Physics notes for Class 11, Class 12, JEE and NEET
Physics notes for Class 11, JEE and NEET, topic by topic: laws and formulas with SI units, solved numericals, common mistakes and practice questions.
28 chapters 240 topics Updated 8 Nov 2026
Chapters
Units and Measurement
NCERT Class 11 Physics, Chapter 1 7 topics
-
SI units
The seven base (fundamental) units, derived units, the radian and steradian, and prefixes, with solved examples.
-
Significant figures
Counting rules, scientific notation, arithmetic and rounding rules, and uncertainty, with solved examples.
-
Errors in measurement
Accuracy and precision, systematic and random errors, absolute and percentage error, and combining errors.
-
Least count: vernier callipers and screw gauge
Least count formulas, how to take readings, and positive and negative zero error with corrections.
-
Dimensions of physical quantities
The seven base dimensions, dimensions of derived quantities, and dimensionless quantities.
-
Dimensional formulae and equations
What they are, how to find them, a table of common formulae, and solved examples.
-
Dimensional analysis
Checking equations, deducing relations such as the pendulum’s period, converting units, and limitations.
Motion in a Straight Line
NCERT Class 11 Physics, Chapter 2 5 topics
-
Frame of reference and displacement
Path length, average velocity vs average speed and x-t graphs, with 5 solved examples.
-
Velocity and speed
v = dx/dt as a limit, the slope of the x-t graph and speed vs velocity, with solved examples.
-
Acceleration
Formula, unit, negative acceleration, v-t graphs and the area under them, with 5 solved examples.
-
Equations of motion
v = v + at, x = vt + ½at, v = v + 2ax, derived by graph and calculus, free fall, stopping distance.
-
Relative velocity
vAB = vA − vB in one and two dimensions, overtaking, rain-umbrella and river boat problems, with examples.
Motion in a Plane
NCERT Class 11 Physics, Chapter 3 9 topics
-
Scalars and vectors
How scalar and vector quantities differ, why current is a scalar, displacement and equal vectors.
-
Multiplying a vector by a number
How the magnitude and direction change, the negative of a vector, parallel and unit vectors.
-
Adding vectors graphically
The triangle and parallelogram laws, the null vector and subtracting vectors, with solved examples.
-
Resolution of vectors
Rectangular components A cos θ and A sin θ, unit vectors, magnitude, direction and direction cosines.
-
Adding vectors by components
Adding vectors by components, magnitude and direction of the resultant, laws of cosines and sines.
-
Position, velocity and acceleration in a plane
r = xî + yĵ, displacement, v = dr/dt along the tangent and a = dv/dt.
-
Constant acceleration in a plane
Vector equations of motion, x and y motions treated separately, with examples.
-
Projectile motion
Formulas and derivations for time of flight, maximum height, horizontal range and the path, with examples.
-
Uniform circular motion
Centripetal acceleration v/R, angular speed, time period and frequency, with solved examples.
Laws of Motion
NCERT Class 11 Physics, Chapter 4 10 topics
-
Aristotle’s fallacy
Why uniform motion needs no net force, how friction misleads us, with solved examples and practice questions.
-
Law of inertia
Galileo’s inclined planes, inertia of rest, motion and direction, mass as its measure, and solved examples.
-
Newton’s first law
Statement, meaning, inertial frames, examples and common mistakes.
-
Newton’s second law
F = dp/dt and F = ma derived, impulse, SI unit of force, 3 solved examples and practice.
-
Newton’s third law
Action and reaction forces, why they never cancel, recoil and other examples, and practice.
-
Conservation of momentum
Derivation from Newton’s laws, recoil of a gun, collisions and explosions, with solved examples.
-
Equilibrium of a particle
Concurrent forces, resolving into components, triangle of forces and Lami’s theorem, with examples.
-
Friction
Static and kinetic friction, the coefficient of friction, laws of friction, angle of repose and rolling friction.
-
Dynamics of circular motion
Mv/R, the highest safe speed on a level road, the banking of roads derivation and solved examples.
-
Solving problems in mechanics
Choosing the system, the step-by-step method, blocks in contact, the Atwood machine and connected bodies.
Work, Energy and Power
NCERT Class 11 Physics, Chapter 5 11 topics
-
Scalar product
A·B = AB cos θ, projection, properties, the component formula and the angle between vectors.
-
Work-energy theorem
Net work equals the change in kinetic energy, its derivation, braking distance and solved examples.
-
Work
W = Fd cos θ, positive, negative and zero work, the joule and other energy units, with solved examples.
-
Kinetic energy
K = ½mv, its link with momentum (K = p/2m), percentage changes and solved examples with practice questions.
-
Work done by a variable force
The area under the force–displacement graph, work as an integral, and solved examples.
-
Work-energy theorem (variable force)
The calculus proof dK = F dx, what it leaves out, and solved examples.
-
Potential energy
Stored energy, gravitational potential energy mgh, F = −dV/dx, and conservative and non-conservative forces.
-
Conservation of mechanical energy
K + V constant for conservative forces, a falling ball and motion in a vertical circle.
-
Potential energy of a spring
Hooke’s law F = −kx, the work done by a spring force, V = ½kx and spring-block energy problems.
-
Power
Average and instantaneous power, P = F·v, the watt, horsepower and kilowatt hour, with solved examples and practice.
-
Collisions
1D formulas derived, the coefficient of restitution, 2D collisions and solved examples.
Systems of Particles and Rotational Motion
NCERT Class 11 Physics, Chapter 6 14 topics
-
Rigid body motion
What a rigid body is, translation, rotation about a fixed axis or point, and rolling without slipping.
-
Centre of mass
Two particles, many particles and rigid bodies, symmetry, composite bodies and cut-outs, with solved examples.
-
Motion of the centre of mass
Velocity and acceleration of the centre of mass, MA = Fext, explosions and boats, with examples.
-
Momentum of a system
P = MV, the second law for a system, conservation and the centre-of-mass frame.
-
Vector product
Ab sin θ, the right-hand rule, properties, unit vectors and the determinant form.
-
Angular velocity
Angular displacement, ω = dθ/dt, v = ωr, the vector v = ω × r and angular acceleration, with examples.
-
Torque and angular momentum
τ = r × F, the moment arm, l = r × p, dL/dt = τ and conservation of angular momentum, solved.
-
Equilibrium of a rigid body
Zero force and zero torque, couples, the principle of moments and the centre of gravity, solved.
-
Experiment: mass with a metre scale
Finding a mass with a metre scale and a knife-edge, with the theory, procedure, precautions and examples.
-
Moment of inertia
I = Σmr, rotational kinetic energy, radius of gyration and I of a ring, disc, rod and sphere, with examples.
-
Parallel and perpendicular axes
Statements, proofs and uses for rods, rings, discs, plates and spheres, with solved examples.
-
Rotational kinematics
Angular displacement, velocity and acceleration, the equations for constant α and the linear analogy.
-
Rotational dynamics
Torque and angular acceleration, τ = Iα, work and power in rotation and the linear comparison, solved.
-
Angular momentum about an axis
L = Iω about a fixed axis, Iω = Iω, skaters, divers and locking discs, with examples.
Gravitation
NCERT Class 11 Physics, Chapter 7 9 topics
-
Kepler’s laws
The law of orbits, the law of areas and the law of periods, T ∝ a, with planetary data and solved examples.
-
Universal law of gravitation
F = Gmm/r, the Moon test, vector form, superposition, the shell theorem and solved examples.
-
Gravitational constant
Its value, unit and dimensions, and Cavendish’s torsion balance experiment, with solved examples.
-
Acceleration due to gravity
The Earth as shells, g = GM/R, g from density and the mass of the Earth, with solved examples.
-
Variation of g
Exact and approximate g(h), g(d) = g(1 − d/R) for a uniform Earth, with solved examples.
-
Gravitational potential energy
Mgh, U = −GMm/r and why it is negative, systems of particles, potential V = −GM/r, examples.
-
Escape speed
Derived from energy, √(2GM/R) = √(2gR) ≈ 11.2 km/s, the Moon’s value and NCERT Example 7.4.
-
Earth satellites
V = √(GM/r), the period and Kepler’s third law, the 85-minute orbit and geostationary orbits.
-
Energy of an orbiting satellite
Kinetic, potential and total energy, E = −GMm/(2r), binding energy and changing orbits, with examples.
Mechanical Properties of Solids
NCERT Class 11 Physics, Chapter 8 7 topics
-
Elasticity and plasticity
Elastic and plastic deformation, permanent set, and why steel is more elastic than rubber.
-
Stress and strain
Stress = F/A, units and dimensions, longitudinal, shearing and hydraulic stress, with solved examples.
-
Hooke’s law
Stress = k × strain, the modulus of elasticity, a wire as a spring, and where the law fails, with solved examples.
-
Stress-strain curve
Proportional limit, yield point, ultimate strength, fracture, permanent set, brittle, ductile, elastomers.
-
Elastic moduli
Young’s, shear and bulk modulus, compressibility, Poisson’s ratio and elastic energy, NCERT examples solved.
-
Experiment: Young’s modulus of a wire
Searle’s apparatus, procedure, precautions, Y = MgL/(πrl), the load-extension graph and error analysis.
-
Applications of elastic behaviour
How thick a crane rope must be, why beams have an I-section, pillars, and a simple estimate of mountain height.
Mechanical Properties of Fluids
NCERT Class 11 Physics, Chapter 9 7 topics
-
Pressure in fluids
Pascal’s law, pressure at depth P = P + ρgh, gauge and absolute pressure, barometers and the hydraulic lift.
-
Streamline and turbulent flow
Steady and turbulent flow, the equation of continuity Av = Av, critical velocity and the Reynolds number.
-
Bernoulli’s principle
The equation and its derivation, Torricelli’s law, dynamic lift and the venturi meter.
-
Viscosity
The coefficient of viscosity, its unit and dimensions, Stokes’ law F = 6πηav and terminal velocity, solved.
-
Experiment: viscosity from terminal velocity
The falling-ball method, Stokes’ law, terminal velocity and its graph against a, precautions and errors.
-
Surface tension
Surface energy, angle of contact, excess pressure in drops and bubbles, capillary rise and detergents, solved.
-
Experiment: surface tension by capillary rise
Capillary rise with a travelling microscope, S = rhρg/2, the effect of detergents, precautions and errors.
Thermal Properties of Matter
NCERT Class 11 Physics, Chapter 10 10 topics
-
Temperature and heat
The difference between them, their SI units, thermal equilibrium, the calorie and solved examples.
-
Measuring temperature
Thermometers, fixed points, the Celsius to Fahrenheit formula, faulty thermometers and solved examples.
-
Ideal-gas equation and absolute temperature
Boyle’s and Charles’ laws, PV = μRT, the gas thermometer, absolute zero and the kelvin scale, with examples.
-
Thermal expansion
Linear, area and volume expansion and their coefficients, thermal stress and water’s anomalous expansion.
-
Specific heat capacity
Heat capacity, specific and molar specific heat, ΔQ = msΔT, units, Cp and Cv, and why water matters.
-
Calorimetry
Heat lost equals heat gained, the calorimeter, the method of mixtures, water equivalent and solved examples.
-
Experiment: specific heat by the method of mixtures
Finding the specific heat capacity of a solid and a liquid, with theory, procedure, precautions and errors.
-
Change of state
Melting, boiling, sublimation, regelation, the triple point and Q = mL, with solved examples.
-
Heat transfer
Conduction, thermal conductivity, convection, radiation, Wien’s law and the Stefan–Boltzmann law, with examples.
-
Newton’s law of cooling
The formula and its derivation, rate of cooling, the exponential cooling curve, the log graph and solved examples.
Thermodynamics
NCERT Class 11 Physics, Chapter 11 10 topics
-
Thermal equilibrium
Definition, equilibrium states, adiabatic and diathermic walls, everyday examples and solved problems.
-
Zeroth law of thermodynamics
The statement, the experiment behind it, how it defines temperature and justifies thermometers.
-
Heat, internal energy and work
Internal energy, heat and work for Class 11 Physics, JEE and NEET: internal energy as a state variable, heat as energy in transit, and solved examples.
-
First law of thermodynamics
First law of thermodynamics for Class 11 Physics, JEE and NEET: ΔQ = ΔU + ΔW, sign conventions, work PΔV at constant pressure, and solved examples.
-
Specific heat capacity of solids, water and gases
Relation between Cp and Cv for Class 11 Physics, JEE and NEET: Mayer’s relation Cp − Cv = R with its derivation, 3R for solids and solved examples.
-
State variables and equation of state
State variables for Class 11 Physics, JEE and NEET: equilibrium states, the equation of state PV = μRT, isotherms, extensive and intensive variables.
-
Thermodynamic processes
Thermodynamic processes for Class 11 Physics, JEE and NEET: isothermal, adiabatic, isochoric, isobaric and cyclic, with work and heat in each.
-
Second law of thermodynamics
Kelvin–Planck and Clausius statements, heat engines, refrigerators and why efficiency is below 1.
-
Reversible and irreversible processes
Conditions for reversibility, why real processes are irreversible, with examples.
-
Carnot engine
The four steps of the Carnot cycle, efficiency η = 1 − T/T with its derivation, Carnot’s theorem and solved examples.
Kinetic Theory
NCERT Class 11 Physics, Chapter 12 6 topics
-
Molecular nature of matter
The atomic hypothesis, Dalton and Avogadro, and how far apart molecules are in solids, liquids and gases.
-
Behaviour of gases
PV = μRT = NkB T, Avogadro’s hypothesis, real versus ideal gases and Dalton’s law of partial pressures.
-
Kinetic theory of an ideal gas
Assumptions, pressure P = (1/3)nm⟨v⟩, kinetic meaning of temperature, rms speed and solved examples.
-
Law of equipartition of energy
Degrees of freedom, ½kB T per mode, and energy of monatomic and diatomic molecules.
-
Specific heat capacity from kinetic theory
Cv, Cp and γ for monatomic, diatomic and polyatomic gases; 3R for solids.
-
Mean free path
Derivation of l = 1/(√2 nπd), collision time, and how l depends on size, density and pressure.
Oscillations
NCERT Class 11 Physics, Chapter 13 8 topics
-
Periodic and oscillatory motion
The difference, examples, period and frequency, displacement and periodic functions.
-
Simple harmonic motion
The definition, x(t) = A cos(ωt + φ), amplitude, phase, phase constant and angular frequency.
-
SHM and uniform circular motion
The reference circle, x and y projections, clockwise motion, solved examples.
-
Velocity and acceleration in SHM
v = −ωA sin(ωt + φ), a = −ωx, speed at any position, phase relations, solved examples.
-
Force law for SHM
Restoring force F = −kx, force constant k = mω, spring period T = 2π√(m/k), spring combinations.
-
Energy in SHM
Kinetic and potential energy, constant total energy E = ½kA, energy graphs and solved examples.
-
The simple pendulum
Forces on the bob, deriving T = 2π√(L/g), the small-angle limit, seconds pendulum and solved examples.
-
Experiment: simple pendulum and loss of energy
Timing the period, finding g, and plotting the square of the amplitude against time to show energy loss.
Waves
NCERT Class 11 Physics, Chapter 14 8 topics
-
Wave motion
Mechanical, electromagnetic and matter waves, local oscillation, energy transport and worked examples.
-
Transverse and longitudinal waves
Particle motion, compressions and rarefactions, which media carry which waves, examples.
-
Displacement relation for a progressive wave
y = a sin(kx − ωt + φ), amplitude, phase, wavelength, k, ω and frequency, with solved examples.
-
Speed of a travelling wave
v = λν, waves on a string, speed of sound, Newton’s formula and the Laplace correction, examples.
-
Principle of superposition of waves
Adding displacements, resultant amplitude 2a cos(φ/2), constructive and destructive interference.
-
Reflection of waves and standing waves
Reflection at a rigid or free end, nodes and antinodes, harmonics of strings and open and closed organ pipes.
-
Experiment: speed of sound with a resonance tube
Finding the first two resonance lengths, v = 2ν(l − l), the end correction, precautions and errors.
-
Beats
Why two close frequencies give a loudness that rises and falls, beat frequency ν − ν, and tuning with beats.
Electric Charges and Fields
NCERT Class 12 Physics, Chapter 1 13 topics
-
Electric charge
Positive and negative charge, charging by rubbing as electron transfer, and how a gold-leaf electroscope works.
-
Conductors and insulators
How they differ, free electrons, where charge goes on each, the metal spoon and semiconductors.
-
Basic properties of electric charge
Additivity, conservation and quantisation (q = ne), the value of e, and NCERT Examples 1.1, 1.2.
-
Coulomb’s law
Statement and formula F = k|qq|/r, ε and k, the vector form, the force in a medium, and solved numericals.
-
Forces between multiple charges
Forces between multiple charges as vector sums of Coulomb forces, and NCERT Examples 1.5 and 1.6.
-
Electric field
E = F/q and the test charge, the field of a point charge and of many charges, the SI unit, and solved examples.
-
Electric field lines
What they show, density and strength, diagrams of simple charges, and why they never cross or form loops.
-
Electric flux
Definition, formula Δϕ = EΔS cos θ, the area vector, SI unit N C m, and NCERT Exercises 1.14 and 1.15 solved.
-
Electric dipole
Dipole moment p = q × 2a, its electric field on the axis and equator with derivation, and the 1/r fall-off.
-
Dipole in a uniform field
τ = p × E = pE sin θ with derivation, zero net force, and non-uniform fields.
-
Continuous charge distribution
Linear, surface and volume charge density with SI units, and the field of a charged ring.
-
Gauss’s law
The statement ϕ = q/ε, the Gaussian surface, flux through a cube, and how it differs from Coulomb’s law.
-
Applications of Gauss’s law
Derivations of the field of a long charged wire, an infinite plane sheet and a thin charged shell.
Electrostatic Potential and Capacitance
NCERT Class 12 Physics, Chapter 2 15 topics
-
Electrostatic potential energy
Definition, why the Coulomb force is conservative, ΔU as external work, the zero at infinity.
-
Electrostatic potential
Electrostatic potential as work per unit charge, potential difference, W = qΔV, volts and electron volts.
-
Potential due to a point charge
The derivation of V = Q/4πεr, its sign, V against E with distance, and NCERT Example 2.1.
-
Potential due to a dipole
Derivation of V = p cos θ/4πεr, its value at axial and equatorial points, and the 1/r fall-off.
-
Potential due to a system of charges
Superposition, a charged shell inside and outside, and NCERT Examples 2.2 and 2.3.
-
Equipotential surfaces
Properties, shapes for a point charge and a uniform field, and the relation between field and potential.
-
Potential energy of a system of charges
Two charges, three or more charges, signs of U, and NCERT Example 2.4 on a square.
-
Potential energy in an external field
U = −pE cos θ, a single charge’s U = qV, two charges, and NCERT Example 2.6.
-
Electrostatics of conductors
Why E = 0 inside, charge on the surface, E = σ/ε just outside, and electrostatic shielding.
-
Dielectrics and polarisation
Polar and non-polar molecules, induced dipoles, P = εχE, and bound surface charge ±σp.
-
Capacitors and capacitance
Two conductors and an insulator, C = Q/V, the farad, µF and pF, and dielectric strength of air.
-
The parallel plate capacitor
Field σ/ε between the plates, zero outside, C = εA/d derivation, and the force between the plates.
-
Effect of a dielectric on capacitance
C = KC, the dielectric constant K = ε/ε, partial slabs, battery connected or not.
-
Combination of capacitors
Same charge or same voltage, 1/C = 1/C + 1/C, C = C + C, and NCERT Example 2.9.
-
Energy stored in a capacitor
Derivation of U = ½CV, energy density ½εE, energy lost in sharing charge, solved examples.
Current Electricity
NCERT Class 12 Physics, Chapter 3 15 topics
-
Electric current
I = q/t, the net charge q − q, current at an instant as dQ/dt, the ampere and electrons per second.
-
Electric currents in conductors
Free electrons in metals, random motion and no net current, and why a cell keeps a steady field.
-
Ohm’s law
V = RI, how R depends on length and area, R = ρl/A, current density, conductivity and j = σE, with examples.
-
Experiment: resistance using Ohm’s law
a wire’s resistance from the ammeter–voltmeter circuit and rheostat, the V–I graph slope, errors and precautions.
-
Drift of electrons
Relaxation time, vd = −eEτ/m, the relation I = neAvd, conductivity σ = neτ/m and mobility μ = eτ/m.
-
Limitations of Ohm’s law
Non-ohmic conductors, V–I graphs that bend, the diode’s one-way current and GaAs, with examples.
-
Resistivity of various materials
Conductors, semiconductors and insulators, the range for metals, and the role of impurities.
-
Temperature dependence of resistivity
ρ = ρ[1 + α(T − T)], metals, nichrome, semiconductors, with examples.
-
Electrical energy and power
P = IV = IR = V/R derived, why resistors heat up, kWh, and why power lines use high voltage.
-
Combination of resistors
The combination formulas R = R + R and 1/R = 1/R + 1/R derived, dividers and reducing networks.
-
Cells, emf and internal resistance
Emf vs terminal voltage, V = ε − Ir, I = ε/(R + r), charging, NCERT exercises.
-
Cells in series and in parallel
The equivalent emf and internal resistance, reversed cells, identical cells and mixed grouping.
-
Kirchhoff’s rules
Junction and loop rules, why they hold, sign conventions, and NCERT Examples 3.5, 3.6 and Exercise 3.7 solved.
-
Wheatstone bridge
Its principle, the balance condition R/R = R/R derived, an unknown resistance, and NCERT Example 3.7.
-
Metre bridge
S = R(100 − l)/l, balance length, end corrections, precautions, and a wire’s resistivity from its length and diameter.
Moving Charges and Magnetism
NCERT Class 12 Physics, Chapter 4 10 topics
-
Magnetic force
F = q(E + v × B), magnetic force |q|vB sin θ, directions, the tesla and force on a wire, with examples.
-
Motion in a magnetic field
Why a charge circles, r = mv/(qB), frequency qB/(2πm), helical paths and the pitch, with examples.
-
Biot–Savart law
The statement and vector form, dB = μI dl sin θ/(4πr), direction of dB, μ and Coulomb’s law, with examples.
-
Field on the axis of a loop
Formula and derivation, μI/(2R) at the centre, arcs, N turns and direction.
-
Ampere’s circuital law
Statement and sign rule, amperian loops, B = μI/(2πr) for a long wire, B inside a thick wire, examples.
-
The solenoid
B = μnI from Ampere’s law, uniform inside and nearly zero outside, direction, ends, examples.
-
Force between parallel currents
Derivation of the force per metre, why like currents attract, and the ampere’s definition.
-
Torque on a current loop
Derivation of τ = IAB sin θ, magnetic moment m = NIA, τ = m × B, and the loop as a magnetic dipole.
-
Moving coil galvanometer
The radial field, φ = (NAB/k)I, conversion to an ammeter and a voltmeter, and its sensitivity.
-
Experiment: galvanometer resistance
The half-deflection method, G = RS/(R − S), k = ε/[(R + G)θ], precautions, examples.
Magnetism and Matter
NCERT Class 12 Physics, Chapter 5 4 topics
-
The bar magnet
Field lines, the bar magnet as an equivalent solenoid, its field on the axis and equator, and the torque m × B.
-
Gauss’s law for magnetism
Statement and formula, zero flux through any closed surface, monopoles, and NCERT Examples 5.3–5.4.
-
Magnetisation and magnetic intensity
M, H, B = μ(H + M), susceptibility χ and relative permeability μr = 1 + χ, with examples.
-
Magnetic properties of materials
χ ranges, examples, superconductors, domains, effect of temperature.
Electromagnetic Induction
NCERT Class 12 Physics, Chapter 6 8 topics
-
Experiments of Faraday and Henry
Magnet and coil, two coils, a key, and the flux change behind them.
-
Magnetic flux
Definition, Φ = BA cos θ and the area vector, SI unit weber, dimensions, curved surfaces, with solved examples.
-
Faraday’s law of induction
Statement, ε = −dΦ/dt and its minus sign, N-turn coils, average emf, with examples.
-
Lenz’s law
The induced current opposes the change in flux, magnet-and-coil cases, open circuits and conservation of energy.
-
Motional emf
Definition, ε = Blv derived from Faraday’s law and the Lorentz force, rods on rails, rotating rods and wheels.
-
Eddy currents
Current loops induced in bulk metal, magnetic braking, damping, induction heating, and why transformer cores are laminated.
-
Inductance
Coaxial solenoids, a solenoid’s self-inductance, back emf, energy stored ½LI and solved examples.
-
AC generator
Working principle, a coil turning in a magnetic field, emf ε = NBAω sin ωt, its derivation and the peak emf.
Alternating Current
NCERT Class 12 Physics, Chapter 7 7 topics
-
AC voltage applied to a resistor
AC voltage applied to a resistor, current in phase, average power ½iR, I = i/√2, 311 V peak, examples.
-
Phasors
AC voltage and current as rotating vectors, phase difference, lead and lag, adding phasors.
-
AC voltage applied to an inductor
AC voltage applied to an inductor, current lagging by π/2, XL = ωL = 2πνL, zero average power, examples.
-
AC voltage applied to a capacitor
AC voltage applied to a capacitor, current leading by π/2, XC = 1/(ωC), why DC is blocked, examples.
-
Series LCR circuit
Phasor-diagram derivation, impedance Z, phase angle, resonance at ω = 1/√(LC), radio tuning, examples.
-
Power in ac circuits
Average power VI cos φ in AC circuits and its derivation, wattless current, power at resonance, NCERT examples.
-
Transformers
Voltage and current ratios, power factor, efficiency, leakage flux, core losses and transmission.
Electromagnetic Waves
NCERT Class 12 Physics, Chapter 8 3 topics
-
Displacement current
Derivation for a charging capacitor, id = ε dΦE/dt, vs conduction current, Ampere–Maxwell law, examples.
-
Electromagnetic waves
Sources, properties, transverse nature, speed c = 1/√(με), B = E/c, energy, with solved examples.
-
Electromagnetic spectrum
Radio waves to gamma rays, NCERT Table 8.1’s wavelength ranges, sources, uses and photon energies.
Ray Optics and Optical Instruments
NCERT Class 12 Physics, Chapter 9 9 topics
-
Spherical mirrors
Spherical mirrors, sign convention, f = R/2, derivation of 1/v + 1/u = 1/f, magnification, solved examples.
-
Refraction
Snell’s law, refractive index and optical density, lateral shift through a slab, real and apparent depth.
-
Experiment: glass slab
Travelling microscope method, n = (a − a)/(a − a), least count, errors and precautions.
-
Total internal reflection
Its two conditions, the critical angle formula, totally reflecting prisms and optical fibres.
-
Lenses
Refraction at a curved surface, thin lens formula 1/v − 1/u = 1/f, magnification, power, combinations.
-
Experiment: focal lengths
Parallax method, index correction, f = uv/(u + v), 1/u–1/v graph, examples.
-
Prism
Refraction through a prism, δ = i + e − A, prism formula n = sin[(A + Dm)/2]/sin(A/2), thin prism.
-
Experiment: prism i–δ graph
Tracing rays with pins, the i–δ graph, reading the angle of minimum deviation and finding the refractive index.
-
Optical instruments
Simple microscope, refracting and Cassegrain telescopes, magnifying power formulas, examples.
Wave Optics
NCERT Class 12 Physics, Chapter 10 7 topics
-
Huygens principle
Wavefronts and rays, spherical and plane waves, secondary wavelets, the missing backwave, solved examples.
-
Refraction and reflection by Huygens principle
Snell’s law from wavefronts, i = r in reflection, wavelength and frequency, solved examples.
-
Coherent and incoherent addition
Sustained interference, path and phase difference, I = 4I cos(φ/2), solved examples.
-
Young’s double-slit experiment
Set-up, path difference xd/D, bright and dark fringes, fringe width β = λD/d, solved examples.
-
Diffraction
The single-slit pattern, minima at θ ≈ nλ/a, central maximum width 2λ/a, interference vs diffraction.
-
Polarisation
Plane-polarised and unpolarised light, polaroids, Malus’ law I = I cosθ, uses and solved examples.
-
Brewster’s law
Polarisation by reflection, the Brewster or polarising angle from tan iB = μ, rays at right angles, solved examples.
Dual Nature of Radiation and Matter
NCERT Class 12 Physics, Chapter 11 7 topics
-
Electron emission
Work function, electron volt to joule, thermionic, field and photoelectric emission, with solved examples.
-
Photoelectric effect
Hertz’s discovery, Hallwachs’ and Lenard’s observations, photoelectrons and the threshold frequency.
-
Experimental study of the photoelectric effect
The photoelectric experiment, its four laws, Kmax = eV0 and the graphs.
-
Photoelectric effect and the wave theory
Why the wave theory fails to explain the threshold, a fixed Kmax and instant emission.
-
Einstein’s photoelectric equation
Kmax = hν − φ0, threshold frequency and wavelength, the V0–ν graph and solved examples.
-
Photon
Particle nature of light, energy E = hν = hc/λ, momentum p = h/λ, properties, photons per second and solved examples.
-
Wave nature of matter
The de Broglie relation λ = h/p, λ = h/√(2mK), electrons through V volts, and why balls show no waves.
Atoms
NCERT Class 12 Physics, Chapter 12 5 topics
-
Rutherford’s nuclear model
Alpha-particle scattering experiment, impact parameter, distance of closest approach and solved examples.
-
Atomic spectra
Emission and absorption spectra, line vs continuous spectrum, hydrogen’s visible lines and solved examples.
-
Bohr model
Three postulates, radius r = na, energy −13.6/n eV, energy levels, ionisation energy and solved examples.
-
Line spectra of hydrogen
hν = Ei − Ef, Lyman, Balmer and Paschen series, the Rydberg formula, number of lines and solved examples.
-
De Broglie and Bohr’s postulate
De Broglie’s standing electron waves, 2πr = nλ, L = nh/2π and the limitations of the Bohr model.
Nuclei
NCERT Class 12 Physics, Chapter 13 6 topics
-
Composition of the nucleus
Protons and neutrons, atomic mass unit, discovery of the neutron, isotopes, isobars and isotones.
-
Size of the nucleus
Nuclear radius formula R = RA1/3, R = 1.2 fm, why nuclear density is constant, and solved examples.
-
Binding energy
E = mc, mass defect, how to calculate binding energy per nucleon, its curve and solved examples.
-
Nuclear force
Properties of nuclear force (strong, short range, charge independent), saturation, the potential energy graph.
-
Radioactivity
Becquerel’s discovery, alpha, beta and gamma decay, how each changes A and Z, what half-life means, and solved examples.
-
Nuclear energy
Why both release energy, Q values, 200 MeV per fission, fusion in the sun and controlled fusion.
Semiconductor Electronics: Materials, Devices and Simple Circuits
NCERT Class 12 Physics, Chapter 14 10 topics
-
Metals, insulators and semiconductors
How conductors, insulators and semiconductors differ, valence and conduction bands and band gaps.
-
Intrinsic semiconductor
Covalent bonds in Si and Ge, electron-hole pairs, hole current, carrier concentration and band diagram.
-
Extrinsic semiconductor
Doping, n-type and p-type with donors and acceptors, majority and minority carriers, mass action law.
-
p-n junction
How it forms, with a diagram, diffusion and drift currents, the depletion region and the barrier potential.
-
Semiconductor diode
Forward and reverse bias, V-I characteristics, knee (threshold) and breakdown voltages, dynamic resistance.
-
Junction diode as a rectifier
Half-wave and full-wave (centre-tap) rectifiers, output frequency, ripple and capacitor filters.
-
Zener diode
Zener and avalanche breakdown, the symbol, the I-V characteristic and its circuit, and the Zener voltage regulator.
-
LED, photodiode and solar cell
How each junction works with light, its bias, its I-V curve and how the band gap sets colour and cut-off.
-
Experiment: identifying components
Identify a diode, LED, resistor and capacitor with a multimeter for JEE Main and NEET Unit 20: tests both ways, the capacitor’s kick and the colour code.
-
Logic gates
OR, AND, NOT, NAND and NOR, with symbols, truth tables, Boolean expressions, De Morgan’s theorem and universal gates.