Time Allowed: 3 Hours | Maximum Marks: 80
This question paper is divided into three sections: Section A (20 Marks), Section B (30 Marks), and Section C (30 Marks).
All questions in Section A are compulsory.
Section B contains short-answer questions with internal choices.
Section C contains long-answer/case-based questions requiring analytical reasoning.
Biochemistry
Short Notes for quick revision:
Proteins are among the most important biomolecules present in living organisms. They perform numerous functions such as enzymatic catalysis, transport, defense, hormonal regulation, muscle contraction, and structural support. The biological activity of a protein depends directly upon its three-dimensional structure.
A protein is made up of amino acids linked together by peptide bonds forming long chains called polypeptides. These polypeptide chains fold into specific structures that determine their functions.
The concept of Centroid is one of the most important ideas in Engineering Mechanics, Strength of Materials, Structural Engineering, Machine Design and Fluid Mechanics.
Whenever we deal with beams, plates, laminae, sections, bending stresses, moments of inertia, or stability problems, the centroid becomes fundamental.
In this article, we shall discuss:
One Dimensional (1D) Objects
Two Dimensional (2D) Objects
Concept of Resultant Area
Mathematical Derivation of Centroid
Varignon’s Theorem of Moments
Centroid of Composite Figures
Centroid of Curves and Lines
Symmetry Conditions
Centroid of Common Geometrical Shapes
Negative Areas (Removed Portions)
Centroid by Integration
Applications of Centroid
Relationship Between Centroid and Moment of Inertia
Parallel Axis Theorem
Practical Engineering Examples
Welcome to your comprehensive study material for Chapter 1 of the NCERT Ganita Prakash textbook: Large Numbers Around Us. This guide is designed to help you master the concepts of large numbers, understand how they behave, and develop a strong spatial and logical sense of their scale.
Chemical Bonding
Periodic Classification of Elements
The ICSE Chemistry paper pattern consists of:
Section I: Compulsory short-answer questions covering the entire syllabus
Section II: Structured analytical questions with internal choices
Focus on:
Application-based questions
Assertion-reasoning
Diagram/data interpretation
Logical chemical analysis
Conceptual understanding rather than rote memorization (ICSE Portal)
The word Trigonometry comes from two Greek words:
Trigon → Triangle
Metron → Measurement
So, trigonometry literally means:
“Measurement of triangles.”
Trigonometry is a branch of mathematics that studies the relationship between:
Sides of triangles
Angles of triangles
Especially, it deals with right-angled triangles.
In ancient times, people needed methods to:
Measure heights of mountains
Find distances between places
Navigate ships in oceans
Observe stars and planets
Since direct measurement was often impossible, mathematicians developed trigonometry.
The development of trigonometry started thousands of years ago.
Important civilizations contributing to trigonometry:
India
Greece
Babylon
Egypt
Arab civilization
Indian mathematicians made major contributions.
Aryabhata
Brahmagupta
Bhaskara I
Bhaskara II
These mathematicians developed:
Sine tables
Astronomical calculations
Angle measurement systems
Molecules of Life (MD-CHM-2.1)
B.Sc. Zoology – RTU Hojai University
Comprehensive Study Material
Living organisms are made up of a large number of chemical substances that perform various structural, physiological, and biochemical functions necessary for life. These chemical substances are known as biomolecules or molecules of life. Biomolecules are organic compounds produced by living organisms and are essential for growth, metabolism, reproduction, energy production, and maintenance of cellular activities. They form the structural and functional basis of all living cells and tissues.
Entrepreneurship in non-mulberry sericulture refers to the establishment and management of silk-related economic activities involving Eri and Muga silkworms for income generation, employment creation, and industrial development. Non-mulberry sericulture is an important agro-based cottage industry in India, especially in Assam and North-East India, where Eri and Muga silk are traditionally produced. This industry combines agriculture, animal rearing, handicrafts, textile production, and trade, thereby providing sustainable livelihood opportunities to rural populations.
Silkworm rearing technology refers to the scientific methods and techniques used for the successful cultivation and management of silkworms for silk production. In non-mulberry sericulture, proper rearing technology is extremely important because the health, growth, cocoon quality, and silk yield of silkworms depend largely on the rearing environment and management practices. Eri and Muga silkworms are highly sensitive to environmental conditions, food quality, hygiene, and diseases. Therefore, scientific rearing methods are essential for obtaining healthy larvae and high-quality silk.
Silkworm rearing involves several activities such as preparation of rearing house, maintenance of environmental conditions, feeding management, cleaning and disinfection, handling of larvae, cocoon formation, and harvesting. Proper rearing technology reduces mortality, prevents diseases, and increases silk productivity.
The rearing house is the place where silkworms are kept and reared throughout their larval stages. A good rearing house provides suitable environmental conditions such as proper temperature, humidity, ventilation, and protection from predators and diseases. The success of sericulture depends greatly on the condition and management of the rearing house.
Sericulture is the scientific method of rearing silkworms for the commercial production of silk. The word sericulture is derived from the Greek word “Sericos” meaning silk and the Latin word “Culture” meaning rearing or cultivation. It is an agro-based cottage industry that combines agriculture and industry because it involves cultivation of host plants as well as processing of silk fibers. Sericulture provides employment opportunities to rural people, especially women and economically weaker sections of society. It is considered an environmentally friendly industry because it produces biodegradable natural fiber.
Silk is one of the oldest and most valuable natural fibers known to humans. It is soft, shiny, strong, elastic, and has excellent dyeing properties. The silk produced by silkworms is mainly composed of a protein called fibroin, which is covered by another protein called sericin.
Coulomb's Law is a fundamental principle of physics that describes the force of attraction or repulsion between two stationary, electrically charged particles. Just as gravity governs how masses interact, Coulomb's Law governs how charges interact.
The law states that the electrical force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
To calculate the electrostatic force ($F$), we use the following equation:
The story is set in the Vijayanagara Empire during the reign of King Krishnadeva Raya. Known as the "Golden Era," this was a time of great art and literature.
The plot centers on a misunderstanding:
The Conflict: The King wrote a poem and recited it to Queen Thirumalambal. Being exhausted, the Queen yawned. The King took this as a personal insult to his poetry and stopped speaking to her.
The Solution: Desperate, the Queen asked Tenali Rama (the King's witty advisor) for help.
The Wit: Tenali Rama didn't argue with the King. Instead, he brought "magic" paddy seeds to court and claimed they would only grow if sown by someone who never yawns.
The Realization: When the King realized everyone (including himself) yawns naturally, he understood that the Queen’s yawn wasn't disrespectful. The royal couple reconciled, and Tenali Rama was rewarded.
Botany Paper II: Embryology of Angiosperms and Gymnosperm Morphology
1. Explain the structure and Development of Embryo Sac
In the context of the Rabindranath Tagore University (RTU), Hojai, botanical questions regarding embryology often require a detailed, step-by-step explanation of Megasporogenesis and Megagametogenesis.
JEE Main Previous Year Questions (2016-2025) on the topic of Units and Measurements:
Match List I with List II:
| List I | List II |
| A. Planck's constant ($h$) | I. $[M^1 L^2 T^{-2}]$ |
| B. Stopping potential ($V_s$) | II. $[M^1 L^1 T^{-1}]$ |
| C. Work function ($\phi$) | III. $[M^1 L^2 T^{-1}]$ |
| D. Momentum ($p$) | IV. $[M^1 L^2 T^{-3} A^{-1}]$ |
Choose the correct answer from the options given below:
(1) A-I, B-III, C-IV, D-II
(2) A-III, B-I, C-II, D-IV
(3) A-II, B-IV, C-III, D-I
(4) A-III, B-IV, C-I, D-II
Based on the NCERT chapter on Complex Numbers and Quadratic Equations, here is a simplified study guide designed to help you visualize and master the basics of Section 4.2.
In the real number system, we cannot solve equations like $x^2 + 1 = 0$ because $x^2 = -1$, and no real number squared results in a negative value. To solve this, mathematicians introduced the symbol $i$ (iota).
The Definition: $i = \sqrt{-1}$
The Property: $i^2 = -1$
A complex number ($z$) is a combination of a Real part and an Imaginary part. It is written in the form:
| Component | Name | Symbol |
| $a$ | Real Part | $Re(z)$ |
| $b$ | Imaginary Part | $Im(z)$ |
Example: In $z = 2 + i5$
The Real part is 2.
The Imaginary part is 5.
Physics Worksheet - 11
Board: CBSE/ICSE/AHSEC
Topic(s): Electric Potential and Potential Energy
Total Marks: 20
Time: 30 minutes
Name: ____________________ Class: _______ Date: ___________
INSTRUCTIONS
• Answer all questions.
• Write neatly and legibly.
• For numerical problems, show your working and include units in your final answer.
• Use k = 8.99 × 10⁹ N m² C⁻² where required.
• Charge of an electron = -1.60 × 10⁻¹⁹ C.
• Charge of a proton = +1.60 × 10⁻¹⁹ C.
SECTION A: MULTIPLE CHOICE QUESTIONS
The definition of electric potential difference between two points is: (1 mark)
a) The force experienced per unit positive charge.
b) The work done in moving a unit positive charge between the points.
c) The product of the electric field and the distance between the points.
d) The total kinetic energy gained by a charge moving between the points.
For your BSc Zoology Major under the NEP (New Education Policy) framework at Rabindranath Tagore University (RTU), Hojai, the study of Chordates typically falls under the Animal Diversity paper. Since your curriculum aligns closely with Gauhati University, these notes are structured for descriptive "Long Answer" type questions, emphasizing classification and comparative characteristics.
The name is derived from Greek (osteon = bone; ichthyes = fish). These are the most diverse group of vertebrates.
Endoskeleton: Primarily composed of bone (calcified).
Body Form: Usually streamlined/fusiform; skin is covered by cycloid, ctenoid, or ganoid scales (rarely placoid).
Mouth: Position is usually terminal (at the tip of the snout).
Respiration: Gills are covered by a protective bony flap called the operculum.
Buoyancy: Possess a swim bladder (air bladder) which helps them maintain depth without constant swimming.
Tail Fin: Usually homocercal (symmetrical lobes).
Reproduction: Mostly oviparous (lay eggs) with external fertilization.
Examples: Labeo rohita (Rohu), Exocoetus (Flying fish), Hippocampus (Sea horse).
Edunes Online Education
The nineteenth century marked a pivotal epoch in the physical sciences, characterized by the strategic transition from treating electricity and magnetism as isolated phenomena to recognizing their unified nature. This conceptual convergence, often referred to as the "great synthesis," laid the essential foundation for modern electrodynamics and fundamentally altered the trajectory of industrial and technological progress.
Initially, the experimental work of Hans Christian Oersted and André-Marie Ampère established the first critical link: the observation that moving electric charges—currents—inherently produce magnetic fields. This discovery, exemplified by the deflection of a compass needle near a current-carrying wire, prompted Michael Faraday to pursue the "converse" inquiry. If electricity could generate magnetism, Faraday reasoned, then magnetism should, under the right conditions, be capable of generating electricity.
The verification of this symmetry was achieved independently and nearly simultaneously around 1830 by two legendary figures:
These theoretical foundations provided the necessary framework to transition from philosophical inquiry into the rigorous experimental phase of electromagnetic research.
In classical electromagnetism, experimental observation serves as the essential prerequisite for the formulation of mathematical laws. The series of experiments conducted by Faraday and Henry provided the empirical evidence required to conclude that varying magnetic fields are the direct cause of induced electric currents in closed circuits.
Synthesizing the outcomes of the foundational Experiments 6.1, 6.2, and 6.3, we categorize the three distinct methods utilized to induce an electromotive force (EMF):
The "Relative Motion" concept emerged as the critical differentiator in these observations. The experiments proved that a static magnetic field is insufficient to generate power; rather, it is the change in the magnetic environment over time that drives the generation of current.
These physical observations necessitated the development of a standardized mathematical definition to quantify the "amount" of magnetism passing through a circuit, leading to the concept of magnetic flux.
Michael Faraday's groundbreaking experiments in 1831 demonstrated electromagnetic induction, the process by which a changing magnetic field creates an electric current in a conductor. This discovery established the fundamental link between electricity and magnetism and led directly to the invention of the electric generator and transformer.
Magnetic Flux \( \Phi_B \) serves as the primary metric for calculating induction and is of strategic importance in predictive physics. It is essentially a measure of the total magnetic field passing through a given area.
Magnetic flux through a plane of area A in a uniform magnetic field B is defined by the scalar product:
\( \Phi_B = \mathbf{B} \cdot \mathbf{A} = BA \cos \theta \)
Crucially, Magnetic Flux is a scalar quantity. The SI unit is the Weber (Wb), equivalent to a Tesla-meter squared \(T \cdot m^2 \).
Faraday formalized these observations into a mathematical law: the magnitude of induced EMF \( \varepsilon \) is equal to the time rate of change of magnetic flux through the circuit.
For a single loop:
\( \varepsilon = -\dfrac{d\Phi_B}{dt} \)
For a coil consisting of N closely wound turns, where the change of flux
associated with each turn is identical:
\( \varepsilon = -N\dfrac{d\Phi_B}{dt} \)
To induce an EMF, the flux must change over time. This is achieved through three specific mechanical or environmental alterations:
Physical Action |
Variable Changed |
Practical Implementation |
|---|---|---|
|
Changing the Magnetic Field |
B |
Moving a magnet or varying primary current. |
|
Altering the Shape/Area |
A |
Shrinking, stretching, or deforming the coil. |
|
Rotating the Coil |
\( \theta \) |
Changing the loop's orientation relative to field lines. |
While Faraday’s Law determines the magnitude of the induced EMF, another principle is required to determine the specific direction in which the resulting current will flow.
The strategic necessity of Lenz’s Law lies in its role in maintaining thermodynamic consistency within electromagnetic systems. Without a rigorous rule for directionality, these systems might appear to violate the fundamental laws of energy.
Lenz’s Law states that the polarity of an induced EMF is such that it tends to produce a current that opposes the change in magnetic flux that produced it. This "opposition" is a specific manifestation of the Law of Conservation of Energy:
The negative sign in Faraday’s mathematical expression: \( \varepsilon = -\dfrac{d\Phi_B}{dt} \) is the formal representation of this principle of opposition.
Understanding these stationary interactions allows us to move from induction in fixed coils to the phenomena observed in conductors moving through space.
Motional EMF occurs when a conductor moves through a uniform, time-independent magnetic field. This provides a pedagogical bridge between mechanical work and electrical energy.
Consider a rod of length \( l \) moving at velocity \( v \) along a U-shaped conductor. We define the enclosed area as \( lx \), where \( x \) is the length of the rectangular loop.
This reveals a profound symmetry: an EMF is induced whether a magnet moves past a stationary conductor or a conductor moves through a stationary magnetic field.
The movement of charge and the resulting fields lead us to the inherent property of "Inductance," which characterizes the circuit's response to such changes.
Inductance is a scalar quantity determined solely by the geometry of the coil and the permeability of the core material. It acts as "electrical inertia," resisting changes in current.
Mutual induction describes how a changing current \( I_2 \) in one coil
induces an EMF: \( \varepsilon_1 \) in a neighboring coil. For two long
co-axial solenoids of length \( l \), where the inner solenoid has
radius \( r_1 \) and \( n_1 \) turns per unit length, and the outer has
\( n_2 \) turns:
\( M = \mu_0 n_1 n_2 \pi r_1^2 l \)
The induced EMF is given by \( \varepsilon_1 = -M \dfrac{dI_2}{dt} \).
The unit is the Henry (H).
Self-induction occurs when a changing current in a coil induces a "Back EMF" within itself. For a long solenoid of area A and n turns per unit length: \( L = \mu_0 n^2 Al \). If the core is filled with a material of relative permeability \( \mu_r \), the inductance becomes \( L = \mu_r \mu_0 n^2 Al \).
In the mechanical analogue, L represents mass (m), and current I represents velocity (v). Consequently, the flux linkage \( N\Phi_B = LI \) is the electromagnetic equivalent of momentum. Work must be done against the back EMF to establish a current, and this energy is stored in the magnetic field: \( U_B = \frac{1}{2} LI^2 \) To compare this with electrostatic energy storage, we examine energy density (u):
In both cases, the energy is proportional to the square of the field strength, demonstrating a fundamental field symmetry.
The shift from theoretical energy storage to practical power application is best realized in the engineering of the generator.
The technological exploitation of electromagnetic induction is most evident in the AC generator, a machine that converts mechanical energy into electrical energy through the continuous rotation of an armature in a magnetic field.
Developed through the insights of Nikola Tesla, the generator uses an armature of N turns and area A rotating at a constant angular speed \( \omega \). The angular speed is linked to the frequency \( \nu \) by \( \omega = 2\pi\nu \). The instantaneous EMF produced is: \( \varepsilon = NBA\omega \sin(\omega t) \) The sine function dictates that the polarity of the EMF changes periodically, creating alternating current (AC). The EMF reaches its extremum when the rate of flux change is greatest \( \theta = 90^\circ \) or \( 270^\circ) \).
The mechanical energy to drive these generators is sourced from hydro-electric (falling water), thermal (steam from coal), or nuclear (steam from nuclear fuel) power.
Electromagnetic induction remains the essential backbone of global progress, serving as the primary mechanism for nearly all industrial power generation.
Machine Design | Mechanical Engineering | B.Tech |
📌 Introduction of IC engingines and Combustion Chambers
| Design Aspect | What It Controls | Effect on Engine |
|---|---|---|
| Shape | Flame travel path | Smooth / violent combustion |
| Size | Compression ratio | Power & efficiency |
| Surface area | Heat loss | Fuel economy |
| Engine Type | Ignition Method | Fuel |
|---|---|---|
| Spark Ignition (SI) | Spark Plug | Petrol |
| Compression Ignition (CI) | Self-ignition due to heat | Diesel |
| Failure Mode | Main Cause | Damage Type |
|---|---|---|
| Overheating | Excess heat | Warping / cracking |
| Detonation | Shock waves | Structural damage |
| Pre-ignition | Wrong timing | Piston & wall damage |
| Corrosion | Chemical attack | Wall thinning |
| Mechanical damage | External factors | Leaks / cracks |
ICSE Class 10 Physics Chapter 2 covers foundational concepts of Work, Energy, and Power, focusing on definitions, formulas, and energy conservation. Key sub-topics include the definition/units of work, potential/kinetic energy, the work-energy theorem, conservation of mechanical energy, and power.
In physics, Work is defined as the product of the component of the force in the direction of the displacement and the magnitude of this displacement. It is not merely physical effort; for work to be "done," a force must cause an object to move.
The general formula for work done ($W$) by a constant force ($F$) causing a displacement ($s$) at an angle ($\theta$) is:
$W$: Work done
$F$: Magnitude of the force applied
$s$: Magnitude of the displacement
$\theta$: The angle between the force vector and the displacement vector
For work to be non-zero, two primary conditions must be satisfied simultaneously:
Application of Force: A net force must act on the body ($F \neq 0$).
Displacement: The body must undergo a displacement in a direction that is not perpendicular to the force ($s \neq 0$).
Work is considered zero ($W = 0$) in the following scenarios:
No Displacement: Pushing against a solid wall. Even if force is high, $s = 0$, so $W = 0$.
Perpendicular Force: When the force is acting at $90^\circ$ to the direction of motion ($\cos(90^\circ) = 0$).
Example: A coolie carrying a load on his head while walking on a level road; the force of gravity is downward, but displacement is horizontal.
Example: Centripetal Force acting on a body in circular motion.
Work is a scalar quantity, meaning it has magnitude but no direction.
| System | Unit | Definition |
| SI System | Joule (J) | $1\text{ J} = 1\text{ Newton} \times 1\text{ Meter}$ |
| CGS System | Erg | $1\text{ erg} = 1\text{ Dyne} \times 1\text{ Centimeter}$ |
Conversion Factor: $1\text{ Joule} = 10^7\text{ ergs}$
The nature of work depends on the angle $\theta$ between force and displacement:
Positive Work ($0^\circ \leq \theta < 90^\circ$): Force and displacement are in the same direction (e.g., a horse pulling a cart).
Negative Work ($90^\circ < \theta \leq 180^\circ$): Force acts in the opposite direction of motion (e.g., Frictional force acting on a moving car).
Zero Work ($\theta = 90^\circ$): As discussed, force is perpendicular to displacement.
In physics, Work is defined as the product of the component of the force in the direction of the displacement and the magnitude of this displacement. It is not merely physical effort; for work to be "done," a force must cause an object to move.
The general formula for work done ($W$) by a constant force ($F$) causing a displacement ($s$) at an angle ($\theta$) is:
$W$: Work done
$F$: Magnitude of the force applied
$s$: Magnitude of the displacement
$\theta$: The angle between the force vector and the displacement vector
For work to be non-zero, two primary conditions must be satisfied simultaneously:
Application of Force: A net force must act on the body ($F \neq 0$).
Displacement: The body must undergo a displacement in a direction that is not perpendicular to the force ($s \neq 0$).
Work is considered zero ($W = 0$) in the following scenarios:
No Displacement: Pushing against a solid wall. Even if force is high, $s = 0$, so $W = 0$.
Perpendicular Force: When the force is acting at $90^\circ$ to the direction of motion ($\cos(90^\circ) = 0$).
Example: A coolie carrying a load on his head while walking on a level road; the force of gravity is downward, but displacement is horizontal.
Example: Centripetal Force acting on a body in circular motion.
Work is a scalar quantity, meaning it has magnitude but no direction.
| System | Unit | Definition |
| SI System | Joule (J) | $1\text{ J} = 1\text{ Newton} \times 1\text{ Meter}$ |
| CGS System | Erg | $1\text{ erg} = 1\text{ Dyne} \times 1\text{ Centimeter}$ |
Conversion Factor: $1\text{ Joule} = 10^7\text{ ergs}$
The nature of work depends on the angle $\theta$ between force and displacement:
Positive Work ($0^\circ \leq \theta < 90^\circ$): Force and displacement are in the same direction (e.g., a horse pulling a cart).
Negative Work ($90^\circ < \theta \leq 180^\circ$): Force acts in the opposite direction of motion (e.g., Frictional force acting on a moving car).
Zero Work ($\theta = 90^\circ$): As discussed, force is perpendicular to displacement.
Energy is defined as the capacity to do work. Like work, it is a scalar quantity.
SI Unit: Joule (J)
CGS Unit: Erg
Relationship: $1 \text{ Joule} = 10^7 \text{ ergs}$
Other Units: * Watt-hour (Wh): $1 \text{ Wh} = 3600 \text{ J}$
Kilowatt-hour (kWh): The commercial unit of electrical energy ($1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$).
Electron volt (eV): Used in atomic physics ($1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$).
Mechanical energy is the energy possessed by a body due to its state of rest or state of motion. It exists in two forms: Potential Energy and Kinetic Energy.
The energy possessed by a body by virtue of its specific position or changed configuration.
Gravitational P.E.: Energy due to height above the earth's surface.
(Where $m$ = mass, $g$ = acceleration due to gravity, and $h$ = height)
Elastic P.E.: Energy stored in a deformed body (like a compressed spring or a stretched rubber band).
The energy possessed by a body by virtue of its state of motion.
(Where $m$ = mass and $v$ = velocity)
This theorem states that the work done by a force on a moving body is equal to the increase (change) in its kinetic energy.
If work is done on the body, K.E. increases.
If work is done by the body against a force (like friction), K.E. decreases.
According to the Law of Conservation of Energy, energy can neither be created nor destroyed; it can only be transformed from one form to another. In the absence of friction (conservative forces), the total mechanical energy (P.E. + K.E.) remains constant.
Example: A Free-Falling Body
At the highest point: K.E. is zero, and P.E. is maximum ($mgh$).
During the fall: P.E. decreases as it converts into K.E.
Just before hitting the ground: P.E. is zero, and K.E. is maximum.
At any point: $P.E. + K.E. = \text{Constant}$.
Energy frequently changes forms to perform useful tasks:
| Device | Energy Conversion |
| Electric Motor | Electrical $\rightarrow$ Mechanical |
| Generator | Mechanical $\rightarrow$ Electrical |
| Photosynthesis | Light $\rightarrow$ Chemical |
| Battery/Cell | Chemical $\rightarrow$ Electrical |
| Electric Bulb | Electrical $\rightarrow$ Light & Heat |
Renewable Sources: Energy from sources that are naturally replenished (Solar, Wind, Hydro, Biomass).
Non-renewable Sources: Sources that will eventually run out (Coal, Petroleum, Natural Gas).
Energy Degradation: During energy transformation, a part of the energy is converted into non-useful forms (usually heat due to friction), which is called the degradation of energy.
Power is defined as the rate of doing work or the rate at which energy is transferred or transformed. While work tells us how much energy is used, power tells us how fast it is being used.
Mathematical Formula:
(Where $P$ is Power, $W$ is Work done, and $t$ is Time taken)
Quantity Type: Scalar quantity.
Power can also be expressed in terms of the force applied to an object and the constant velocity at which it moves.
Since $W = F \times s$ (Force $\times$ Displacement), we can substitute this into the power formula:
Because $\frac{s}{t} = v$ (Velocity), the formula becomes:
Key Takeaway: For a machine to maintain a higher speed ($v$) while applying a specific force ($F$), it requires more power.
Power is measured in various units depending on the scale of the work being done:
One Watt is defined as the power of an agent which does work at the rate of 1 Joule per second.
Kilowatt (kW): $1 \text{ kW} = 10^3 \text{ W}$
Megawatt (MW): $1 \text{ MW} = 10^6 \text{ W}$
Gigawatt (GW): $1 \text{ GW} = 10^9 \text{ W}$
Historically used for engines and motors:
1 hp = 746 W (approximately 0.75 kW)
The power spent by a source depends on two factors:
The amount of work done by the source: Power is directly proportional to work ($P \propto W$).
The time taken by the source: Power is inversely proportional to time ($P \propto \frac{1}{t}$).
Example: If two people climb the same set of stairs, the one who reaches the top faster has spent more power, even though both performed the same amount of work.
| Feature | Work | Power |
| Definition | Measure of energy transfer. | Rate of energy transfer. |
| Time Factor | Independent of time. | Dependent on time. |
| SI Unit | Joule (J) | Watt (W) |
| To find... | Use Formula | Given Variables |
| Standard Power | $P = \frac{W}{t}$ | Work and Time |
| Mechanical Power | $P = F \times v$ | Force and Velocity |
| Electrical Power | $P = V \times I$ | Voltage and Current |
