Electromotive Force - Definition, Formula, Unit, Difference, FAQs

What is Electromotive Force?

Emf Definition: The amount of work done in the energy transformation (or conversion) and the electricity that travels through the electrical source or generator is defined as the electromotive force (EMF). The electromotive force (EMF) symbol is $\varepsilon$. Internal resistance leads to the development of emf.

Symbol for Electromotive Force

The symbol for Electromotive Force (emf) is: ε (epsilon)

Formula of EMF

There are three formulas for EMF depending on the EMF generated

Induced EMF

$
\mathcal{E}=-N \frac{d \Phi}{d t}
$

where,

• $\mathcal{E}$ is the induced EMF
• $N$ is the number of turns in the coil
• $\Phi$ is the magnetic flux

Motional EMF

The formula for motional emf is given as:

$
\mathcal{E}=B \cdot l \cdot v
$

where,

• $B$ is the magnetic field strength
• $l$ is the length of the conductor
• $v$ is the velocity of the conductor relative to the magnetic field.

Static EMF ( EMF in a battery)

$
\mathcal{E}=V+I \cdot r
$

where,

• $V$ is the terminal voltage of the battery
• $I$ is the current flowing through the circuit
• $r$ is the internal resistance of the battery

Unit and Dimension of Electromotive Force

Unit of Electromotive Force:

The SI unit of electromotive force (EMF) is the volt (V). One volt is defined as the electromotive force when one joule of energy is supplied to move one coulomb of electric charge through a circuit.

$
1 \text { volt }=\frac{1 \text { joule }}{1 \text { coulomb }}
$

Hence,

$
\text { Volt }=\frac{\text { Joule }}{\text { Coulomb }}
$

Dimension of Electromotive Force:

Electromotive force is defined as the work done per unit charge.

$
\mathrm{EMF}=\frac{\text { Work }}{\text { Charge }}
$

Since,

$
\text { Work }=\left[M L^2 T^{-2}\right] \quad \text { and } \quad \text { Charge }=[I T]
$

Therefore, the dimensional formula of electromotive force is:

$
[E M F]=M^1 L^2 T^{-3} I^{-1}
$

Types of EMF

Primary EMF or Static EMF

• It is generated by the difference in electric potential
• Battery and thermocouples are examples of static EMF

Induced EMF

• It is generated by the relative motion between the conductor and the magnetic field.
• Two types of induced EMF: motional EMF and transfer EMF

What is the Source of EMF and Define EMF of a cell?

Consider a basic circuit of a bulb connected to a battery to dispel these doubts.

The battery (or any other electro-voltaic cell) can be thought of as a two-terminal device with one terminal at a higher potential than the other. The positive terminal, which has a higher electric potential, is sometimes referred to as the positive terminal and is usually denoted by a plus sign. The negative terminal, which is labeled with a minus sign, is the lower-potential terminal. This is referred to as the electromotive force or EMF source.

There is no flow of charges within the electromotive force source when the source is separated from the light. Charges flow from one terminal to another, passing through the bulb after the battery is reconnected to the bulb. This causes the bulb to shine. Positive charges leave the positive terminal, pass through the lamp, and enter the negative terminal of the emf source in positive current flow, also known as conventional current flow. This is how you set up an EMF source.

Now, what is the emf of a cell?

The potential difference created at both ends of a battery is the electromotive force of a cell.

Difference Between EMF and Terminal Voltage

Difference Between Electromotive Force and Potential Difference

Potential Difference

The amount of work done in transporting a positive unit charge from one location to the other target point is described as the potential difference between two points in an electric circuit.

Work done is divided by the amount of charge transported equals the potential difference.

$\mathrm{V}=\frac{\mathrm{W} }{ \mathrm{q}}$

Here, the Potential Difference symbol is V

Example

When we state that the potential difference between two points is 3 volts, we mean that it takes 3 joules of energy to move a positive unit charge between them.

Terminal Voltage

Terminal voltage definition is when a current is supplied, the terminal voltage is the actual potential difference across the supply terminals.

Note:

When electrons move from negative to positive terminals in a closed circuit, the terminal voltage falls below the EMF value.

Internal Resistance

Chemical reactions within the cell can't keep up with the pace of charge separation to maintain maximal charge separation. Charges must flow between the electrolyte and the terminals, and there is always some internal resistance to this $(r)$.

As a result, there is an internal voltage drop equal to $Ir$ while current flows and the terminal voltage formula is given by $\mathrm{V}_{\mathrm{T}}=\varepsilon-\mathrm{Ir}$.

Note that when current $I=0$, the terminal voltage is equal to $\varepsilon$.

Here is a representation of the voltage source and internal resistance for your better understanding.

Factors Affecting EMF

1. Rate of change of magnetic flux
2. Number of turns in the coil
3. Magnetic flux density
4. Area of the coil
5. Velocity of conductor

Also read:

• NCERT Exemplar Solutions for All Subjects
• NCERT Notes For All Subjects
• NCERT Solutions for All Subjects