Physics At A Glance for Class XI & XII, Engineering Entrance and other Competitive Exams

Cover
Contents
Preface
Acknowledgements
To the Students
Chapter 1: Mathematical Tools
	1.1 Trigonometry
		1.1.1 Formulae for Compound Angle
		1.1.2 Transformational Formula
		1.1.3 Formulae for Multiple and Sub-multiple Angles
		1.1.4 Trigonometric Equations
		1.1.5 Value of (2π ± θ)
		1.1.6 Value of
		1.1.7 Inverse Trigonometric Functions
	1.2 Algebra
		1.2.1 Quadratic Equation
		1.2.2 Determinants
		1.2.3 Determinant of Third Order
		1.2.4 Progression
		1.2.5 Geometric Progression
		1.2.6 Some Important Summation of Series
		1.2.7 Binomial Theorem for Any Index
		1.2.8 Exponential and Logarithmic Series
	1.3 Calculus
		1.3.1 Limits
		1.3.2 Basic Formulae of Limit
		1.3.3 Continuity
		1.3.4 Differentiability and Differentiate
		1.3.5 For Two Functions: u and v
		1.3.6 Chain Rule
		1.3.7 D.C. of Some Important Functions
		1.3.8 Maxima and Minima
		1.3.9 Integration
		1.3.10
Indefinite Integration
		1.3.11 Integration by Parts
		1.3.12 Integration of Some Standard Functions
		1.3.13
Definite Integration
		1.3.14 Property
of Definite Integration
		1.3.15 Trigonometric Series
Chapter 2: Units, Dimensions and Experimental Skills
	2.1 Introduction
	2.2 Applications of Dimensional Analysis
	2.3 Limitations of Dimensional Analysis
	2.4 Errors and Accuracy
		2.4.1 Rules to Determine the Signifi cant Figures
		2.4.2 Rounding Off
	2.5 Types of Errors
		2.5.1 Constant Errors
		2.5.2 Systematic Errors
		2.5.3 Random Errors
		2.5.4 Gross Errors
	2.6 Propagation of Errors
		2.6.1 Addition
		2.6.2 Subtraction
		2.6.3 Multiplication
		2.6.4 Division
		2.6.5 Power of Observed Quantities
	2.7 Vernier Callipers
		2.7.1 Determination of Least Count
		2.7.2 Determination of Zero Error and Zero Correction
		2.7.3 Reading a Vernier
Chapter 3: Vectors and Scalars
	3.1 Physical Quantities
		3.1.1 Scalar Quantities
		3.1.2 Vector Quantities
		3.1.3 Dot Product of Two Vectors
		3.1.4 Cross Product of Two Vectors
		3.1.5 Triple Product of Vectors
	3.2 Scalar and Vector Field: Gradient, Divergence and Curl
		3.2.1 Scalar Field
		3.2.2 Vector Field
		3.2.3 Vector Differential Operator (Del Vector)
		3.2.4 Gradient
		3.2.5 Divergence of a Vector
		3.2.6 Curl or Rotation of a Vector
Chapter 4: Motions in One, Two and Three Dimensions
	4.1 Basic definitions
		4.1.1 In One-dimensional Motion
		4.1.2 One-dimensional Motion with Uniform Acceleration
		4.1.3 One-dimensional Motion with Non-uniform Acceleration
		4.1.4 In Two-dimensional Motion
		4.1.5 Two- or Three-dimensional Motion with Uniform Acceleration
		4.1.6 Two- or Three-dimensional Motion with Non-uniform Acceleration
		4.1.7 Projectile Motion
		4.1.8 Projection Upon an Inclined Plane
		4.1.9 Projection Down the Inclined Plane
	4.2 Swimmer's Problem or River-boat Problem
		4.2.1 Circular Motion
Chapter 5: Laws of Motion and Friction
	5.1 Inertia
	5.2 Linear Momentum
	5.3 Force
		5.3.1 System of Forces
		5.3.2 Condition for Equilibrium of Concurrent Forces
	5.4 Lami's Theorem
	5.5 Newton's Laws of Motion
	5.6 Newton's Second Law in Component Form
		5.6.1 Newton's Second Law in Non-inertial Frame
		5.6.2 Apparent Weight of a Body in a Lift
	5.7 Spring
	5.8 Non-concurrent Coplanar Forces
Chapter 6: Work, Energy, Power and Circular Motion
	6.1 Work Done
		6.1.1 By a Constant Force
		6.1.2 By a Variable Force
		6.1.3 By Area Under F-x Graph
	6.2 Power of a Force
		6.2.1 Conservative and Non-conservative Forces
	6.3 Potential Energy
		6.3.1 Relation Between Potential Energy (U) and Conservative
Force (F)
		6.3.2 Principle of Conservation of Mechanical Energy
		6.3.3 Work-energy Theorem
		6.3.4 Types of Equilibrium
		6.3.5 Circular Motion
		6.3.6 Turning of a Cyclist Around a Corner on the Road
		6.3.7 A Car Taking a Turn on a Level Road
		6.3.8 Banking of Tracks
		6.3.9 Stability of a Vehicle on a Horizontal Turn
		6.3.10 Conical Pendulum
		6.3.11 Centrifugal Force
		6.3.12 Coriolis Force
Chapter 7: Centre of Mass and Collision
	7.1 Centre of Mass
		7.1.1 Position of Centre of Mass of Discrete System of Particles
		7.1.2 Position of Centre of Mass of Continuous System of Particles
		7.1.3 Position of Centre of Mass of More Than Two Rigid Bodies
		7.1.4 Position of Centre of Mass of a Rigid Body from Which Some Portion Is Removed
	7.2 Motion of the Centre of Mass
		7.2.1 Conservation of Linear Momentum
	7.3 Collision
		7.3.1 Head-on Elastic Collision
		7.3.2 Head-on Inelastic Collision
		7.3.3 Oblique Collision (Both Elastic and Inelastic)
		7.3.4 Linear Impulse
		7.3.5 Solving Problems Relative to CM Frame
		7.3.6 Variable Mass
Chapter 8. Rotational and Rolling Motion
	8.1 Angular Displacement
	8.2 Angular Velocity
	8.3 Angular Acceleration
		8.3.1 Relation Between Linear and Angular Velocity
		8.3.2 Relation Between Linear and Angular Acceleration
		8.3.3 Equations of Motion of Rotating Body
	8.4 Rotational Dynamics
	8.5 Angular Impulse
		8.5.1 Angular Momentum of Rolling Body
		8.5.2 Moment of Inertia of a Discrete Rotating System
		8.5.3 Moment of Inertia of a Continuous Rotating System
		8.5.4 Theorem on Moment of Inertia
		8.5.5 Rolling of a Body on Horizontal Rough Surface
		8.5.6 Rolling of a Body on Inclined Rough Surface of Inclination θ
		8.5.7 For Rolling with Forward Slipping
	8.6 Radius of Gyration
		8.6.1 Couple
		8.6.2 Conditions for Equilibrium of a Rigid Body
Chapter 9: Gravitation
	9.1 Properties of Gravitational Force
		9.1.1 Inertial Mass and Properties of Inertial Mass
	9.2 Gravitational Mass
	9.3 Acceleration Due to Gravity
	9.4 Gravitational Field Strength
	9.5 Gravitational Potential
	9.6 Gravitational Potential Energy
		9.6.1 Relation Between Field Strength E 
and Potential V
Chapter 10: Solids and Fluids
	10.1 Intermolecular Forces
	10.2 Types of Bonding
	10.3 Four States of Matter
	10.4 Elasticity
		10.4.1 Strain
		10.4.2 Stress
		10.4.3 Elastic Moduli
		10.4.4 Interatomic Force Constant (k)
		10.4.5 Cantilever and Beam
		10.4.6 Torsion of a Cylinder and Workdone in Twisting
		10.4.7 Compressibility
		10.4.8 Elastic Relaxation Time
		10.4.9 Ductile Materials
		10.4.10 Brittle Materials
	10.5 Fluids
		10.5.1 Pressure Due to a Liquid
		10.5.2 Variation of Pressure in a Fluid with the Height from the Bottom of the Fluid
		10.5.3 Hydrostatic Force Due to Many Liquid Layers
		10.5.4 Pascal's Law
		10.5.5 Archimede's Principle
		10.5.6 Variation of Pressure in a Liquid in a Container If the Container Is to Be Accelerated
	10.6 Surface Tension
		10.6.1 Effect of Temperature on Surface Tension
		10.6.3 Effect of Impurity on Surface Tension
	10.7 Surface Energy
		10.7.1 Angle of Contact
		10.7.2 Excess Pressure Due to Surface Tension
		10.7.3 Radius of New Bubble When Two Bubbles Coalesce
		10.7.4 Radius of Interface
		10.7.5 Capillarity
		10.7.6 Zurin's Law
		10.7.7 Poiseuille's Formula and Liquid Resistance
		10.7.8 Stoke's Law and Terminal Velocity
		10.7.9 Reynold's Number
		10.7.10 Bernouilli's Theorem
		10.7.11 Torricelli's Theorem
Chapter 11: Oscillations and Waves (Acoustics)
	11.1 Different Equations in SHM
	11.2 Graphs Related to SHM
		11.2.1 Spring Block System
		11.2.2 Pendulum
		11.2.3 Physical Pendulum
	11.3 Some Other Important Points Concerning SHM
		11.3.1 Wave Equation
		11.3.2 Plane Progressive Harmonic Wave
		11.3.3 Longitudinal Wave
		11.3.4 Wave Speed
		11.3.5 Echo
		11.3.6 Stationary Waves
Chapter 12: Thermometry and Thermodynamics
	12.1 Temperature
		12.1.1 Thermal Expansion
		12.1.2 Effect of Temperature on Different Physical Quantities
	12.2 Kinetic Theory of Gases
		12.2.1 Real Gases
	12.3 Thermodynamics
		12.3.1 Entropy
		12.3.2 Refrigerator or Heat Pump
		12.3.3 Second Law of Thermodynamics
		12.3.4 Third Law of Thermodynamics
Chapter 13: Calorimetry and Heat Transfer
	13.1 Units of Calorimetry
		13.1.1 Specific Heat Capacity
		13.1.2 Dulong and Petit's Law
		13.1.3 Principle of Calorimetry
		13.1.4 Change of State or Phase
	13.2 Heat Transfer
		13.2.1 Heat Conduction Through a Rod
	13.3 Wiedemann–Franz Law
		13.3.1 Thermal Convection
		13.3.2 Radiation
	13.4 Emittance, Absorptance and Energy Density
		13.4.1 Monochromatic or Spectral Emittance (El), Radiant Emittance or Radiance (E)
		13.4.2 Monochromatic Absorptance (al)
		13.4.3 Monochromatic or Spectral Energy Density (Ul) and Radiant Enegry Density (U)
	13.5 Fraunhofer Lines
		13.5.1 Colours: Primary and Complementary
Chapter 14: Electric Field, Potential and Gauss Law
	14.1 Properties of Electric Charge
		14.1.1 Quarks
		14.1.2 Electric Lines of Force
		14.1.3 Electric Flux
		14.1.4 Electric Dipole
	14.2 Principle of Electrostatic Generator (Van de Graff Generator)
		14.2.1 Behaviour of a Conductor in an Electrostatic Field
		14.2.2 Charged Soap Bubble
	14.3 Atmospheric Electricity
		14.3.1 Main Features of Atmospheric Electricity
Chapter 15: Capacitors
	15.1 Capacitance
	15.2 Isolated Conductor
	15.3 Parallel Plate Capacitor
	15.4 Spherical Capacitor
	15.5 Cylindrical Capacitor
	15.6 Combination of Capacitors
	15.7 Dielectrics
		15.7.1 Polarization of Dielectric Medium Placed in an Electric Field
Chapter 16: Ohm's Law, Thermal and Chemical Effect of Electricity
	16.1 Electric Current
		16.1.1 Series Combination
		16.1.2 Parallel Combination
	16.2 Resistance of a Conductor
		16.2.1 Variation of Resistivity
	16.3 Ohm's Law: V = IR 180
	16.4 How to Find Equivalent Resistance
		16.4.1 Successive Reduction Method
		16.4.2 Using Symmetry of the Circuit
		16.4.3 Using Star-delta Conversion Method
		16.4.4 Using Infinite Ladder Method
	16.5 Colour Code for Carbon Resistors
		16.5.1 Superconductivity
		16.5.2 Potentiometer
	16.6 Study About R–C Circuit
	16.7 R–C Discharging Circuit
		16.7.1 Power or Heat
	16.8 Faraday's Law of Electrolysis
		16.8.1 First Law
		16.8.2 Second Law
Chapter 17: Magnetic Effect of Current and Magnetism
	17.1 Magnetic Field Produced by Moving Charge or Current
	17.2 Magnetic Force on a Moving Charge in Uniform Magnetic Field
	17.3 Path of a Charged Particle in Uniform Magnetic Field
	17.4 List of Formulae in Uniform Circular Motion
		17.4.1 To Find Velocity and Position at Time t
		17.4.2 Helical Path
	17.5 Deviation of Charge Particle in Magnetic Field
		17.5.1 Lorentz Force
		17.5.2 Cyclotron
	17.6 Magnetic Force on a Current Carrying Wire in a Uniform Magnetic Field
	17.7 Magnetic Force on a Curved Wire in Uniform B
	17.8 Torque on a Current Carrying Coil Placed Inside a Magnetic Field
	17.9 Magnetic Field at a Point Due to a Current or System of Current
	17.10 List of Formulae
	17.11 Ampere's Circuital Law (ACL)
	17.12 Magnet and Its Characteristics
	17.13 Properties of a Magnet
	17.14 Magnetic Lines of Force and Their Characteristics
		17.14.1 Intensity of Magnetization
		17.14.2 Magnetic Permeability
		17.14.3 Magnetic Susceptibility
	17.15 Earth's Magnetism
Chapter 18: Electromagnetic Induction and Alternating Current
	18.1 Magnetic Flux
		18.1.1 Faraday and Lenz Law (I from B)
		18.1.2 Lenz’s Law
	18.2 Mechanism of Electromagnetic Induction Across a Conductor
	18.3 How to Solve Problems Related to Motional EMF
		18.3.1 Self-inductance
		18.3.2 Mutual Inductance (M)
		18.3.3 Inductor (Solenoid and Toroid)
		18.3.4 Current Growth in L–R Circuit
		18.3.5 Current Decay in L–R Circuit
		18.3.6 LC-oscillatory Circuit
		18.3.7 Alternating Current (AC)
		18.3.8 Choke Coil
		18.3.9 Transformer
Chapter 19: Electromagnetic Waves and Wave Optics
	19.1 Conduction Current
	19.2 Displacement Current
	19.3 Modified Ampere Circuital Law
		19.3.1 Maxwell's Equations
	19.4 Electromagnetic Waves
	19.5 Electromagnetic Spectrum
		19.5.1 Radiowaves (Frequency Range: 500 kHz to About 1000 MHz)
		19.5.2 Microwaves (Frequency Range: 1 GHz to 100 GHz)
		19.5.3 Infrared (IR) Waves (Frequency Range: 1011 Hz to 5 × 1014 Hz)
		19.5.4 Visible Light (Frequency Range: 4 ¥ 1014 Hz to About 7 × 1014 Hz)
		19.5.5 Ultraviolet (UV) Radiation (Frequency Range: 1014 Hz to 1017 Hz)
		19.5.6 X-rays (Frequency Range: 1017 Hz to 1019 Hz)
		19.5.7 Gamma Rays (Frequency Range: 1018 Hz to 1022 Hz)
	19.6 Some Useful Key Points
	19.7 Wave Optics
		19.7.1 Coherent Sources
		19.7.2 Interference
		19.7.3 Division of Wavefront
		19.7.4 Division of Amplitude
	19.8 Young's Double Slit Experiment
	19.9 Diffraction of Light
		19.9.1 Fraunhofer Diffraction Due to a Single Slit
		19.9.2 Fraunhofer Diffraction at a Circular Aperture
	19.10 Diffraction at a Plane Grating
	19.11 Polarization of Light
		19.11.1 Wave Front
Chapter 20: Ray Optics and Optical Instruments
	20.1 Reflection of Light
	20.2 Characteristics of Image Due to Reflection by a Plane Mirror
		20.2.1 Effect of Rotation of Plane Mirror on the Image
		20.2.2 Number of Images Formed by Two Inclined Plane Mirrors
		20.2.3 Concept of Velocity of Image in the Plane Mirror
	20.3 Curved Mirrors
		20.3.1 Concept of Velocity of Image in Spherical Mirrors
	20.4 Refraction of Light
	20.5 Laws of Refraction
		20.5.1 Refraction at Plane Surface
		20.5.2 Total Internal Refl ection
		20.5.3 Refractive Index (R.I.) and Critical Angle
		20.5.4 Spherical Refracting Surfaces
		20.5.5 Refraction from Spherical Surface
	20.6 Lens
		20.6.1 Lens Maker's Formula
		20.6.2 Nature of Image Formation by Convex Lens and Concave Lens
		20.6.3 Concept of Velocity of Image in the Refraction Through Spherical Surface and Plane Surface
		20.6.4 Concept of Velocity of Image in the Refraction Through Lens
	20.7 Power of the Lens
		20.7.1 Combinations of the Lenses
	20.8 Prism
	20.9 Defects of Vision of Human Eye
		20.9.1 Simple Microscope
		20.9.2 Compound Microscope
		20.9.3 Astronomical Telescope
		20.9.4 Terrestrial Telescope
Chapter 21: Atoms and Nuclei
	21.1 Atoms
		21.1.1 Dalton's Atomic Theory
		21.1.2 Thomson's Atomic Model
		21.1.3 Rutherford's Atomic Model
		21.1.4 Impact Parameter and Angle of Scattering
		21.1.5 Bohr's Atomic Model
		21.1.6 Bohr's Formulae
		21.1.7 Hydrogen Spectrum
		21.1.8 Kossel Diagram
		21.1.9 Energy Level Diagram of Hydrogen Atom
		21.1.10 Wave Model
		21.1.11 Work Function
		21.1.12 Electron Emission
		21.1.13 Photoelectric Effect
		21.1.14 Properties of Photon
	21.2 Matter Wave or de Broglie Wave or Wavelength
	21.3 X-Rays
		21.3.1 Mosley's Law
		21.3.2 Isotopes
		21.3.3 Isobars
		21.3.4 Isotones
		21.3.5 Isomers
		21.3.6 Mass Defect (Δm)
		21.3.7 Binding Energy (ΔE)
		21.3.8 Packing Fraction (P)
		21.3.9 Radioactivity
	21.4 Nuclear Fission
	21.5 Nuclear Fusion
Chapter 22: Semiconductor Devices and Communication System
	22.1 Intrinsic Semiconductor
	22.2 Extrinsic Semiconductor
	22.3 P-N Junction
	22.4 Half-wave Rectifier
	22.5 Full-wave Rectifier
	22.6 Diodes
	22.7 Transistor
	22.8 Transistor Configuration
	22.9 Logic Gates
		22.9.1 OR Gate
		22.9.2 AND Gate
		22.9.3 NOT Gate
	22.10 Universal Building Blocks
		22.10.1 Arithmetic Circuits
	22.11 Principles of Communication
		22.11.1 Analog Communication
		22.11.2 Digital Communication
		22.11.3 Radio Communication
		22.11.4 Need for Modulation
		22.11.5 Demodulation
	22.12 Types of Modulation
		22.12.1 Amplitude Modulation
		22.12.2 Power in AM Wave
		22.12.3 Limitations of Amplitude Modulation
		22.12.4 Frequency Modulation
		22.12.5 Modulation Factor or Index
		22.12.6 Deviation Ratio
		22.12.7 Percent Modulation
		22.12.8 Pulse Modulation
		22.12.9 Data Communication Modem
		22.12.10 Propagation of Electromagnetic Waves in Atmosphere
		22.12.11 Satellite Communication
		22.12.12 Optical Fibre Communication
		22.12.13 Communication System
		22.12.14 Message Signals
		22.12.15 Line Communication
Appendices
	A.1 Physical Constants
	A.2 List of Scientific Instruments
	A.3 Inventors and Their Inventions
	A.4 List of Nobel Laureates in Physics