Circular Motion Angular Displacement Angular Velocity Angular Acceleration Angular Velocity and Its Relation with Linear Velocity Uniform Circular Motion (UCM) Radial Acceleration Dynamics of Uniform Circular Motion - Centripetal Force Centrifugal Forces Banking of Roads Vertical Circular Motion Due to Earth’s Gravitation Equation for Velocity and Energy at Different Positions of Vertical Circular Motion Kinematical Equations for Circular Motion in Analogy with Linear Motion. Angular Displacement Angular Velocity Angular Acceleration Angular Velocity and Its Relation with Linear Velocity Uniform Circular Motion (UCM) Radial Acceleration Dynamics of Uniform Circular Motion - Centripetal Force Centrifugal Forces Banking of Roads Vertical Circular Motion Due to Earth’s Gravitation Equation for Velocity and Energy at Different Positions of Vertical Circular Motion Kinematical Equations for Circular Motion in Analogy with Linear Motion. Rotational Dynamics Rotational Dynamics Circular Motion and Its Characteristics Applications of Uniform Circular Motion Vertical Circular Motion Moment of Inertia as an Analogous Quantity for Mass 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 Overview: Rotational Dynamics Rotational Dynamics Circular Motion and Its Characteristics Applications of Uniform Circular Motion Vertical Circular Motion Moment of Inertia as an Analogous Quantity for Mass 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 Overview: Rotational Dynamics Mechanical Properties of Fluids Fluid and Its Properties Thrust and Pressure Pressure of liquid Pressure Exerted by a Liquid Column Atmospheric Pressure Gauge Pressure and Absolute Pressure Hydrostatic Paradox Pascal’s Law Application of Pascal’s Law Measurement of Atmospheric Pressure 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 Viscous Force or Viscosity Stokes’ Law Terminal Velocity Continuous and Discontinuous Functions Bernoulli's Equation Applications of Bernoulli’s Equation Overview: Mechanical Properties of Fluids Fluid and Its Properties Thrust and Pressure Pressure of liquid Pressure Exerted by a Liquid Column Atmospheric Pressure Gauge Pressure and Absolute Pressure Hydrostatic Paradox Application of Pascal’s Law Measurement of Atmospheric Pressure 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 Viscous Force or Viscosity Terminal Velocity Continuous and Discontinuous Functions Bernoulli's Equation Applications of Bernoulli’s Equation Overview: Mechanical Properties of Fluids Gravitation Newton’s Law of Gravitation Periodic Time Kepler’s Laws Binding Energy and Escape Velocity of a Satellite Weightlessness Variation of ‘G’ Due to Lattitude and Motion Variation in the Acceleration>Variation in Gravity with Altitude Communication satellite and its uses Composition of Two S.H.M.’S Having Same Period and Along Same Line Newton’s Law of Gravitation Binding Energy and Escape Velocity of a Satellite Variation of ‘G’ Due to Lattitude and Motion Variation in the Acceleration>Variation in Gravity with Altitude Communication satellite and its uses Composition of Two S.H.M.’S Having Same Period and Along Same Line Angular Momentum Definition of M.I., K.E. of Rotating Body Rolling Motion Physical Significance of M.I (Moment of Inertia) Torque and Angular Momentum Theorems of Perpendicular and Parallel Axes M.I. of Some Regular Shaped Bodies About Specific Axes Definition of M.I., K.E. of Rotating Body Physical Significance of M.I (Moment of Inertia) Torque and Angular Momentum Theorems of Perpendicular and Parallel Axes M.I. of Some Regular Shaped Bodies About Specific Axes Kinetic Theory of Gases and Radiation Gases and Its Characteristics Classification of Gases: Real Gases and Ideal Gases Mean Free Path Expression for Pressure Exerted by a Gas Root Mean Square (RMS) Speed Interpretation of Temperature in Kinetic Theory Law of Equipartition of Energy Specific Heat Capacity Absorption, Reflection, and Transmission of Heat Radiation Perfect Blackbody Emission of Heat Radiation Kirchhoff’s Law of Heat Radiation and Its Theoretical Proof Spectral Distribution of Blackbody Radiation Wien's Displacement Law Stefan-boltzmann Law of Radiation Overview: Kinetic Theory of Gases and Radiation Gases and Its Characteristics Classification of Gases: Real Gases and Ideal Gases Expression for Pressure Exerted by a Gas Root Mean Square (RMS) Speed Interpretation of Temperature in Kinetic Theory Law of Equipartition of Energy Specific Heat Capacity Absorption, Reflection, and Transmission of Heat Radiation Perfect Blackbody Emission of Heat Radiation Kirchhoff’s Law of Heat Radiation and Its Theoretical Proof Spectral Distribution of Blackbody Radiation Wien's Displacement Law Stefan-boltzmann Law of Radiation Overview: Kinetic Theory of Gases and Radiation Oscillations Periodic and Oscillatory Motion Simple Harmonic Motion (S.H.M.) Differential Equation of Linear S.H.M. Projection of U.C.M.(Uniform Circular Motion) on Any Diameter Phase of K.E (Kinetic Energy) K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M. Composition of Two S.H.M.’S Having Same Period and Along Same Line Some Systems Executing Simple Harmonic Motion Periodic and Oscillatory Motion Simple Harmonic Motion (S.H.M.) Differential Equation of Linear S.H.M. Projection of U.C.M.(Uniform Circular Motion) on Any Diameter Phase of K.E (Kinetic Energy) K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M. Composition of Two S.H.M.’S Having Same Period and Along Same Line Some Systems Executing Simple Harmonic Motion Thermodynamics Thermodynamics Thermal Equilibrium Measurement of Temperature Heat, Internal Energy and Work First Law of Thermodynamics Thermodynamic State Variables and Equation of State Thermodynamic Process Heat Engine Refrigerators and Heat Pumps Entropy and Second Law of Thermodynamics Carnot Cycle and Carnot Engine Overview: Thermodynamics Thermal Equilibrium Measurement of Temperature Heat, Internal Energy and Work First Law of Thermodynamics Thermodynamic State Variables and Equation of State Thermodynamic Process Refrigerators and Heat Pumps Entropy and Second Law of Thermodynamics Carnot Cycle and Carnot Engine Overview: Thermodynamics 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. 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 Periodic and Oscillatory Motion Overview: 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. 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 Periodic and Oscillatory Motion Overview: Oscillations Elasticity Eneral Explanation of Elastic Property Stress and Strain Hooke’s Law Elastic Energy Elastic Constants and Their Relation Determination of ‘Y’ Behaviour of Metal Wire Under Increasing Load Application of Elastic Behaviour of Materials Eneral Explanation of Elastic Property Stress and Strain Elastic Constants and Their Relation Determination of ‘Y’ Behaviour of Metal Wire Under Increasing Load Application of Elastic Behaviour of Materials Superposition of Waves Superposition of Waves Progressive Waves Reflection of Waves Stationary Waves Free and Forced Vibrations Harmonics and Overtones Sonometer Beats Characteristics of Sound Musical Instruments The Speed of a Travelling Wave Speed of Wave Motion Study of Vibrations of Air Columns Overview: Superposition of Waves Superposition of Waves Progressive Waves Reflection of Waves Stationary Waves Free and Forced Vibrations Harmonics and Overtones Characteristics of Sound Musical Instruments The Speed of a Travelling Wave Speed of Wave Motion Study of Vibrations of Air Columns Overview: Superposition of Waves Surface Tension Molecular Theory of Surface Tension Surface Tension Capillarity and Capillary Action Effect of Impurity and Temperature on Surface Tension Molecular Theory of Surface Tension Surface Tension Capillarity and Capillary Action Effect of Impurity and Temperature on Surface Tension Wave Optics Introduction to Wave Optics Nature of Light Light as a Wave Huygens Principle Reflection of Light at a Plane Surface Refraction of Light at a Plane Boundary Between Two Media Polarisation of Light Interference Diffraction of Light Resolving Power of Optical Instruments Overview: Wave Optics Introduction to Wave Optics Nature of Light Light as a Wave Huygens Principle Reflection of Light at a Plane Surface Refraction of Light at a Plane Boundary Between Two Media Polarisation of Light Diffraction of Light Resolving Power of Optical Instruments Overview: Wave Optics Wave Motion Wave Motion Introduction Simple Harmonic Progressive Waves, Reflection of Transverse and Longitudinal Waves Change of Phase Principle of Superposition of Waves Formation of Beats Beats Wave Motion Introduction Simple Harmonic Progressive Waves, Reflection of Transverse and Longitudinal Waves Change of Phase Principle of Superposition of Waves Formation of Beats Stationary Waves Study of Vibrations in a Finite Medium Formation of Stationary Waves on String Study of Vibrations of Air Columns Free and Forced Vibrations Forced Oscillations and Resonance Study of Vibrations in a Finite Medium Formation of Stationary Waves on String Study of Vibrations of Air Columns Free and Forced Vibrations Forced Oscillations and Resonance Electrostatics Concept of Electrostatics Application of Gauss' Law Electric Potential and Potential Difference Electric Potential Due to a Point Charge Equipotential Surfaces Electrical Energy of Two Point Charges and of a Dipole in an Electrostatic Field Free and Bound Charges Combination of Capacitors Displacement Current Energy Stored in a Charged Capacitor Van De Graaff Generator Uniformly Charged Infinite Plane Sheet and Uniformly Charged Thin Spherical Shell (Field Inside and Outside) Overview: Electrostatics Concept of Electrostatics Application of Gauss' Law Electric Potential and Potential Difference Electric Potential Due to a Point Charge Equipotential Surfaces Electrical Energy of Two Point Charges and of a Dipole in an Electrostatic Field Free and Bound Charges Combination of Capacitors Displacement Current Energy Stored in a Charged Capacitor Van De Graaff Generator Uniformly Charged Infinite Plane Sheet and Uniformly Charged Thin Spherical Shell (Field Inside and Outside) Overview: Electrostatics Kinetic Theory of Gases and Radiation Concept of an Ideal Gas Assumptions of Kinetic Theory of Gases Derivation for Pressure of a Gas Degrees of Freedom Derivation of Boyle’s Law Thermal Equilibrium First Law of Thermodynamics Heat Engine Temperature and Heat Qualitative Ideas of Black Body Radiation Wien's Displacement Law Green House Effect Stefan's Law Maxwell Distribution Specific Heat Capacities - Gases Law of Equipartition of Energy Concept of an Ideal Gas Assumptions of Kinetic Theory of Gases Derivation for Pressure of a Gas Degrees of Freedom Derivation of Boyle’s Law Thermal Equilibrium First Law of Thermodynamics Temperature and Heat Qualitative Ideas of Black Body Radiation Wien's Displacement Law Green House Effect Maxwell Distribution Specific Heat Capacities - Gases Law of Equipartition of Energy Current Electricity Introduction Tо Current Electricity Kirchhoff’s Laws Wheatstone Bridge Galvanometer Moving Coil Galvanometer Overview: Current Electricity Introduction Tо Current Electricity Kirchhoff’s Laws Wheatstone Bridge Moving Coil Galvanometer Overview: Current Electricity Wave Theory of Light Photoelectric Effect and Wave Theory of Light Huygens Principle Construction of Plane and Spherical Wave Front, Wave Normal Reflection and Refraction of Plane Wave at a Plane Surface Using Wave Fronts Electric Polarisation of Dielectrics Brewster's Law Beats Photoelectric Effect and Wave Theory of Light Huygens Principle Construction of Plane and Spherical Wave Front, Reflection and Refraction of Plane Wave at a Plane Surface Using Wave Fronts Electric Polarisation of Dielectrics 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 Magnetic Field Due to a Current-carrying Conductor: Biot-savart's 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 at the Axis of a Circular Current-carrying Loop Magnetic Lines for a Current Loop Ampere’s Circuital Law Applications of Ampere’s Circuital Law > Magnetic Field of a Toroidal Solenoid Overview: Magnetic Fields Due to Electric Current Magnetic Fields Due to Electric Current 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 Magnetic Field Due to a Current-carrying Conductor: Biot-savart's 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 at the Axis of a Circular Current-carrying Loop Magnetic Lines for a Current Loop Ampere’s Circuital Law Applications of Ampere’s Circuital Law > Magnetic Field of a Toroidal Solenoid Overview: Magnetic Fields Due to Electric Current Interference and Diffraction Interference of Light Conditions for Producing Steady Interference Pattern Interference of Light Waves and Young’s Experiment Analytical Treatment of Interference Bands Measurement of Wavelength by Biprism Experiment Fraunhofer's Diffraction Due to a Single-slit Rayleigh’s Criterion Resolving Power of a Microscope and Telescope Interference Vs Diffraction Interference of Light Conditions for Producing Steady Interference Pattern Interference of Light Waves and Young’s Experiment Analytical Treatment of Interference Bands Measurement of Wavelength by Biprism Experiment Fraunhofer's Diffraction Due to a Single-slit Rayleigh’s Criterion Resolving Power of a Microscope and Telescope Interference Vs Diffraction Magnetic Materials Selection of 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 Classification of Magnetic Materials Hysteresis: Retentivity and Coercivity Permanent Magnet Magnetic Shielding Overview: Magnetic Materials Selection of 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

Classification of Magnetic Materials Hysteresis: Retentivity and Coercivity Permanent Magnet Magnetic Shielding Overview: Magnetic Materials Electromagnetic Induction Introduction to Electromagnetic Induction Faraday's Laws of Electromagnetic Induction Lenz's Law Flux of a Vector 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 Overview of Electromagnetic Induction Introduction to Electromagnetic Induction Faraday's Laws of Electromagnetic Induction Flux of a Vector Field Motional Electromotive Force (e.m.f.) Induced Emf in a Stationary Coil in a Changing Magnetic Field 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 Overview of Electromagnetic Induction Electrostatics Mechanical Force on Unit Area of a Charged Conductor Energy Density of a Medium Concept of Condenser The Parallel Plate Capacitor Capacity of Parallel Plate Condenser Effect of Dielectric on Capacitance Energy of Charged Condenser Condensers in Series and Parallel, Van-deGraaff Generator Mechanical Force on Unit Area of a Charged Conductor Energy Density of a Medium Concept of Condenser The Parallel Plate Capacitor Capacity of Parallel Plate Condenser Effect of Dielectric on Capacitance Energy of Charged Condenser Condensers in Series and Parallel, Van-deGraaff Generator AC Circuits Introduction to Ac and Aс Circuits Values of Alternating Current Phasors AC Voltage Applied to a Resistor AC Voltage Applied to an Inductor AC Voltage Applied to a Capacitor AC Voltage Applied to a Series LCR Circuit Power in AC Circuit LC Oscillations Electric Resonance Sharpness of Resonance: Q Factor Choke Coil Overview: AC Circuits Introduction to Ac and Aс Circuits Values of Alternating Current AC Voltage Applied to a Resistor AC Voltage Applied to an Inductor AC Voltage Applied to a Capacitor AC Voltage Applied to a Series LCR Circuit Power in AC Circuit LC Oscillations Electric Resonance Sharpness of Resonance: Q Factor Overview: AC Circuits Current Electricity Meter Bridge Dual Nature of Radiation and Matter Understanding Dual Nature of Radiation and Matter The Photoelectric Effect Wave-particle Duality of Electromagnetic Radiation Photo Cell De Broglie Hypothesis Davisson and Germer Experiment Wave-particle Duality of Matter Overview: Dual Nature of Radiation and Matter Understanding Dual Nature of Radiation and Matter The Photoelectric Effect Wave-particle Duality of Electromagnetic Radiation De Broglie Hypothesis Davisson and Germer Experiment Wave-particle Duality of Matter Overview: Dual Nature of Radiation and Matter Magnetic Effects of Electric Current Ampere’s Circuital Law Moving Coil Galvanometer Cyclotron Ampere’s Circuital Law Moving Coil Galvanometer Magnetism Current Loop as a Magnetic Dipole : Magnetic Dipole Moment of Current Loop Magnetic Dipole Moment of a Revolving Electron Magnetisation and Magnetic Intensity Magnetic Properties of Materials Curie Temperature Current Loop as a Magnetic Dipole : Magnetic Dipole Moment of Current Loop Magnetic Dipole Moment of a Revolving Electron Magnetisation and Magnetic Intensity Magnetic Properties of Materials Curie Temperature Structure of Atoms and Nuclei Structure of the Atom and Nucleus Thomson’s Atomic Model Geiger-marsden Experiment Rutherford’s Atomic Model Atomic Spectra Neils Bohr’s Model of an Atom Atomic Nucleus Constituents of a Nucleus Isotopes Atomic and Nuclear Masses Size of the Nucleus Mass Defect and Binding Energy Binding Energy Curve Forms of Energy > Nuclear Energy Nuclear Binding Energy Radioactive Decays Law of Radioactive Decay Overview: Structure of Atoms and Nuclei Structure of the Atom and Nucleus Thomson’s Atomic Model Geiger-marsden Experiment Rutherford’s Atomic Model Neils Bohr’s Model of an Atom Constituents of a Nucleus Atomic and Nuclear Masses Size of the Nucleus Mass Defect and Binding Energy Binding Energy Curve Forms of Energy > Nuclear Energy Nuclear Binding Energy Radioactive Decays Law of Radioactive Decay Overview: Structure of Atoms and Nuclei Semiconductor Devices Basics of Semiconductor Devices p-n Junction Diode as a Rectifier Special Purpose P-n Junction Diodes Bipolar Junction Transistor (BJT) Logic Gates Overview: Semiconductor Devices Basics of Semiconductor Devices p-n Junction Diode as a Rectifier Special Purpose P-n Junction Diodes Bipolar Junction Transistor (BJT) Overview: Semiconductor Devices Electromagnetic Inductions Introduction to Electromagnetic Induction Self Inductance Mutual Inductance Transformers Need for Displacement Current Coil Rotating in Uniform Magnetic Induction Alternating-Current Generator Reactance and Impedance LC Oscillations Inductance and Capacitance Resonant Circuits Power in AC Circuit Lenz’s Law and Conservation of Energy Introduction to Electromagnetic Induction Self Inductance Mutual Inductance Need for Displacement Current Coil Rotating in Uniform Magnetic Induction Alternating-Current Generator Reactance and Impedance LC Oscillations Inductance and Capacitance Resonant Circuits Power in AC Circuit Lenz’s Law and Conservation of Energy Electrons and Photons Photoelectric Effect - Hertz’s Observations Photoelectric Effect - Hallwachs’ and Lenard’s Observations Einstein’s Equation - Particle Nature of Light Particle Nature of Light Photoelectric Effect - Hertz’s Observations Photoelectric Effect - Hallwachs’ and Lenard’s Observations Einstein’s Equation - Particle Nature of Light Particle Nature of Light Atoms, Molecules and Nuclei Alpha-particle Scattering and Rutherford’s Nuclear Model of Atom Bohr’s Model for Hydrogen Atom Hydrogen Spectrum Atomic Masses and Composition of Nucleus Radioactivity Law of Radioactive Decay Atomic Mass, Mass - Energy Relation and Mass Defect Nuclear Binding Energy Nuclear Fusion de-Broglie Relation Wave Nature of Matter Wavelength of an Electron Davisson and Germer Experiment Continuous and Characteristics X-rays Mass Defect and Binding Energy Alpha-particle Scattering and Rutherford’s Nuclear Model of Atom Bohr’s Model for Hydrogen Atom Hydrogen Spectrum Atomic Masses and Composition of Nucleus Law of Radioactive Decay Atomic Mass, Mass - Energy Relation and Mass Defect Nuclear Binding Energy de-Broglie Relation Wave Nature of Matter Wavelength of an Electron Davisson and Germer Experiment Continuous and Characteristics X-rays Mass Defect and Binding Energy Semiconductors Energy Bands in Materials Extrinsic Semiconductor Applications of n-type and p-type Semiconductors Special Purpose P-n Junction Diodes Semiconductor Diode Voltage Regulator I-V Characteristics of Led Transistor and Characteristics of a Transistor Transistor as an Amplifier (Ce-configuration) Transistor as a Switch Oscillators Digital Electronics and Logic Gates Energy Bands in Materials Extrinsic Semiconductor Applications of n-type and p-type Semiconductors Special Purpose P-n Junction Diodes Semiconductor Diode Voltage Regulator I-V Characteristics of Led Transistor and Characteristics of a Transistor Transistor as an Amplifier (Ce-configuration) Transistor as a Switch Digital Electronics and Logic Gates Communication Systems Basic Terminology Used in Electronic Communication Systems Bandwidth of Signals Bandwidth of Transmission Medium Need for Modulation and Demodulation Production and Detection of an Amplitude Modulated Wave Space Communication Propagation of EM Waves Modulation and Its Necessity Basic Terminology Used in Electronic Communication Systems Bandwidth of Signals Bandwidth of Transmission Medium Need for Modulation and Demodulation Production and Detection of an Amplitude Modulated Wave Space Communication Propagation of EM Waves Modulation and Its Necessity A capacitor stores electrical potential energy when it is charged. This energy is associated with the electric field set up between its plates, not merely with charge “sitting” on the plates. A useful analogy is a water tank being filled against gravity: as the water level rises, further filling requires more work. In the same way, as a capacitor charges, the potential difference rises, so adding more charge requires increasing work. Definition: Energy Stored in a Capacitor The work done in the transfer of charge q between the two plates of a capacitor, which gets stored in the form of potential energy of the system, is called the energy stored in a capacitor. Formula: Energy Stored / Work Done in a Capacitor W = \[\frac {1}{2}\]qV U = \[\frac {Q^2}{2C}\] ​= \[\frac {1​}{2}\]QV = \[\frac {1}{2}\]​CV 2 SI unit: Joule (J) Stepwise Derivation Consider a capacitor of capacitance C. At some intermediate stage of charging, let the charge on it be q. Then the potential difference across it is: V = \[\frac {q}{C}\] If an additional small charge dq is supplied, the small work done is: dW = V dq = \[\frac {q}{C}\]dq Total work done in charging the capacitor from 0 to the final charge Q is: W = \[\int_0^Q\frac{q}{C}dq\] W = \[\frac{1}{C}\int_0^Qqdq=\frac{1}{C}\left[\frac{q^2}{2}\right]_0^Q\] W = \[\frac{Q^2}{2C}\] Since this work is stored as energy: U = \[\frac{Q^2}{2C}\]​ Using Q = CV, the equivalent forms become: U = \[\frac{Q^2}{2C}=\frac{1}{2}QV=\frac{1}{2}CV^2\] The energy stored in a charged capacitor is actually stored in the electric field between its plates. For a parallel-plate capacitor, the energy density of the electric field is: where u is energy per unit volume, and E is electric field intensity. Energy density indicates how much electrical energy is stored per unit volume of the field. This is an important bridge between electrostatics and field-based physics. A parallel-plate capacitor (3 × 10⁻⁹ F) is connected to 400 V. A dielectric slab (K = 3, thickness 3 cm) completely fills the space. The voltage is kept constant. What is the change in energy when the slab is removed? At constant voltage, energy U = \[\frac {1}{2}\]CV 2 , so energy ∝ capacitance. Steps in simple words With air: use given C = 3 × 10⁻⁹ F and V = 400 V. U air = \[\frac {1}{2}\]CV 2 = 24 × 10 −5 J. With dielectric: new capacitance C′ = kC = 3 × 3 × 10 −9 = 9 × 10 −9 F. U dielectric = \[\frac {1}{2}\]C′V 2 = 72 × 10 −5 J. Change in energy = U dielectric − U air = (72 − 24) × 10 −5 = 48 × 10 −5 J. Conclusion in one line: When the dielectric is present, energy is higher by 48 × 10 −5 J at constant voltage. (a) A 900 pF capacitor is charged by 100 V. Find the stored energy. (b) Then it is disconnected and connected to another 900 pF capacitor (uncharged). Find a new total energy. Capacitance C = 900 pF = 900 × 10 −12 F, voltage V = 100 V. Charge: Q = CV = 900 × 10 −12 × 100 = 9 × 10 −8 C. Energy: U = \[\frac {1}{2}\]CV 2 = \[\frac {1}{2}\]QV. U = \[\frac {1}{2}\] × 9 × 10 −8 × 100 = 4.5 × 10 −6 J. Simple meaning: This is how much energy the single capacitor stores when charged to 100 V. Now two equal capacitors (both 900 pF) are connected, so the final charges are shared equally. Let the final potential be V′. Then each capacitor has Q′ = CV′. Total charge is conserved: Q total = Q. So each gets Q′ = Q/2. Therefore V′ = Q′/C = (Q/2)/C = V/2. Energy in each capacitor: \[\frac {1}{2}\]Q′V′. Total energy = 2 × \[\frac {1}{2}\]Q′V′ = Q′V′ = \[\frac {1}{4}\]QV. Numerically: U final = 2.25 × 10 −6 J. Final energy is half of the initial: 4.5 × 10 −6 → 2.25 × 10 −6 J. The “missing” energy is lost as heat and electromagnetic radiation when charge flows during connection. Shaalaa.com | Capacitor and Capacitance part 19 (Energy Stored in Capacitors, Energy density) Related Questions VIEW ALL [45] Two capacitors of capacitances 4⋅0 µF and 6⋅0 µF are connected in series with a battery of 20 V. Find the energy supplied by the battery. A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor? Consider the situation shown in figure. The switch is closed at t = 0 when the capacitors are uncharged. Find the charge on the capacitor C 1 as a function of time t. A capacitor of capacitance 12.0 μF is connected to a battery of emf 6.00 V and internal resistance 1.00 Ω through resistanceless leads. 12.0 μs after the connections are made, what will be (a) the current in the circuit (b) the power delivered by the battery (c) the power dissipated in heat and (d) the rate at which the energy stored in the capacitor is increasing? Prove that, if an insulated, uncharged conductor is placed near a charged conductor and no other conductors are present, the uncharged body must be intermediate in potential between that of the charged body and that of infinity. An air-filled parallel plate capacitor has a uniform electric field `overset(->)("E")` in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is ______ (∈ 0 = permittivity of free space) Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor. A 20 μF capacitor is joined to a battery of emf 6.0 V through a resistance of 100 Ω. Find the charge on the capacitor 2.0 ms after the connections are made. 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