Topics
Rotational Dynamics
- Rotational Dynamics
- Circular Motion and Its Characteristics
- Kinematics of Rotational Motion About a Fixed Axis
- Non-uniform circular motion
- Dynamic of Circular Motion
- Centrifugal Forces
- Applications of Uniform Circular Motion
- Vehicle Along a Horizontal Circular Track
- Well (or Woll) of Death
- Vehicle on o Banked Rood
- Conical Pendulum
- Vertical Circular Motion
- Point Moss Undergoing Vertical Circular Motion Under Gravity
- Sphere of Death
- Moment of Inertia as an Analogous Quantity for Mass
- Moment of Inertia of a Uniform Disc
- Radius of Gyration
- Theorems of Perpendicular and Parallel Axes
- Angular Momentum or Moment of Linear Momentum
- Expression for Torque in Terms of Moment of Inertia
- Conservation of Angular Momentum
- Rolling Motion
11th Std
Vectors
- Vector Analysis
- Vector Operations>Multiplication of a Vector by a Scalar
- Vector Operations>Addition and Subtraction of Vectors
- Vector Operations>Triangle Law for Vector Addition
- Vector Operations>Law of parallelogram of vectors
- Resolution of Vectors
- Multiplication of Vectors
- Scalar Product(Dot Product)
- Vector Product (Cross Product)
- Characteristics of Vector Product
- Concept of Calculus
- Differential Calculus
- Integral Calculus
Mechanical Properties of Fluids
- Fluid and Its Properties
- Pressure of liquid
- Pressure Due to a Liquid Column
- Atmospheric Pressure
- Absolute Pressure and Gouge Pressure
- Hydrostatic Paradox
- Pascal’s Law
- Applications of Pascal's Law > Hydraulic lift
- Applications of Pascal's Law > Hydraulic Brakes
- Pressure Measurement
- Mercury Barometer (Simple Barometer)
- Open Tube Manometer
- Surface Tension
- Molecular Theory of Surface Tension
- Surface Tension and Surface Energy
- Angle of Contact
- Effect of Impurity and Temperature on Surface Tension
- Excess Pressure Across the Free Surface of a Liquid
- Explanation of Formation of Drops and Bubbles
- Capillarity and Capillary Action
- Fluids in Motion
- Critical Velocity and Reynolds Number
- Viscosity
- Coefficient of viscosity
- Stokes’ Law
- Terminal Velocity
- Continuous and Discontinuous Functions
- Bernoulli's Equation
- Applications of Bernoulli's equation > Speed of efflux
- Applications of Bernoulli's Equation > Ventury Tube
- Applications of Bernoulli's Equation > Lifting up of on Aeroplane
- Applications of Bernoulli's Equation > Working of on Atomizer
- Applications of Bernoulli's Equation > Blowing off of Roofs by Stormy Wind
- Archimedes' Principle
Error Analysis
12th Std
Motion in a Plane
- Introduction of Motion in a Plane
- Rectilinear Motion
- Displacement
- Path Length
- Average Velocity
- Average Speed
- Instantaneous Velocity
- Instantaneous Speed
- Position-time, Velocity-time and Acceleration-time Graphs
- Acceleration in Linear Motion
- Relative Velocity
- Motion in Two Dimensions - Motion in a Plane
- Average and Instantaneous Velocities
- Acceleration in a Plane
- Equations of Motion in a Plane with Constant Acceleration
- Relative Velocity in Two Dimensions
- Projectile Motion
- Uniform Circular Motion (UCM)
- Key Parameters of Circular Motion
- Centripetal Acceleration
- Conical Pendulum
Kinetic Theory of Gases and Radiation
- Gases and Its Characteristics
- Classification of Gases: Real Gases and Ideal Gases
- Mean Free Path
- Pressure of Ideal Gas
- Root Mean Square (RMS) Speed
- Interpretation of Temperature in Kinetic Theory
- Law of Equipartition of Energy
- Degrees of Freedom
- Bonding in Some Homonuclear Diatomic Molecules
- Specific Heat Capacity
- Moyer's Relation
- Monatomic Gases
- Diatomic Gases
- Polyatomic Gases
- Absorption, Reflection, and Transmission of Heat Radiation
- Interaction of Thermal Radiation and Matter
- Perfect Blackbody
- Ferry's Blackbody
- Emission of Heat Radiation
- Coefficient of Emission or Emissivity
- Kirchhoff’s Law of Heat Radiation and Its Theoretical Proof
- Spectral Distribution of Blackbody Radiation
- Wien's Displacement Law
- Stefan-boltzmann Law of Radiation
- Prevost's Theory of Heat Exchange
Thermodynamics
- Thermodynamics
- Thermal Equilibrium
- Zeroth Law of Thermodynamics
- Heat, Internal Energy and Work
- Internal Energy (U)
- Heat
- Internal Energy and Change in Internal Energy
- First Law of Thermodynamics
- Thermodynamic state variables
- Thermodynamic Equilibrium
- Thermodynamic State Variables and Equation of State
- The p-V diagram
- Thermodynamic Process
- Work Done During a Thermodynamic Process
- Heat Added During a Thermodynamic Process
- Classification of Thermodynamic Processes
- Reversible and Irreversible Processes
- Isothermal Processes
- Isobaric process
- Isochoric process
- Adiabatic Processes
- Cyclic Process
- Free Expansion
- Heat Engine
- The Heat Engine Cycle and the p-V Diagram
- Refrigerators and Heat Pumps
- Heat Flow from a Colder Region to a Hotter Region
- Refrigerator
- Performance of a Refrigerator
- Air Conditioner
- Heat Pump
- Entropy and Second Law of Thermodynamics
- Carnot Cycle and Carnot Engine
- Sterling Cycle
Laws of Motion
- Introduction to Laws of Motion
- Aristotle’s Fallacy
- Newton’s Laws of Motion
- Newton's First Law of Motion
- Newton’s Second Law of Motion
- Newton's Third Law of Motion
- Types of Forces>Real and Pseudo Forces
- Inertial and Non-inertial Frames of Reference
- Types of Forces>Fundamental Forces in Nature
- Types of Forces>Contact and Non-Contact Forces
- Types of Forces>Conservative and Non-Conservative Forces
- Types of Forces>Work Done by a Variable Force
- Work Energy Theorem
- Principle of Conservation of Linear Momentum
- Collisions
- Perfectly Inelastic Collision
- Coefficient of Restitution e
- Expressions for Final Velocities in Elastic Head-On Collision
- Loss of Kinetic Energy in Perfectly Inelastic Head-On Collision
- Collision in Two Dimensions
- Impulse of a Force
- Necessity of Defining Impulse
- Rotational Analogue of a Force: Moment of a Force Or Torque
- Couple and Its Torque
- Proof of Independence of the Axis of Rotation
- Mechanical Equilibrium
- States of Equilibrium
- Centre of Mass>Mathematical Understanding of Centre of Mass
- Centre of Mass>Velocity of Centre of Mass
- Centre of Mass>Acceleration of Centre of Mass
- Centre of Mass>Characteristics of Centre of Mass
- Centre of Gravity
Oscillations
- Oscillations
- Explanation of Periodic Motion
- Linear Simple Harmonic Motion (S.H.M.)
- Differential Equation of Linear S.H.M.
- Acceleration (a), Velocity (v) and Displacement (x) of S.H.M.
- Amplitude (A), Period (T) and Frequency (N) of S.H.M.
- Combination of Springs
- Reference Circle Method
- Phase in S.H.M.
- Graphical Representation of S.H.M.
- Composition of Two S.H.M.’S Having Same Period and Along Same Line
- The Energy of a Particle Performing S.H.M.
- Simple Pendulum
- Angular S.H.M. and It's Differential Equation
- Damped Oscillations
- Free Oscillations, Forced Oscillations and Resonance Oscillations
Gravitation
- Concept of Gravitation
- Kepler’s Laws
- Law of Orbit or Kepler's First Law
- Law of Areas or Kepler's Second Law
- Law of Periods or Kepler's Third Law
- Newton's Universal Law of Gravitation
- Acceleration Due to Gravity (Earth’s Gravitational Acceleration)
- Variation in the Acceleration>Variation in Gravity with Altitude
- Variation in the Acceleration>Variation in Gravity with Depth
- Variation in the Acceleration>Variation in Gravity with Latitude and Rotation of the Earth
- Variation in the Acceleration>Effect of the shape of the Earth
- Gravitational Potential Energy
- Escape Velocity
- Expression for Gravitational Potential Energy
- Connection of Potential Energy Formula with mgh
- Potential and Potential Difference
- Earth Satellites
- Projection of Satellite
- Weightlessness in a Satellite
- Time Period of Satellite
- Energy Associated with Satellite
- Critical Velocity
Thermal Properties of Matter
- Thermal Properties of Matter
- Temperature and Heat
- Measurement of Temperature
- Absolute Zero and Absolute Temperature
- Ideal Gas Equation
- Thermal Expansion
- Linear Expansion
- Areal Expansion
- Volume Expansion
- Relation Between Coefficient of Expansion
- Specific Heat Capacity
- Specific Heat Capacity of Solids and Liquids
- Specific Heat Capacity of Gas
- Heat Equation
- Thermal Capacity
- Calorimetry
- Change of State
- Analysis of Observation>From Point A to B
- Analysis of Observation>From Point B to D
- Evaporation vs Boiling
- Boiling Point and Pressure
- Concept of Desublimation (Deposition)
- Phase Diagram
- Gas and Vapour
- Latent Heat
- Heat Transfer
- Conduction
- Thermal Conductivity
- Coefficient of Thermal Conductivity
- Thermal Resistance
- Applications of Thermal conductivity
- Convection
- Application of Convection
- Free and Forced Convection
- Radiation
- Newton’s Law of Cooling
Superposition of Waves
- Introduction to Superposition of Waves
- Progressive Waves
- Reflection of Waves
- Superposition of Waves
- Stationary Waves
- Formation of Stationary Waves on String
- Equation of Stationary Wave on a Stretched String
- Properties of Stationary Waves
- Comparison of Progressive Waves and Stationary Waves
- Free and Forced Vibrations
- Harmonics and Overtones
- End Correction
- Study of Vibrations of Air Columns
- Vibrations of Air Column in a Pipe Open at Both Ends
- Practical Determination of End Correction
- Vibrations Produced in a String
- Laws of a Vibrating String
- Sonometer
- Beats
- Characteristics of Sound
- Musical Instruments
Sound
- Sound Waves
- Types of Waves
- Common Properties of All Waves
- Transverse Waves
- Longitudinal Waves
- Mathematical Expression of a Wave
- The Speed of Travelling Waves
- Principle of Superposition of Waves
- Echo, Reverberation and Acoustics
- Qualities of Sound
- Doppler Effect
- Source Moving and Listener Stationary
- Listener Approaching a Stationary Source with Velocity
- Both Source and Listener are Moving
- Common Properties between Doppler Effect of Sound and Light
- Major Differences between Doppler Effects of Sound and Light
Wave Optics
- Introduction of Wave Optics
- Nature of Light
- Light as a Wave
- Huygens’ Theory
- Reflection of Light at a Plane Surface
- Refraction of Light at a Plane Boundary Between Two Media
- Polarization
- Interference
- Coherent and Incoherent Sources and Sustained Interference of Light
- Young's Double Slit Experiment and Expression for Fringe Width
- Conditions for Producing Steady Interference Pattern
- Methods for Obtaining Coherent Sources
- Optical Path
- Diffraction of Light
- Fresnel and Fraunhofer Diffraction
- Experimental Set up for Fraunhofer Diffraction
- Fraunhofer Diffraction Due to a Single Slit
- Young’s Double Slit vs Single Slit
- Resolving Power
- Rayleigh’s Criterion
- Resolving Power of a Microscope and Telescope
Optics
- Fundamental Concepts of Light
- Nature of Light
- Ray Optics Or Geometrical Optics
- Cartesian Sign Convention
- Reflection of Light
- Reflection>Reflection from a Plane Surface
- Reflection>Reflection from Curved Mirrors
- Total Internal Reflection
- Applications of Total Internal Reflection
- Refraction at a Spherical Surface and Lenses
- Thin Lenses and Their Combination
- Refraction at a Single Spherical Surface
- Lens Makers' Equation
- Dispersion of Light
- Analysis of Prism
- Thin Prisms
- Some Natural Phenomena Due to Sunlight
- Defects of Lenses
- Optical Instruments
- Simple Microscope or a Reading Glass
- Compound Microscope
- Telescope
Electrostatics
- Concept of Electrostatics
- Gauss’s Law
- Application of Gauss' Law
- Electric Potential and Potential Difference
- Electric Potential Due to a Point Charge
- Electric Field due to an Electric Dipole
- Electric Field Due to a System of Charges
- Equipotential Surfaces
- Electrical Energy of Two Point Charges and of a Dipole in an Electrostatic Field
- Conductors and Insulators
- Free Charges and Bound Charges Inside a Conductor
- Dielectrics
- Electric Polarisation of Matter
- Capacitors and Capacitance
- Combination of Capacitors
- Capacitance of a Parallel Plate Capacitor with and Without Dielectric Medium Between the Plates
- Displacement Current
- Energy Stored in a Charged Capacitor
- Van De Graaff Generator
Current Electricity
Electrostatics
- Concept of Electrostatics
- Electric Charge
- Basic Properties of Electric Charge
- Additive Nature of Charge
- Quantization of Charge
- Conservation of Charge
- Force between Charges
- Coulomb’s Law
- Scalar Form of Coulomb’s Law
- Relative Permittivity or Dielectric Constant
- Definition of Unit Charge from the Coulomb’s Law
- Coulomb's Law in Vector Form
- Principle of Superposition
- Electric Field
- Electric Field Intensity Due to a Point-Charge
- Practical Way of Calculating Electric Field
- Electric Lines of Force
- Electric Flux
- Gauss’s Law
- Electric Dipole
- Couple Acting on an Electric Dipole in a Uniform Electric Field
- Electric Intensity at a Point Due to an Electric Dipole
- Continuous Charge Distribution
Semiconductors
- Concept of Semiconductors
- Electrical Conduction in Solids
- Band Theory of Solids
- Intrinsic Semiconductor
- Extrinsic Semiconductor
- n-type semiconductor
- p-type semiconductor
- Charge neutrality of extrinsic semiconductors
- p-n Junction
- Basics of Semiconductor Devices
- Applications of Semiconductors and P-n Junction Diode
- Thermistor
- Advantages and Disadvantages of Semiconductor Devices
Magnetic Fields Due to Electric Current
- Magnetic Fields Due to Electric Current
- Magnetic force
- Cyclotron
- Helical Motion
- Magnetic Force on a Wire Carrying a Current
- Force on a Closed Circuit in a Magnetic Field
- Torque on a Current-Loop in a Uniform Magnetic Field
- Magnetic Dipole Moment
- Magnetic Potential Energy of a Dipole
- Biot-Savart Law
- Force of Attraction Between Two Long Parallel Wires
- Magnetic Field Produced by a Current in a Circular Arc of a Wire
- Applications of Biot-Savart's Law > Magnetic Field on the Axis of a Circular Current-Carrying Loop
- Magnetic Lines for a Current Loop
- Ampere's Law
- Applications of Ampere’s Circuital Law > Magnetic Field of a Toroidal Solenoid
Electric Current Through Conductors
- A combination of resistors in both series and parallel
- Potential Difference and Emf of a Cell
- Cells, Emf, Internal Resistance
Magnetic Materials
- Magnetic Materials
- Torque Acting on a Magnetic Dipole in a Uniform Magnetic Field
- Origin of Magnetism in Materials
- Magnetisation and Magnetic Intensity
- Magnetic Properties of Materials
- Diamagnetism
- Paramagnetism
- Ferromagnetism
- Effect of Temperature
- Hysteresis: Retentivity and Coercivity
- Permanent Magnet
- Magnetic Shielding
Electromagnetic Waves and Communication System
Electromagnetic Induction
- Electromagnetic Induction
- Faraday's Laws of Electromagnetic Induction
- Lenz's Law
- Flux of the Field
- Motional Electromotive Force (e.m.f.)
- Induced Emf in a Stationary Coil in a Changing Magnetic Field
- Generators
- Back Emf and Back Torque
- Induction and Energy Transfer
- Eddy Currents or Foucault Currents
- Self Inductance
- Energy Stored in a Magnetic Field
- Energy Density of a Magnetic Field
- Mutual Inductance
- Transformers
AC Circuits
- AC Circuits
- A.C. Generator
- Average and RMS Values
- Phasors
- Different Types of AC Circuits: AC Voltage Applied to a Resistor
- Different Types of AC Circuits: AC Voltage Applied to an Inductor
- Different Types of AC Circuits: AC Voltage Applied to a Capacitor
- Different Types of AC Circuits: AC Voltage Applied to a Series LCR Circuit
- Power in AC Circuit
- LC Oscillations
- Electric Resonance
- Sharpness of Resonance: Q Factor
- Choke Coil
Measurements
- Measurements
- Physical Quantities
- Unit and Its Types
- Unit Systems
- The International System of Units (SI)
- Rules and Conventions for Writing SI Units and Their Symbols
- Measurement of Length
- Measuring Smaller Distances
- Measuring Larger Distances
- Devices for Measuring Length
- Measurement of Mass
- Measurement of Time
- Dimensions and Dimensional Analysis
- Accuracy, Precision and Uncertainty in Measurement
- Errors in Measurements>Systematic Errors
- Estimation of Errors
- Combination of Errors
- Significant Figures
Dual Nature of Radiation and Matter
- Dual Nature of Radiation and Matter
- The Photoelectric Effect
- Experimental Study of Photoelectric Effect
- Observations from Experiments on Photoelectric Effect
- Failure of Wove Theory on Photoelectric Effect
- Einstein's Postulate of the Photoelectric Equation
- Wave-particle Duality of Electromagnetic Radiation
- Photo Cell
- De Broglie Hypothesis
- Davisson and Germer Experiment
- Wave-particle Duality of Matter
- Particle Nature of Electromagnetic Radiation: Planck's Quantum Theory of Radiation
Scalars and Vectors
Structure of Atoms and Nuclei
- Structure of the Atom and Nucleus
- Thomson’s Atomic Model
- Geiger-marsden Experiment
- Lord Rutherford’s Atomic model
- Atomic Spectra
- Bohr’s Atomic Model
- Radii of the Orbits
- Energy of the Electrons
- Limitations of Bohr's Model
- De Broglie's Explanation
- Atomic Nucleus
- Nuclear Binding Energy
- Radioactive Decays
- Law of Radioactive Decay
- Forms of Energy > Nuclear Energy
- Nuclear Fission
- Nuclear Fusion
- Dalton's Atomic Theory
- Hydrogen Spectrum
- Radioactivity
Friction in Solids and Liquids
Semiconductor Devices
- Basics of Semiconductor Devices
- p-n Junction Diode as a Rectifier
- Half Wave Rectifier
- Full Wave Rectifier
- Ripple Factor
- Filter circuits
- Special Purpose P-n Junction Diodes
- Applications of semiconductors : Rectifier diode, LED, Zener diode, Photo diode, Photovoltaic cell, BJT, FET, SCR., MOSFET
- Bipolar Junction Transistor (BJT)
- Basics of Logic Gates
Magnetic Effect of Electric Current
- Flow of Charges (Electrons) Between Conductor
- Drift Speed
- Limitations of Ohm’s Law
- Forms of Energy > Electrical Energy
- Concept of Power
- Resistors
- Specific Resistance
- Variation of Resistance with Temperature
- Electro-Motive Force of a Cell
- Cells in Series
Magnetism
- Concept of Magnetism
- Magnetic Lines of Force
- The Bar Magnet
- Gauss' Law of Magnetism
- The Earth’s Magnetism
Estimated time: 4 minutes
Maharashtra State Board: Class 11
Definition: Series Combination of Springs
A combination in which two or more springs are connected end to end such that the effective spring constant is given by the reciprocal sum of individual spring constants is called series combination of springs.
Maharashtra State Board: Class 11
Definition: Parallel Combination of Springs
A combination in which two or more springs are connected side by side such that the effective spring constant is the sum of individual spring constants is called parallel combination of springs.
Maharashtra State Board: Class 11
Formula: Combination of Springs
| Property | Series Combination | Parallel Combination |
|---|---|---|
| Effective spring constant (two springs) | \[\frac{1}{k}=\frac{1}{k_1}+\frac{1}{k_2}\] | k = k1 + k2 |
| Effective spring constant (n identical springs) | keq = \[\frac{k}{2}\] (for 2 springs) keq = \[\frac{k}{n}\] (for n springs) |
keq = nk |
| Time period of oscillations | T = 2π \[\sqrt{\frac{m(k_1 + k_2)}{k_1 k_2}}\] | T = 2π \[\sqrt{\frac{m}{k_1 + k_2}}\] |
