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.

High Monochromaticity of Laser Light

High Monochromaticity:

A laser beam is highly monochromatic. The monochromaticity of the laser beam is much more than that of any traditional monochromatic source. The line spread of a laser beam is very small in comparison to the light from a traditional source. This difference arises because conventional sources emit wave trains of very short duration and length, whereas, laser emit continuous waves of very long duration. The random spontaneous emission in the laser cavity is one of the mechanisms that determine a laser's ultimate spectral line width. It should be noted that no light source including laser light source, is perfectly monochromatic but a better approximation to the ideal condition may be considered in the case of the laser beam. The spread of light from a normal monochromatic source range over a wavelength of the order of $100 -1000 \overset{\circ}{A}$ while in lasers it is of the order of few angstroms $(\lt 10 \overset{\circ}{A})$ only.
High monochromaticity of laser
The high spectral purity of laser radıation leads directly to applications in basic scientific research including photochemistry, luminescence excitation spectroscopy absorption, Raman spectroscopy, and also in communication. The degree of non-monochromaticity $\xi$ of light is characterized by the spread in frequency of a line by the line width $\Delta \nu $ and is expressed as:

$\xi=\frac{\Delta \nu}{ \nu_{\circ}}$

where $\nu_{\circ}$ is the central frequency. If $\Delta \nu $ approaches zero the degree of non-monochromaticity tends to zero which is an ideal condition. Absolute monochromaticity $(\Delta \nu =0)$ is not attainable in practice even with laser light. The spreads of two light sources, laser light, and normal light, are shown in the figure above. The degree of non-monochromaticity may also be written in terms of coherence time $(\tau_{C})$ or coherence length $(L_{C})$ as follows:

$\xi=\frac{1}{\tau_{C} \: \nu_{\circ}}$

$\xi=\frac{c}{L_{C} \: \nu_{\circ}}$

This relation shows that the monochromaticity will be large for higher values of coherence time or coherence length. The bandwidth of a laser light from a high-quality He-Ne gas laser is of the order of $500Hz$ $(\Delta \nu =500 Hz)$ corresponding to coherence length of the order of $600 km$ $(\tau_{C} = 2 \times l0^{-3} sec)$.

Conversion of Galvanometer into a Voltmeter

What is a voltmeter?

A voltmeter is an instrument used to measure potential differences between two points in an electric circuit directly in volts. The instrument measuring the potential difference of the order of millivolt $(mV)$ is called a millivoltmeter. An ideal voltmeter has infinite resistance.

Galvanometer used as voltmeter:

To use the galvanometer as a voltmeter in the circuit, The resistance of the galvanometer should be very high or almost infinite as compared to the other resistance of the circuit. Because the internal resistance of an ideal voltmeter is infinity.

So a high resistance is connected in series with the galvanometer (pivoted-type moving-coil galvanometer).

When a high resistance is connected in series to the galvanometer then the resultant resistance increases as compared to the other resistance of the circuit and it can be easily used as an ammeter and the actual potential difference can be measured through it.
Conversion of galvanometer into a voltmeter
Mathematical Analysis:

Let us consider, $G$ is the resistance of the coil of the Galvanometer, and the $i_{g}$ current, passing through it, produces full-scale deflection. If $V$ is the maximum potential difference that exists between two points $a$ and $b$ in the circuit. On connecting the galvanometer across the points $a$ and $b$, a current $i_{g}$ passes through the galvanometer and a high resistance $R$ is connected in series with galvanometer then

$i_{g}= \frac{V}{G + R}$

$G + R= \frac{V}{i_{g}}$

$R= \left(\frac{V}{i_{g}}\right ) - G$

If the current $i_{g}$ in the coil produces a full-scale deflection, then for the potential difference $V$ between the points $a$ and $b$, there will be a full scale deflection. Thus, on connecting a resistance $R$ of the above valve in series with the galvanometer, the galvanometer will become a voltmeter of range $0$ to $V$ Volt.

Note:

For the voltmeter, a high resistance is connected in series with the galvanometer and so the resistance of a voltmeter is very high compared to that of a galvanometer.

Resistance of voltmeter

$R_{v}=R+G$

Light Detection And Ranging (LIDAR)

LIDAR (Light Detection And Ranging):

The laser system used for monitoring the environment is known as LIDAR. LIDAR is an acronym that stands for "Light Detection And Ranging".

Before the discovery of the laser, the study of the atmosphere was carried out using an optical beam, the source being the search light. One such experiment was performed by Hulbert in 1937 to study the turbidity of the atmosphere. After the discovery of the laser as a source of an optical highly coherent beam, the study of the atmosphere was revolutionised.

A pulsed laser beam is transmitted into the atmosphere. It is scattered by the particles present in the atmosphere. The scattered radiations are picked up by a receiver. The receiver removes the background sunlight by using different filters. The scattered light gives information regarding the particles present in the atmosphere. Although microwaves can also give these characteristics, the results from laser beams are better in resolution and clarity. The different particles present in the atmosphere in colloidal form can be studied by a LIDAR. A schematic diagram of such a setup is shown in the Figure Below.
Light Detection And Ranging
A photo detector is used to measure the time dependence of the intensity of the back-scattered laser beam. The time variation can be easily converted into the height (range) from which the laser beam has been back scattered the figure below shows a plot of time dependence of back scattered laser beam, which corresponds to height in the case of clear atmosphere with no aerosols, i.e., back scattering is by pure molecular gases such as $N_{2}$, $O_{2}$, $Ar$ etc. These molecules have dimensions much smaller than optical wavelength.

The scattering is of Rayleigh type. The figure below shows a plot of time dependence of backscattered light in the atmosphere contained aerosols (colloidal particles). These particles have dimensions comparable with the wavelength of laser light. This is Mie scattering. The curve in the figure below has kinks at points A and B between heights h and h. These kinks are due to the fact that between points $A$ and $B$, there are aerosols that are responsible for a greater intensity than that for a clear atmosphere. This implies the presence of aerosols between heights $h_{1}$ and $h_{2}$. With LIDAR, it is also possible to study the concentration and sizes of the aerosols present in the atmosphere. These are very important in atmospheric pollution studies.
Graph between range Vs laser radiance at receiver

Comparison between electric charge and mass

Electric Charge:

1.) An electric charge can be positive, negative, or neutral.

2.) The electric charge of a body is always quantized and follows the equation: $q=ne$

3.) The electric charge of a body remains unaffected by its speed.

4.) Charge is strictly conserved.

5.) Electrostatic forces between two charged bodies can be either attractive or repulsive.

6.) Electrostatic forces between multiple charges can sometimes cancel each other out.

7.) A charged body always carries some mass.

Mass:

1.) The mass of a body is always positive.

2.) Unlike charge, mass quantization has not yet been established.

3.) The mass of a body increases with its speed.

4.) Mass is not conserved by itself as some of the mass may get changed into energy or vice versa.

5.) Gravitational forces between two masses are always attractive.

6.) Gravitational forces between multiple bodies never completely cancel out.

7.) A body with mass may not necessarily have a net charge.

Weak nuclear force or interaction and its properties

What is weak nuclear force? 

Weak nuclear force is an act between only elementary particles involved in the nuclear process of $\beta$ - decay. The $\beta$ decay are two types

1.) Beta Pluse Decay
2.) Beta Minus Decay

1.) Beta Plus Decay:

When a beta plus decay occurs, a proton converts into a neutron and releases a positron $\&$ an electron-neutrino. It also reduces one atomic number of an element and converts it into another element.
Beta Plus Decay
2.) Beta Minus Decay:

When a beta minus decay occurs, a neutrons convert into a proton and releases an electron $\&$ electron-antineutrino. It also increases one atomic number of an element and converts it into another element.
Beta Minus Decay
In addition to beta decay, some scientists also find many other types of weak force like "charged-current" or "neutral-current". The charge is required for "charged-curent" but not for "neutral-current"; because of that, there are two types of charged carriers: one is the $W$ boson charge carrier and $Z$ boson.

Important properties of weak nuclear force :

1. Any process involving neutrino and antineutrino is governed by weak nuclear force because these particles can experience only weak interaction and not strong nuclear interaction.

2. The strength of weak nuclear force is greater than gravitational force and less than electromagnetic force.

3. It operates only in the range of nuclear size ($ \approx 10^{-15} m$).

4. The messenger particles that transmit the weak nuclear force between elementary particles are the massive vector bosons ($W^{\pm}, Z^{\circ}$).

5. The decay of in weak nuclear force (e.g., the decay of a pion to a muon and a neutrino) is much slower than the decay caused by strong nuclear or electromagnetic forces.

Description of Errors in Measurement

Errors in Measurement

The following errors are likely to occur in the measurement of a physical quantity:

(1) Systematic Errors (arise due to known causes. The experimenter has control over the errors)
(2) Random Errors (arise due to unknown causes. The experimenter has no control over the errors)

(1) Systematic Errors:

When a measurement always has the same error (i.e. the nature or sign of the error is always of the same type, positive or negative), it is called systematic error.

Systematic errors occur due to known causes. These errors can be removed by knowing the causes.

Types of Systematic Errors:

(i) Constant Errors: If the measuring instrument is faulty from the point of view of its structure or design. That is, if the measurement marks made on the measuring instrument are wrong (faulty graduations), then by using such an instrument the error is always the same in all the observations. Such an error is called a constant error.

To remove static errors, an error-free measuring instrument should be used in place of the faulty measuring instrument and if this is not possible, then the nature of the error in the faulty instrument should be determined and measurements should be made as many times as possible.

(ii) Errors Due to Instruments: Such measuring instruments are error-free from the point of view of structure or design, but their excessive use causes defects in these instruments. Like zero error in vernier calipers or screw gauges, etc. Before starting the observation, such errors are found in all the measuring instruments used so that the final result of the measurement can be accurate.

(iii) Personal Errors: Those errors which arise due to the carelessness of the experimenter or the person doing the measurement are called personal errors. It does not depend on measuring instruments. This error can be reduced by increasing caution and taking readings correctly.

(iv) Errors caused by external factors (Errors due to External Reasons): Errors caused in observation due to changes in pressure, temperature, humidity, air velocity, etc. while taking observations are called errors caused by external factors.

These types of errors can be eliminated by adopting appropriate precautions and making possible arrangements to control environmental change. Can be done.

(2) Random Errors:

Such errors over which the experimenter has no control are called irregular errors. If the temperature, pressure, or humidity of the environment suddenly changes rapidly during observation or the supply voltage changes suddenly in any electrical experiment or the value of the earthquake exceeds the normal limit, then such changes have different effects in different experiments which affects the value of observation. These errors can be eliminated to a great extent by taking measurements several times and finding their average. Actual value can be found.

Description of Force and their Types

Force:

Force is a push or pull by which the state of the object changes or tends to change.

Types of forces:

There are two types of forces-

1.) Contact Force
2.) Non-Contact Force

1.) Contact force:

When there is physical contact between the two objects by push or pull then it is known as contact force.

For Example:

i.) When a coiled spring is stretched (pulled), the two ends of the spring must be in actual contact with the person's hands.
ii.) Kicking a football, and pulling a cart are also contact forces.

Types of Contact Force:

I.) Applied Force
II.) Frictional Force
III.) Normal Force
IV.) Tension Force
V.) Air Resistance (Drag Force)
VI.) Elastic or Restoring force

I.) Applied Force:

When a force is exerted by a person or an object to another person or object then this force is known as applied force.

$F=ma$

Example: Pushing a shopping cart, pulling a door open.

II.) Frictional Force:

When two surfaces are in motion relative to each other and in contact then a force acting in the opposite direction of the motion of one surface over the other is called the force of friction. The frictional force is also called the force of friction or simply friction.

$F=\mu R$

A smooth surface exerts a lesser force of friction than a rough surface. The rolling frictional froce is always less than the sliding frictional force.

Types of Friction Force:

i.) Static Friction:

When the frictional force is applied on the object due state of the rest of the object then frictional force is known as static friction.

ii.) Kinetic Friction:

When the frictional force is applied to the object due motion of the object then frictional force is known as dynamic friction.

iii.) Limiting Friction:

The maximum value of static frictional force is known as limiting friction.

Example: Rubbing hands together, a car’s brakes stopping a vehicle

III.) Normal Reaction Force:

When an object is placed on a surface (or another object), the object exerts a force on the surface (or another object) vertically downwards. However, the object does not move in the direction of the force. This is because the surface (or another object) exerts an equal and opposite force on the object vertically upwards. then this force is called normal reaction force.

$Normal \: reaction \: force (N) = Weight \: of \: the \: object (mg) $

Example: A book resting on a table, a person standing on the ground.

IV.) Tension force:

The force on the string, rope, or cable due to pulled tight is known as Tension. Force is transmitted through a s when pulled tight.

Example: A person pulling a rope in a tug-of-war, a hanging lightbulb.

V.) Air Resistance (Drag Force):

It is a type of friction force that acts against objects moving through the air.

Example: A parachute slowing down a skydiver, wind resistance on a car.

VI.) Spring Force (Elastic Force Or Restoring force):

A force that always acts in the opposite direction of the object's displacement is known as elastic or restoring force.

Example: A compressed spring in a toy, a rubber band being stretched.

2. Non-Contact Forces (Act at a distance)

I.) Gravitational Force (F)

The force of attraction between two heavy objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

$F=G \frac{m_{1}m_{2}}{r^{2}}$

This force is most effective between very heavy objects like satellites, Planets Su,n and Stars.

Example: Objects falling to the ground, Earth’s gravity keeping the Moon in orbit.

II.) Electromagnetic Force:

When electric force and magnetic force are applied perpendicular to each other on charged particles then a force acts perpendicular to both this force is known as electromagnetic force.

The force between charged objects include both electric force and magnetic forces.

Example: Lightning (electric force), magnets attracting iron nails.

i.) Magnetic Force:

The force between magnetic materials, either attracting or repelling is known as magnetic force. The magnitude of magnetic force due to moving charge is described by Lorentz's law ($F=qvB sin \theta$)and direction is described by Fleming's left-hand rule. Similarly, the magnetic force due to the conductor is described by the formula $F=iBl sin\theta$ that is deduced by Lorentz's law, and the direction of force in a conductor is also described by Fleming's left-hand rule.

Example: A compass needle pointing north, fridge magnets sticking to a fridge.

ii.) Electric Force:

The attraction and repulsion force between the charges is known as the electric force. The magnitude of this force is described by Coulomb's law and the direction is described by the vector form of Coulomb's Law.

$F=\frac{1}{4\pi \epsilon_{\circ} K} \frac{q_{1}q_{2}}{r^{2}}$

IV.) Nuclear Forces: The force between the nucleons (i.e. proton and neutron) is known as nuclear force. Nuclear forces are two types.

i.) Strong Nuclear Force:

It is the very strongest and short-distance force that holds protons and neutrons together in an atomic nucleus.

ii.) Weak Nuclear Force:

When the nucleus is involved in radioactive $\beta$ decay then the force between the particles is known as weak nuclear force. The force is involved in the reaction of nuclear fission and fusion.

Example: The energy released in nuclear reactions, like in the Sun or nuclear power plants.

Finding Significant Figures in a Measurement

What is significant Figure?

The total number of digits (i.e. doubtful digit and confirm digits) in any measurement is known as significant figure.

Or

The digits that reflect the precision of the measurement are called significant figures.

Counting of Significant Figures in any Measurement:

Knowing the significant figures in a measure is based on the following rules-

(1) All non-zero numbers are significant figures.

For example, $46.3598$ has $6$ significant figures.

(2) All zero numbers between two non-zero numbers are significant figures.

For example, $600.8049$ has $7$ significant figures.

(3) If there is no non-zero number before the decimal point, then all the digits in the number except the zero numbers immediately after the decimal point are significant figures.

For example, $0.002809$ has $4$ significant figures.

(4) The zero after any non-zero digit to the right of the decimal point is a significant figure.

For example, $0.46920$ has $0$ significant figures.

(5) If a number is multiplied by a power of $10$, it does not affect the number of significant figures.

For example, $6.75\times 10^{3}$ has $3$ significant figures.

(6) Choosing different units does not change the number of significant figures.

For example, if a measurement is $2346 km$, then in different units, this measurement will be $23460 m$, $2346000 cm$ or $23460000 mm$. Here, the number of significant figures in each measurement is $4$.

Limitations of Dimensional Analysis

Limitations of Dimensional Analysis:

(1) It is not possible to find the numerical value of constants $k$ (dimensionless) present in the formulas by this method. It can be obtained by experiment or other method.

(2) If any physical quantity depends on more than three quantities, then the mutual relation between these quantities cannot be established by this method. However, the dimensional correctness of any given equation of this type can be checked.

(3) If any physical quantity depends on only three physical quantities, but the dimensions of two of the three quantities are the same, then also the mutual relation between these quantities cannot be established by the dimensional method, but the dimensional correctness can be checked.

(4) If an equation has more than one term on one side, like $v=u+at$ (Here two terms on the right side), then this equation cannot be derived by dimensional method. That is, such relations cannot be derived in which there is a positive $(+)$ or negative $(-)$ sign anywhere. But whether the equation is dimensionally correct or not, can be checked.

(5) Deduction of equations containing trigonometric ratios ($ sin \theta$, $cos \theta$, $tan \theta$, etc.), variable exponential ($e^{x}$) and logarithmic ($log\:x$) terms is not possible by dimensional analysis method, but their dimensional truth can be checked.

(6) Whether a physical quantity is vector or scalar cannot be determined by the dimensional analysis method.

(7) If the constant in an equation is not dimensionless, then the dimensional analysis method cannot be used for the deduction of that equation.

(8) For a physical relation represented by an equation to be true, it is a necessary condition for this equation to be in dimensional balance, but only dimensional balance is not sufficient for the physical relation to be true. That is,

"Even if the equation is true physically and mathematically, it may not be true dimensionally."

Difference between Forced Vibrations and Resonant Vibrations

Forced Vibrations:

1. The vibrations of a body under an external periodic force of frequency different from the natural frequency of the body, are called forced vibrations.

2. The amplitude of vibration is small.

3. The vibrations of the body are not in phase with the external periodic force.

4. These vibrations last for a very short time after the periodic force has ceased to act.

Resonant Vibrations:

1. The vibrations of a body under an external periodic force of frequency exactly equal to the natural frequency of the body, are called resonant vibrations.

2. The amplitude of vibration is very large.

3. The vibrations of the body are in phase with the external periodic force.

4. These vibrations last for a long time after the periodic force has ceased to act.

Difference between Natural Vibrations and Damped Vibrations

Natural Vibrations:

1. The amplitude of natural vibrations or free vibrations remains constant and the vibrations continue forever.

2. Natural vibrations never lose energy during vibrations.

3. There are no external forces acting on the vibrating body. The vibrations are only under the restoring force.

4. The frequency of vibrations depends on the size and shape of the body and it remains constant.

Damped Vibrations:

1. The amplitude of damped vibrations gradually decreases or reduces with time and ultimately the vibrations cease.

2. In each vibration, there is some energy loss in the form of heat.

3. Besides the restoring force, a frictional or damping force acts on the body to oppose its motion.

4. The frequency of damped vibrations is less than the natural frequency. The decrease in frequency of vibrations depends on the damping force.

Difference between Natural (Free) Vibrations and Forced Vibrations

Natural (Free) Vibrations:

1.) The vibrations of a body in absence of any resistive or external force are called natural vibrations.

2.) The frequency of vibration depends on the shape and size of the body.

3.) The frequency of vibration remains Constant.

4.) The amplitude of vibration remains constant with time (in absence of surrounding medium).

Forced Vibrations:

1.) The vibrations of a body in a medium in presence of an external periodic force are called forced vibrations.

2.) The frequency of vibration is equal to the frequency of the applied force.

3.) The frequency of vibration changes with change in the frequency of the applied force.

4.) The amplitude of vibration depends on the frequency of the applied force.

Renewable Energy Sources

Renewable Energy Sources:

Various renewable energy sources are as follows:

Solar Energy:

The solar energy is a non conventional energy source. It is very cost effective clean and non polluted renewable energy source and reduces the greenhouse gas effect.

The Solar Energy is derived from the Sun radiation and can be utilised by photosynthesis, photo voltaic cell, photo thermoelectric system.

The sun release the enormous amount of energy and it's rate of radiation is $3.7 \times 10^{20}$ megawatt while the earth receive the radiation at rate by $1.85 \times 10^{11}$ megawatt. So energy radiation by the sun is several times more than the consumption of radiation in the earth.

Advantages:

1.) It is very clean energy.

2.) It is non polluted energy source.

3.) It is zero cost energy source and low maintenance cost.

4.) It has zero noise in operation.

Disadvantages :

1.) Energy source cannot utilise properly at night, cloudy atmosphere and rainy day.

2.) It has required large surface area to collect the energy source from Sun.

Hydro energy:

The hydro energy is derived from moving and falling water which convert into mechanical energy and utilise for production of electrical energy through turbine.

The water is stored in reservoir or dam has high potential energy and when water flow or fall under the gravity then it rotate the turbine and produces the electricity.

Advantages:

1.) It is very clean energy source.

2.) It produce zero pollution.

3.) It has zero fuel cost.

4.) It requires low maintenance cost.

5.) It is reliable energy source.

Disadvantages:

1.) It can cause climate change due to high amount of storage of water in mountains.

2.) It can cause flood and disrupt ecosystem.

Wind energy:

Wind energy is also non polluting energy source and it has tremendous potential to fulfill the demand of energy of the country.

It is estimated that only $2 \%$ of solar energy fall on the earth and converted into kinetic energy of the atmospheric molecules or atoms. The highest kinetic energy of atmosphere is found in the lower to mid troposphere layer which is lowest layer of atmosphere because of that this kinetic energy can be easily converted to the mechanical energy which can futher utilise for the production of electrical energy and other energy production.

Advantage:

1.) It is useful for remote places for the production of electricity.

2.) The availability of the source is zero cost.

Disadvantages:

1.) This energy source cannot be properly utilised where wind is available at very higher location.

2.) It is unreliable because flow of wind cannot be continuous all the time.

Wave Energy:

The wave energy is available on the surface of sea. The floating propeller is placed on the surface of the shallow water near to shores and due to motion of wave propeller get start to rotate and this rotational energy is used to derive the turbines.

Advantages:

1.) This is clean or cheap energy source.

2.) The size of the machine for the collection of wave is comparatively smaller than solar device.

Disadvantages:

Corrrosion of material used in plant.

Geothermal energy:

This is the energy is produced due to hot rocks present inside the earth. The temperature of the earth increases with increase in depth below the surface of the earth. The hot molted rock is present at center or core of the earth this causes volcano action. The hot rock is pull out from volcano and used to produce the steam by heating water. This steam is further utilised for the operation of turbine to produce the electricity.

Advantages:

It is cheap source which requires small area for the operation or production of the electricity.

Disadvantages:

1.) It causes the air pollution due to production of gases like $H_{2}S$ and $NH_{3}$in steam waste.

2.) It is also causes noise pollution due to drilling operation.

Basics of Third Generation Solar Cells and Their Types

Third Generation Solar Cells :

They are proposed to be very different from the previous semiconductor devices as they do not rely on a traditional p-n junction to separate photogenerated charge carriers.

For space applications quantum well devices (quantum dots, quantum ropes etc.) and devices incorporating carbon nanotubes are being studied with a potential for up to $45 %$ production efficiency.

For terrestrial applications, these new devices include photoelectrochemical cells, polymer solar cells, nanocrystal solar cells,dye sensitized solar cells and are still in the research phase.

Types of Third Generation Solar Cells :

A.) Organic Photovoltaic Cell :
Organic Photovoltaic Solar Cell
1. The solar cells based on organic semiconductor can provide a low cost alternative for photovoltaic solar.

2. The thickness of the active layer of organic solar cells is only $100 nm$ thin, which is about $1000$ times thinner than the crystalline silicon solar cells, and it is about 10 times thinner than the current inorganic thin film solar cells.

3. In the low material consumption per solar cell and the relatively simpler cell processing of organic semiconductors, there is a large potential for low cost large area solar cells.

4. Due to this reason, there is a considerable interest in organic photovoltaic devices.

5. Their principal advantage is that they are flexible and can bend without breaking, unlike $Si$, which is brittle.

6. They are also very light and cheap.

7. They may folded or cut into required size and can still be used.

B.) Dye Sensitized Solar Cell (DSSC):
Dye Sensitized Solar Cell (DSSC)
1. Dye Sensitized Solar Cell converts any visible light into electrical energy.

2. The dye sensitized solar cells can be considered as a thin film solar cell device. This technology is not yet commercialized but is on the verge of commercialization.

3. The dye sensitized solar cells can be made flexible. It has a very good potential for being a low cost effect solar cell technology.

4. This is mainly possible because of the large availability and low cost of the ingredient material as well as due to the low processing temperatures.

5. The dye sensitized solar cells is a photo-electro-chemical device. In its operation it involves a photon, an electron and a chemical reaction.

6. The operation of dye sensitized solar cell is considered similar to that of a photosynthesis process.

7. The DSSC has a number of attractive features; it is simple to make using conventional roll-printing techniques, is semi-flexible and semi- transparent which offers different type of uses not applicable to glass-based systems, and cost of most of the materials used in DSSC are very low.

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