# What are the important Differences and Similarities Between Electromotive Force (emf) and Potential Difference

Electromotive Force (emf)

Electromotive Force (EMF) is the voltage or electric potential difference generated by a source of electrical energy. It is the driving force that causes electric charges (usually electrons) to move through a circuit. EMF is measured in volts (V) and is represented by the symbol “ε” or “E.”

Nature of EMF

EMF is not an actual force in the classical sense, despite its name. It is better understood as the potential energy per unit charge supplied by the source of electrical energy. When a circuit is connected to an EMF source, the electric charges experience a potential difference, and the presence of this potential difference enables the flow of electric current through the circuit.

Sources of Electromotive Force

EMF can be produced by various sources, including:

• Batteries: Chemical reactions inside a battery create a potential difference between its positive and negative terminals, providing a continuous flow of electric charges.
• Generators: Electromagnetic induction is used in generators to produce EMF as mechanical energy is converted into electrical energy.
• Photovoltaic Cells (Solar Cells): Photons of light striking the semiconductor material in photovoltaic cells create a potential difference, generating electricity.
• Thermocouples: The junction of two dissimilar metals exposed to different temperatures generates EMF, which is used in temperature measurement.

EMF and Terminal Voltage

It’s essential to differentiate between EMF and terminal voltage. EMF refers to the total potential difference across the source of electrical energy, while the terminal voltage is the potential difference measured across the terminals of the source when it is connected to a circuit. The terminal voltage may be less than the EMF due to internal resistance in the source or losses in the circuit.

Relationship between EMF, Current, and Resistance

According to Ohm’s law, the current (I) flowing through a circuit is directly proportional to the EMF (E) and inversely proportional to the total resistance (R) in the circuit. This relationship is described by the formula:

I = E / R

Conservation of Energy and EMF

EMF is associated with the conversion of one form of energy into electrical energy. According to the law of conservation of energy, the total energy supplied by the EMF source is equal to the energy dissipated in the circuit and the energy converted into other forms, such as heat or light.

EMF in Inductive and Capacitive Circuits

In circuits containing inductors or capacitors, EMF can manifest differently due to the storage and release of energy in these components. Inductors store energy in magnetic fields, while capacitors store energy in electric fields. As a result, the EMF in such circuits can exhibit transient behavior during the charging and discharging processes.

Potential Difference

Potential Difference, also known as Voltage, is the difference in electric potential energy per unit charge between two points in an electric field. It represents the work done to move a positive test charge from one point to another within an electric field. Potential Difference is measured in volts (V) and is represented by the symbol “V.”

Nature of Potential Difference

Potential Difference is a scalar quantity, meaning it has magnitude but no specific direction. It indicates the electrical potential energy difference between two points in an electric circuit or field. Electric charges flow from points of higher potential (higher voltage) to points of lower potential (lower voltage).

Potential Difference in an Electric Field

In an electric field created by electric charges, the potential difference between two points is determined by the distribution of charges and the distance between the points. The potential difference is directly proportional to the amount of electric potential energy difference between the points.

Measuring Potential Difference

The potential difference between two points in a circuit or an electric field is measured using a voltmeter. A voltmeter is connected in parallel to the two points under consideration, and it reads the potential difference directly.

Relationship between Potential Difference, Work, and Charge

The potential difference (V) between two points is related to the work (W) done in moving a charge (Q) between those points by the equation:

Potential Difference (V) = Work (W) / Charge (Q)

Potential Difference in Electrical Circuits

In electrical circuits, potential difference plays a crucial role in the flow of electric current. When there is a potential difference across a conductor, it creates an electric field, causing the charges (usually electrons) to move through the circuit, creating an electric current.

Series and Parallel Circuits

In series circuits, the potential difference across each component adds up to the total potential difference of the circuit. In parallel circuits, all components have the same potential difference across them, which is equal to the potential difference across the voltage source.

Conservation of Energy and Potential Difference

Potential difference is associated with the conservation of energy. The electrical potential energy gained or lost by charges moving through an electric field is equivalent to the work done on them, as described by the potential difference.

Important Differences Between Electromotive Force (emf) and Potential Difference

 Basis of Comparison Electromotive Force (EMF) Potential Difference (Voltage) Definition Source of energy Energy difference Nature Driving force Potential energy Symbol Representation ε or E V Measurement Measured across the source Measured across two points in a circuit Energy Transformation Converts energy Represents energy difference Work on Charges Drives charges through the circuit Determines charge movement Circuit Components Provided by energy sources (batteries, generators) Exists across circuit elements (resistors, capacitors) Units Volts (V) Volts (V)

Similarities Between Electromotive Force (emf) and Potential Difference

• Both are related to electrical energy and electric potential.
• Both are measured in volts (V) in the International System of Units (SI).
• Both represent the work done per unit charge in moving charges in an electric field.
• Both play a significant role in understanding and analyzing electrical circuits.
• Both are essential concepts in electromagnetism and electrical engineering.
• Both are scalar quantities, meaning they have magnitude but no specific direction.

Numerical question with answer of Electromotive Force (emf) and Potential Difference.

Question:

A battery has an electromotive force (EMF) of 12 volts (V). When connected to a circuit, the potential difference measured across the battery terminals is 11.5 volts (V). Calculate the internal resistance of the battery.

To find the internal resistance (r) of the battery, we can use the formula for potential difference in a circuit:

Potential Difference (V) = EMF (ε) – (Internal Resistance (r) × Current (I))

Given:

EMF (ε) = 12 V

Potential Difference (V) = 11.5 V

Assuming the current (I) flowing through the circuit is constant, we can rearrange the formula to solve for the internal resistance:

Internal Resistance (r) = (EMF (ε) – Potential Difference (V)) / Current (I)

Now, let’s assume the current (I) is 2 amperes (A) for this example.

Using the formula:

Internal Resistance (r) = (12 V – 11.5 V) / 2 A = 0.5 V / 2 A = 0.25 ohms (Ω)

So, the internal resistance of the battery is 0.25 ohms (Ω).