__What is Electromotive Force?__

**Electromotive force **of a source of electric current supply is defined as the *potential difference** between the terminals of the cell in open circuit i.e. when no **current** is drawn from the cell.*

- In short form electromotive force is written as emf.
- Electromotive force is not a
*force*, rather it is the*work done*by a cell to bring a unit positive*charge*from one terminal to the other terminal of the cell. - In short form, electromotive force is written as EMF.

EMF of a cell doesn’t depends upon –

- Size of the electrodes of the cell.
- Distance between the electrodes of cell.
- Quantity of electrolyte used in the cell.

__Terminal Potential Difference__

**Terminal potential difference **of a cell is defined as the potential difference between the terminals of the cell when it is connected to a closed circuit i.e. when current is being drawn from the cell by circuit.

## Cell

*A cell is defined as a device which provides source of electric supply and uses chemical energy to convert it into electrical energy. It is also called a source of electromotive force.*

- A cell has two terminals by which the external circuit is connected.
- The positive terminal is called
and negative terminal is called a*anode*.**cathode** - When a conductor is connected between these terminals, cell drives an
*electric current*through it.

To get higher electromotive force or current in the circuit, many cells are collectively used in series or in parallel or in mixed combination. A combination of such cells is called a ** battery**.

__Internal Resistance__

*Internal resistance of a cell is defined as the opposition offered by the electrolyte and electrodes of a cell to the flow of electric current through it.*

Consider a cell of e.m.f ( E ) and internal resistance ( r ) is connected to a circuit having external resistance ( R ) as shown in figure.

- When the key ( K ) is open no current is drawn from the cell. So, the voltmeter reads the value of EMF of the cell.
- When the key ( K ) is closed current is drawn from the cell in the circuit. So, the voltmeter will read potential difference of the cell.

Since, ( R ) and ( r ) are connected in series, therefore current through the circuit will be –

I = \left ( \frac { E }{ R + r } \right )

Or, \quad E = ( IR + Ir ) ………. (1)

Since external resistor ( R ) is also connected in parallel to the electrodes of the cell, so the terminal potential difference is the potential difference across the resistor ( R ) .

Therefore, \quad V = IR …….. (2)

Hence, equation (1) becomes –

E = V + Ir

Or, \quad V = E - Ir ……… (3)

This shows that terminal potential difference is less than the EMF of the cell.

Hence, now the voltmeter reads the value of terminal potential difference ( V ) of the cell which is less than initial reading of EMF ( E ) .

__Electromotive Force & Potential Difference__

Sl. No. | Electromotive Force. | Potential Difference. |

1 | It is a measurable quantity when the circuit is open. | It is a measurable quantity when the circuit is closed. |

2 | Electromotive force is independent of any external resistance in the circuit. | Potential difference between two points in a circuit is proportional to the resistance between these points. |

3 | Electromotive force is greater than potential difference between two terminals of the cell. | Potential difference between two terminals of the cell is less than electromotive force. |

4 | Electromotive force is a term which is related to the source of supply of electric current. | Potential difference is a general term which indicates the effect of electric current in circuit. |

5 | Variation of electromotive force ( E ) with external resistance ( R ) is shown in figure (A). From graph it can be concluded that ( E ) is independent of external resistance ( R ) . | Variation of potential difference ( V ) with external resistance ( R ) is shown in figure (B). From graph it can be concluded that ( V ) is directly proportional to external resistance ( R ) . |

Following figures shows the effect of external resistance on EMF and potential difference of a cell.

Figure (A) shows effect of external resistance on EMF of a cell and figure (B) shows effect of external resistance on terminal potential difference.

__Charging of a Cell or Battery__

Consider that a cell or battery of EMF ( E ) and internal resistance ( r ) is being charged by a charger.

The charging voltage ( V ) is kept equal to or more than EMF ( E ) of the cell which is under charging.

Therefore, net potential difference across the cell will be ( V - E )

This net potential difference is equal to the voltage drop inside the cell.

Therefore, \quad ( V - E ) = Ir

Or, \quad V = ( E + Ir )

Therefore, charging voltage must be kept greater than the EMF of cell being charged at least by an amount ( Ir ) where ( I ) is the charging current and ( r ) is the internal resistance of the cell.