equal to EMF.	Potential difference may depend on circuit condition and current.

15. Relation Between EMF and Electrical Energy

If the EMF is , the energy supplied for charge is

In a real cell, part of this energy is used in the external circuit and part is dissipated in the internal resistance.

For a cell supplying current,

This shows that the energy supplied by the source is shared between the external circuit and the inside of the cell.

16. EMF and Electrical Power

If a source has EMF and current , the total electrical power supplied by the source is

Power used in the external circuit is

Power lost in internal resistance is

The main idea is that some energy of a real cell is dissipated in its own internal resistance.

17. How is EMF Measured?

High-Resistance Voltmeter

If a very high-resistance voltmeter is connected across a cell in an open circuit, very little current flows. Therefore, the measured terminal voltage is very close to the EMF.

Potentiometer

A potentiometer can be used for a more accurate comparison or measurement of EMF. At balance, it effectively draws no current from the source.

At school level, the open-circuit reading of a high-resistance voltmeter may be taken as an approximate value of EMF.

18. Solved Example 1: Finding EMF

Question: A cell supplies 8 J of energy to move 4 C of charge through a circuit. Find the EMF of the cell.

Answer: 2 V

19. Solved Example 2: Finding Energy

Question: How much energy does a 12 V battery supply when 5 C of charge passes through the circuit?

Answer: 60 J

20. Solved Example 3: Terminal Voltage

Question: A cell has EMF 1.5 V, internal resistance 0.2 Ω and supplies a current of 0.5 A. Find its terminal voltage.

For a cell supplying current,

Answer: 1.4 V

21. Solved Example 4: Internal Resistance

Question: A cell has EMF 2.0 V. When a current of 0.5 A flows, its terminal voltage is 1.8 V. Find its internal resistance.

Therefore,

Answer: 0.4 Ω

22. Solved Example 5: Open Circuit

Question: A cell has EMF 3 V and internal resistance 0.5 Ω. What is its terminal voltage when the circuit is open?

In an open circuit,

Therefore,

Answer: 3 V

23. Everyday Examples of EMF

Dry Cell

A common dry cell has a nominal EMF of about 1.5 V.

Rechargeable Cell

Many NiMH rechargeable cells have a nominal voltage of about 1.2 V.

9 V Battery

The familiar rectangular 9 V battery is used in many small electronic circuits.

Vehicle Battery

Many small vehicle electrical systems use a 12 V battery system.

The value printed on a battery is generally a nominal value. Actual terminal voltage may vary with state of charge, current and internal resistance.

24. Common Misconceptions

Mistake 1: EMF is an Actual Force

No. EMF is not a mechanical force. It measures energy per unit charge.

Mistake 2: The Unit of EMF is Newton

No. The unit of EMF is volt (V).

Mistake 3: EMF and Electric Current are the Same

No. EMF is the energy supplied per unit charge, while electric current is the amount of charge flowing per unit time.

Mistake 4: EMF is Always Greater Than Terminal Voltage

No. In a real cell supplying current, EMF is usually greater; in an open circuit they are approximately equal; during charging, terminal voltage can be greater.

Mistake 5: A Battery Creates Electrons

No. A battery does not create new electrons. It uses chemical energy to separate charge and maintain a potential difference.

Mistake 6: EMF is Zero in an Open Circuit

No. A cell can have EMF even when current is zero.

Mistake 7: Internal Resistance Means the Resistance of the External Wire

No. Internal resistance is the resistance inside the cell or battery.

25. Important Formulae for Exams