Difference Between E.M.F And Voltage

Electromotive Force (EMF) and voltage are key to the functioning of electrical devices and systems. EMF measures the energy supplied by a source, like a battery or generator, per unit charge, while voltage represents the potential difference between two points in a circuit. In practical applications, EMF is essential in power generation, helping to convert mechanical energy into electrical energy, while voltage governs the operation of everyday electronics, from light bulbs to smartphones.

1.0Electromotive Force(EMF)

The potential difference across a cell's terminals when it is not supplying any current is referred to as the cell's electromotive force (emf). This represents the energy provided by the cell per unit charge as it moves through the entire circuit, including the cell itself.

NOTE: Work done by a cell to bring a unit positive charge from one terminal to the other terminal of the cell is called emf. The name electromotive  force is misleading because EMF is not a force but it is work done per unit charge.

Factors on which EMF depends on

1. Nature of electrolyte                     

2. Metal of electrodes

EMF does not depend on

1.  Area of plates                 
2. Distance between the electrodes
3. Quantity of electrolyte               
4. Size of cell

2.0Voltage or Terminal Potential Difference

• When current is drawn through a cell or current is supplied to it then the potential difference across its terminals is called terminal voltage.                  
• When I current is drawn from cell then terminal voltage V is less than its e.m.f i.e., V=E-Ir

When Cell Is Discharging

Current inwards the cell is from cathode to anode.

Current $I=\frac{E}{R+r}$

E=IR+Ir=V+Ir

V=E-Ir

• When current is extracted from a cell, the potential difference across its terminals is lower than the cell's electromotive force (emf). The greater the current drawn, the smaller the terminal potential difference becomes. If a large current is extracted from the cell, the terminal potential difference decreases significantly.

When Cell Is Getting Charged

• Current inside the cell is from anode to cathode.
• Current $I=\frac{V-E}{r}$

V=E+Ir

• During charging, the terminal potential difference is greater than the EMF of the cell.

When Cell Is In The Open Circuit       

•  In open Circuit R=∞  

$I=\frac{E}{R+r}=0\Rightarrow V=E$   

• In an open circuit, terminal potential difference is equal to the EMF and is the maximum potential difference which a cell can provide.                                    

When Cell Is Short Circuited

In short circuit R=0

$I=\frac{E}{R+r}=\frac{E}{r}\text{ and }V=IR=0$

Note:

1. In short circuit, current from the cell is maximum and terminal potential difference is zero.
2. At the time of charging a cell, when current is being supplied to it, the terminal voltage is greater than the EMF E

                    V=E+Ir              ( V>E)

Illustration: When a resistance of 4 is connected to a cell then a current 2A flow through it.If the cell is connected to a resistance of 9 then current is decreased by 50% Find the current through the cell if its terminals are directly connected by a connecting wire.

Solution: $i=\frac{E}{R+r}=2A$

$i=\frac{E}{4+r}$ ……..(1)

$i^{\prime }=\frac{i}{2}=\frac{E}{9+r}$ ……(2)           

$\left(i^{\prime }=\frac{50}{100}i=\frac{i}{2}A\right)$

(1) Divided by (2)

$\frac{2}{1}=\frac{E}{4+r}\times \frac{9+r}{E}\Rightarrow 8+2r=9+r\Rightarrow r=1\Omega$

From equation (1)

24+1=EE=10V

Current through cell during short circuit = $\frac{E}{r}=\frac{10}{1}=10\mathrm{A}$

3.0Difference Between EMF And Voltage