Difference between Electromotive Force (EMF) and Potential Difference (PD)

Difference between EMF vs. Potential Difference

Electromotive Force (EMF) Potential Difference (PD)
1. Work done by a source to move a unit charge once around the entire complete circuit. 1. Work done in moving a unit charge from one specific point to another in a circuit .
2. Maximum voltage across the terminals of a source when no current flows (open circuit). 2. Voltage measured between any two points when current is flowing (closed circuit).
3. Exists even when the circuit is open/disconnected. 3. Exists only when the circuit is closed and current flows.
4. Originates from non-electrostatic sources (like chemical reactions in a cell). 4. Originates from the electrostatic field set up by charge buildup across terminals.
5. It is the **cause**. Applying an EMF creates a potential difference. 5. It is the **effect** produced by the EMF.
6. Equal to the sum of potential drops across all components, including internal resistance. 6. Measured across individual components; each element has its own potential drop.
7. Larger than the potential difference across any single component in the circuit. 7. Always less than the overall EMF during circuit discharge.
8. Independent of external resistance in the circuit. 8. Depends directly on external resistance and current ($V = IR$).

Electric Cell : Properties | Types

What is Electric Cell?

Ans: An electric cell (or electrochemical cell) is a device that converts chemical energy (or light/thermal energy) into electrical energy. It acts as a source of direct current (DC) by maintaining a steady potential difference across a closed circuit.

1. Electrical properties of a Cell:

The electric cell have three fundamental electrical properties :

i) Electromotive Force (EMF, $E$): The work done by source in taking a unit charge once round the complete circuit.

$E= \frac{W}{q}$

ii) Terminal Voltage ($V$): The actual potential difference across the cell's terminals when it supplies current $I$ to an external load resistance $R$ (closed circuit).

iii) Internal Resistance ($r$): The property of electrolyte and electrodes in cell that oppose the flow of current.

Discharging Equation: When a cell supplies current $I$ to an external circuit:

$V = E - I r$

Charging Equation: When an external source charges the cell:

$V = E + I r$

2. Types of Cells

Cells are classified based on their underlying mechanism, chemical reversibility, and application.

A. Primary Cells (Non-Rechargeable): In primary cells, the internal chemical reaction is irreversible. Once the active chemical reactants are consumed, the cell can no longer generate electricity.

Working Principle: Direct conversion of chemical energy into electrical energy via non-reversible redox reactions.

Characteristics: High energy density, low initial cost, lightweight, but cannot be recharged.

Examples:

Simple Voltaic Cell: Copper anode (+) and Zinc cathode (-) in dilute sulfuric acid (${H}_2S{O}_4$).

Daniell Cell: Copper in $CuSO_4$ solution and Zinc in $ZnSO_4$ solution separated by a porous pot or salt bridge.

Dry Cell (Leclanché Cell): Zinc container (-) with a central carbon rod (+) surrounded by manganese dioxide ($MnO_2$) and ammonium chloride ($NH_4\Cl$) paste. Used in remotes and clocks.

B. Secondary Cells (Rechargeable / Accumulators): In secondary cells, the chemical reaction is reversible. Applying an external electrical current forces the reaction in reverse, restoring the chemical state (charging).

Working Principle: Reversible energy conversion (Electrical $\rightarrow$ Chemical during charging; Chemical $\rightarrow$ Electrical during discharging).

Characteristics: Reusable for hundreds to thousands of cycles, lower internal resistance, capable of supplying high currents.

Examples:

Lead-Acid Accumulator:It is used in automobiles (like in heavy motor vehicle) and home for backup power (inverters).

Lithium-Ion (Li-ion) Cell:It is used in smartphones, laptops, and electric vehicles (EVs).

Nickel-Cadmium (NiCd) & NiMH Cells:It is used in low power and rechargeable AA/AAA batteries (It is made up of standard dry cell ).

C. Fuel Cells: Fuel cells continuously convert the chemical energy of a fuel supplied from an external tank (such as hydrogen) and an oxidant (oxygen) directly into electricity.

Working Principle: Continuous supply of fuel $\rightarrow$ continuous electric current and water byproduct.

Characteristics: High operating efficiency ($\approx 60-70\%$), zero greenhouse gas emissions.

D. Photovoltaic (Solar) Cells: Unlike electrochemical cells, solar cells convert light energy (photons) directly into electrical energy via the photovoltaic effect in semiconductor $p-n$ junctions (typically silicon), without relying on chemical reactions.

Description of the units and scale of energy

Description:

Unit of Energy

The SI unit of energy is the Joule (J), named after the English physicist James Prescott Joule.

1 Joule is defined as the work done when a force of one Newton is applied to an object and the object is displaced by 1 metre in the direction of the applied force:

$1 J = 1 N·m = 1 kg·m^{2}·s^{-2}$

Other Common Units of Energy

Unit Symbol Equivalent in Joules Used In
Electronvolt eV $1.6 × 10^{-19} J$ Atomic & nuclear physics
Calorie cal $4.184 J$ Thermodynamics, food
Kilocalorie kcal $4184 J$ Nutrition
Kilowatt-hour kWh $3.6 × 10^{6} J$ Electrical energy
Erg erg $10^{-7} J$ CGS system
British Thermal Unit BTU $1055 J$ Engineering (UK/US)

Scale of Energy — From Smallest to Largest

Scale Energy (Joules) Example
$10^{-34} J$ Quantum scale Energy of a photon of a radio wave
$10^{-19} J$ Atomic scale 1 electronvolt (ionisation energy)
$10^{-18} J$ Molecular scale Energy of a chemical bond
$10^{-3} J$ Millijoule Energy in SHM of a spring (small oscillation)
$1 J$ Joule KE of a 1 kg mass moving at √2 m/s
$10^{3} J$ Kilojoule Energy in a food biscuit
$10^{6} J$ Megajoule Energy of a 1-tonne car at 160 km/h
$10^{9} J$ Gigajoule Daily energy use of a household
$10^{15} J$ Petajoule Energy released by a small nuclear bomb
$10^{22} J$ Astronomical scale Kinetic energy of Earth's rotation
$10^{41} J$ Stellar scale Energy released by a supernova explosion

Gaussian Surface and its Properties

Gaussian Surface and its Properties:

The Gaussian surface is a hypothetical or imaginary closed three-dimensional surface. This surface is used to calculate the electric flux through a vector field (i.e. gravitational field, electric field, or magnetic field).

Examples:

Gaussian surfaces are surfaces of spheres, cylinders, cubes, etc. There are some surfaces which cannot be used as Gaussian surfaces like the surface of disc, square etc.

Essential properties of Gaussian surface are :

1. The Gaussian surface must be closed surface to clearly define the regions, inside, on, and outside the surface.

2. A Gaussian surface is constructed to pass through the point at which the electric field is being calculated.

3. The shape of the Gaussian surface depends upon the shape or symmetry of the charge distribution (i.e. the source).

4. For systems with discrete charges, the surface should not intersect any point charge, as the electric field is undefined at the location of a point charge. However, the surface can intersect continuous charge distributions

5. The electric flux through the surface depends solely on the total charge enclosed within it, not on the external charges.

6. The electric field at any point on the Gaussian surface is influenced by both internal and external charges.

7.If the electric flux is zero through the surface, it does not necessarily mean the electric field is zero. However, if the electric field is zero at every point on the surface then the electric flux will be definitely zero.

8. If a closed surface encloses no net charge, the total electric flux through it will be zero—regardless of whether the external electric field is uniform or varying.

Population of energy level and it thermal equilibrium condition

Population of energy level:

The number of atoms per unit volume in any energy level is called the population of that energy level.

The population $N$ of any energy level $E$ depends on the temperature $T$ which can be described by

$N=e^{-\left(\frac{E}{kT}\right)}$

Where $k \rightarrow$ Boltzmann's Constant

The above equation is called the Boltzmann equation.

Population of energy level at thermal equilibrium condition:

At thermal equilibrium, the number of atoms (Population) at each energy level decreases exponentially with increasing energy level, as shown in the figure below.
Population of atoms in energy levels
Let us consider, two energy levels $E_{1}$ and $E_{2}$. The population of these energy levels can be calculated by

$N_{1}=e^{\left(-\frac{E_{1}}{kT} \right)} \quad (1)$

$N_{2}=e^{\left(-\frac{E_{2}}{kT} \right)} \quad (2)$

The ratio of the population in these two levels is called the relative population.

$\frac{N_{2}}{N_{1}}= \frac{e^{\left(-\frac{E_{2}}{kT} \right)}}{e^{\left(-\frac{E_{1}}{kT} \right)}}$

$\frac{N_{2}}{N_{1}}= e^{\left(-\frac{(E_{2}-E_{1})}{kT} \right)} $

$\frac{N_{2}}{N_{1}}= e^{-\frac{\Delta E}{kT} } $

This equation is known as Boltzmann's distribution. The above equation suggests the relative population is dependent on two factors.

1.) The energy difference $(\Delta E)$

2.) The absolute temperature $T$

Ferromagnetic Substances and Its Properties

Description:

The atoms of these materials like paramagnetic material have permanent magnetic dipole moments. The similar natures of dipoles are grouped in a small region called domain. These domains have a net magnetic moment in a particular direction. In the material, there are a large number of domains having magnetic moments in different directions making the net magnetic moment of the entire material zero. When the external magnetic field is applied to such ferromagnetic materials, then either the domains are oriented in such a way as to align with the direction of the field, or the size of the favorable domain increases. Generally, in the strong applied field the domains are aligned and in the weak field the size of the favorable domain increases. In both cases, the material is strongly magnetized in the direction of the applied external magnetic field.
Ferromagnetic Substances
Properties of Ferromagnetic Substances:

The properties of ferromagnetic substances are similar to the properties of diamagnetic substances but the difference is that diamagnetic substances are weakly magneties and ferromagnetic substances strongly magenties in the presence of magnetic field.

Properties of Ferromagnetism:

1.) If these materials are placed in an external magnetic field, they are strongly magnetized in the direction of the applied external magnetic field.

2.) Due to unpaired electrons, the atoms of ferromagnetic materials have a net magnetic dipole moment.

3.) Ferromagnetism arises due to the formation of domains.

4.) Magnetic susceptibility of these materials is high and positive and also inversely proportional to the absolute temperature:

$\chi=\frac{C}{T-T_{c}}$

where $T_{c}$ is Curie temperature.

5.) Relative permeability of these materials is much greater than 1.

6.) Magnetic moment is high but along the direction of the applied magnetic field.

7.) $Fe$, $Ni$, $Co$, etc. are examples of paramagnetic materials.

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