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Class 12 PhysicsChapter Notes

14 chapters · Definitions, key points, formulas & exam tips · Updated 2025-26

Ch 1 Ch 2 Ch 3 Ch 4 Ch 5 Ch 6 Ch 7 Ch 8 Ch 9 Ch 10 Ch 11 Ch 12 Ch 13 Ch 14

Ch 1

Electric Charges and Fields

Key Definitions

Electric Charge: A fundamental property of matter. Two types: positive and negative. Unit: Coulomb (C).

Coulomb's Law: Force between two point charges: F = kq₁q₂/r². Directly proportional to product of charges, inversely to square of distance.

Electric Field: Force per unit positive charge at a point. E = F/q. Unit: N/C or V/m.

Key Points to Remember

→Charge is quantised: q = ne where e = 1.6 × 10⁻¹⁹ C.
→Charge is conserved — total charge in an isolated system remains constant.
→Electric field lines: start from positive, end at negative charge. Never cross.
→Gauss's Law: total electric flux through a closed surface = q/ε₀.
→Electric field inside a conductor = 0.
→Field due to infinite plane sheet of charge: E = σ/2ε₀.

Formulas & Equations

F = kq₁q₂/r² = q₁q₂/(4πε₀r²)

E = F/q = kq/r²

Electric flux: Φ = E·A cosθ

Gauss's Law: Φ = q_enclosed/ε₀

Exam Tips

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Principle of superposition: net force = vector sum of individual forces.

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Electric dipole: two equal and opposite charges separated by distance 2l. p = q × 2l.

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Torque on dipole in field: τ = pE sinθ.

Ch 2

Electrostatic Potential and Capacitance

Key Definitions

Electric Potential: Work done per unit positive charge in bringing it from infinity to a point. Unit: Volt (V).

Capacitance: Ability to store charge. C = Q/V. Unit: Farad (F).

Dielectric: Insulating material between capacitor plates that increases capacitance by factor K (dielectric constant).

Key Points to Remember

→Equipotential surface: potential is same at all points. Field is perpendicular to it.
→Work done in moving charge on equipotential surface = 0.
→Capacitors in series: 1/C = 1/C₁ + 1/C₂. In parallel: C = C₁ + C₂.
→Energy stored: U = ½CV² = Q²/2C = QV/2.
→Dielectric increases capacitance by factor K.
→Van de Graaff generator: accumulates high voltage using electrostatic principles.

Formulas & Equations

V = kq/r

C = ε₀A/d (parallel plate)

Energy: U = ½CV²

With dielectric: C = Kε₀A/d

Exam Tips

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Potential due to a dipole: V = kp cosθ/r² — direction matters.

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Common capacitor questions: find equivalent capacitance of networks.

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Effect of inserting dielectric: if battery connected — charge increases, V unchanged; if disconnected — V decreases, charge unchanged.

Ch 3

Current Electricity

Key Definitions

Drift Velocity: Average velocity acquired by electrons in a conductor due to an applied electric field. vd = eEτ/m.

Resistivity: Resistance of unit length and unit cross-sectional area of a conductor. ρ = RA/l. Unit: Ω·m.

EMF: The work done per unit charge by the source in moving charge around the complete circuit. Unit: Volt.

Key Points to Remember

→Ohm's law: V = IR (valid for metallic conductors at constant temperature).
→Resistivity increases with temperature for metals; decreases for semiconductors.
→Kirchhoff's Current Law (KCL): sum of currents at a junction = 0.
→Kirchhoff's Voltage Law (KVL): sum of EMFs = sum of potential drops in any loop.
→Wheatstone bridge balanced condition: R₁/R₂ = R₃/R₄.
→Terminal voltage of a cell: V = E − Ir (during discharge).

Formulas & Equations

R = ρl/A

I = nAevd

V = E − Ir

Balanced bridge: P/Q = R/S

Exam Tips

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For Wheatstone bridge problems: identify the four arms correctly before applying the balance condition.

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Potentiometer vs voltmeter: potentiometer draws no current from the circuit — more accurate.

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When cells are connected in series: E_total = E₁ + E₂; internal resistance adds up.

Ch 4

Moving Charges and Magnetism

Key Definitions

Lorentz Force: Force on a moving charge in combined electric and magnetic fields: F = q(E + v × B).

Biot-Savart Law: Magnetic field due to a current element: dB = μ₀Idl sinθ/(4πr²). Direction by right-hand rule.

Moving Coil Galvanometer: Instrument to detect small currents. Deflection θ = NBA/k × I. Converted to ammeter (shunt) or voltmeter (series resistance).

Key Points to Remember

→Force on current-carrying conductor: F = BIL sinθ. Maximum when θ = 90°.
→Force per unit length between parallel wires: F/L = μ₀I₁I₂/(2πd). Attractive if currents in same direction.
→Ampere's law: ∮B·dl = μ₀I_enclosed. Used to find B due to infinite wire and solenoid.
→Inside a solenoid: B = μ₀nI (n = turns per unit length).
→Cyclotron frequency: f = qB/(2πm) — independent of speed.
→Torque on current loop: τ = NIAB sinθ = MB sinθ.

Formulas & Equations

F = qvB sinθ

B at centre of circular loop: B = μ₀I/(2r)

B due to infinite wire: B = μ₀I/(2πd)

Torque: τ = NIAB sinθ

Exam Tips

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Conversion to ammeter: shunt S = Ig × G/(I − Ig) — connected in parallel.

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Conversion to voltmeter: R = V/Ig − G — connected in series.

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Cyclotron: only for charged particles. Electrons not used (relativistic effects).

Ch 5

Magnetism and Matter

Key Definitions

Magnetic Dipole Moment: m = IA for a current loop. For a bar magnet: M = m × 2l. Unit: A·m².

Magnetisation: Net magnetic dipole moment per unit volume of a material. M = M/V.

Susceptibility: χ = M/H. Positive for paramagnetic, small negative for diamagnetic, large positive for ferromagnetic.

Key Points to Remember

→Diamagnetic: weakly repelled by magnet. χ is small negative. Example: Bismuth, Copper.
→Paramagnetic: weakly attracted by magnet. χ is small positive. Example: Aluminium, Oxygen.
→Ferromagnetic: strongly attracted. χ is very large. Example: Iron, Nickel, Cobalt.
→Earth's magnetism: angle of declination (geographical vs magnetic north) and angle of dip.
→Curie's law: χ ∝ 1/T for paramagnetic substances. Above Curie temperature, ferromagnetics become paramagnetic.
→Hysteresis: energy loss per cycle = area enclosed in B-H curve. Used to select core material.

Formulas & Equations

B = μ₀(H + M) = μ₀μᵣH

χ_paramagnetic = C/T (Curie's law)

Field on axial line: B = μ₀ × 2M/(4πr³)

Field on equatorial line: B = μ₀M/(4πr³)

Exam Tips

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Soft iron: high permeability, low retentivity — used in transformer cores and electromagnets.

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Steel: high retentivity — used in permanent magnets.

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Distinguish between magnetic field B (flux density) and magnetic intensity H.

Ch 6

Electromagnetic Induction

Key Definitions

Magnetic Flux: Φ = BA cosθ. Total number of field lines passing through a surface. Unit: Weber (Wb).

Self Inductance: L = NΦ/I. Measure of a coil's tendency to oppose change in current. Unit: Henry (H).

Mutual Inductance: M = N₂Φ₂/I₁. EMF induced in one coil due to changing current in another. Unit: Henry (H).

Key Points to Remember

→Faraday's First Law: whenever magnetic flux through a circuit changes, EMF is induced.
→Faraday's Second Law: induced EMF = −dΦ/dt (Faraday's law; negative sign = Lenz's law).
→Lenz's law: induced current direction opposes the change causing it.
→Motional EMF: ε = BvL (conductor of length L moving at velocity v in field B).
→Self inductance of solenoid: L = μ₀n²V = μ₀n²Al.
→Eddy currents: induced in solid conductors; cause energy loss but used in induction heating, braking.

Formulas & Equations

ε = −dΦ/dt = −N × dΦ/dt

ε = BvL (motional EMF)

L = μ₀n²Al

ε_self = −L × dI/dt

Exam Tips

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Lenz's law is conservation of energy — work done against the induced force = electrical energy generated.

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Eddy currents reduced by laminating the core.

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Self induction opposes change in current — like inertia for current.

Ch 7

Alternating Current

Key Definitions

RMS Value: I_rms = I₀/√2. The DC equivalent value that produces the same heating effect. Similarly V_rms = V₀/√2.

Impedance: Total opposition to AC current flow. Z = V_rms/I_rms. Unit: Ohm. For LCR series: Z = √(R² + (X_L − X_C)²).

Resonance: Condition when X_L = X_C, so Z = R (minimum). Resonant frequency: f₀ = 1/(2π√LC).

Key Points to Remember

→In purely resistive circuit: voltage and current are in phase.
→In purely inductive circuit: current lags voltage by π/2.
→In purely capacitive circuit: current leads voltage by π/2.
→Power in AC: P = V_rms × I_rms × cosφ (cosφ = power factor).
→At resonance: current is maximum, impedance is minimum (= R), power factor = 1.
→Transformer: V₁/V₂ = N₁/N₂ = I₂/I₁ (ideal transformer, energy conserved).

Formulas & Equations

X_L = ωL = 2πfL

X_C = 1/ωC = 1/(2πfC)

Z = √(R² + (X_L − X_C)²)

f₀ = 1/(2π√LC)

Exam Tips

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Power factor cosφ = R/Z. Purely inductive or capacitive circuit: cosφ = 0 (no power consumed).

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Q-factor = ω₀L/R = 1/(ω₀CR) — measures sharpness of resonance.

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Transformer works only on AC, not DC.

Ch 8

Electromagnetic Waves

Key Definitions

Displacement Current: I_d = ε₀ × dΦ_E/dt. Current equivalent due to changing electric flux. Introduced by Maxwell to make Ampere's law consistent.

Electromagnetic Wave: A transverse wave consisting of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation.

Key Points to Remember

→Speed of EM waves in vacuum: c = 1/√(μ₀ε₀) = 3 × 10⁸ m/s.
→E and B are perpendicular to each other and to direction of propagation.
→Relationship: E₀/B₀ = c.
→EM spectrum (increasing frequency): Radio → Microwave → Infrared → Visible → UV → X-rays → Gamma rays.
→Radio waves: communication. Microwaves: radar, cooking. IR: remote sensing. UV: sterilisation. X-rays: medical imaging. Gamma: cancer treatment.
→EM waves carry both energy and momentum — exert radiation pressure.

Formulas & Equations

c = E₀/B₀ = 1/√(μ₀ε₀)

I_displacement = ε₀ × dΦ_E/dt

λ = c/f

Exam Tips

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Ozone layer absorbs UV — that's why ozone depletion is dangerous.

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EM waves do not need a medium — they travel through vacuum.

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Frequency determines type of EM wave; wavelength changes with medium but frequency doesn't.

Ch 9

Ray Optics and Optical Instruments

Key Definitions

Total Internal Reflection: When light travels from denser to rarer medium at angle greater than critical angle — no refraction, complete reflection. Basis of optical fibres.

Power of a Lens: P = 1/f. Convex lens: positive P. Concave lens: negative P. Unit: Dioptre (D).

Magnification: Ratio of image size to object size. For mirrors: m = −v/u. For lenses: m = v/u.

Key Points to Remember

→Mirror formula: 1/v + 1/u = 1/f. Sign convention: distances measured from pole.
→Lens maker's formula: 1/f = (n−1)(1/R₁ − 1/R₂).
→For lenses in contact: 1/f = 1/f₁ + 1/f₂. P_total = P₁ + P₂.
→Critical angle: sin C = 1/n (n = refractive index of denser medium).
→Compound microscope magnification: m = L/f_e × D/f_o (image at infinity).
→Astronomical telescope magnification: m = f_o/f_e (image at infinity).

Formulas & Equations

1/v + 1/u = 1/f (mirror and lens)

n = sin i/sin r (Snell's law)

sin C = 1/n

P = 1/f (dioptre)

Exam Tips

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Convex mirror always forms virtual, erect, diminished image — used in rear-view mirrors.

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Optical fibre works on TIR — internet cables use glass fibre.

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Aperture rule: larger aperture = better resolution but more aberration.

Ch 10

Wave Optics

Key Definitions

Coherent Sources: Sources that emit light of same frequency with a constant phase difference. Required for sustained interference.

Fringe Width: Distance between two consecutive bright or dark fringes in YDSE: β = λD/d.

Polarisation: Restriction of transverse oscillations of EM waves to one plane. Possible only for transverse waves — confirms transverse nature of light.

Key Points to Remember

→Huygen's principle: every point on a wavefront is a source of secondary wavelets.
→Condition for constructive interference (bright fringe): path difference = nλ.
→Condition for destructive interference (dark fringe): path difference = (2n+1)λ/2.
→In YDSE: fringe width β = λD/d. Fringe width increases with λ and D; decreases with d.
→Single slit diffraction: first minimum at θ = λ/a where a is slit width.
→Malus's law: I = I₀cos²θ (intensity after passing through analyser).

Formulas & Equations

β = λD/d (fringe width in YDSE)

Path difference at nth fringe: nλ

Malus's law: I = I₀cos²θ

Brewster's angle: tanθ_B = n

Exam Tips

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If YDSE is immersed in water: λ_water = λ/n, so β decreases by factor n.

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Polaroid: used in sunglasses, camera filters, LCD screens.

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Interference: two sources needed. Diffraction: single slit/aperture.

Ch 11

Dual Nature of Radiation and Matter

Key Definitions

Work Function: Minimum energy needed to eject an electron from a metal surface. φ = hν₀. Unit: eV.

Photoelectric Effect: Emission of electrons from a metal surface when light of frequency above threshold falls on it. Explained by Einstein (1905).

de Broglie Wavelength: λ = h/p = h/mv. Every particle has wave-like properties. Verified by Davisson-Germer experiment for electrons.

Key Points to Remember

→Einstein's equation: KE_max = hν − φ = h(ν − ν₀).
→Stopping potential V₀: eV₀ = hν − φ. Slope of V₀ vs ν graph = h/e.
→KE_max depends on frequency, NOT intensity. Intensity increases the number of photoelectrons.
→Wave nature of particles: de Broglie λ = h/√(2mK). For electron accelerated through V: λ = h/√(2meV).
→Davisson-Germer experiment: electron diffraction from Nickel crystal confirmed wave nature.
→Heisenberg's uncertainty principle: Δx · Δp ≥ h/(4π).

Formulas & Equations

E = hν = hc/λ

KE_max = hν − φ

λ = h/mv (de Broglie)

λ = h/√(2meV) for electron

Exam Tips

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Photoelectric effect cannot be explained by wave theory — quantum explanation was needed.

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Threshold frequency: minimum frequency below which no photoelectron is emitted regardless of intensity.

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de Broglie wavelength is significant only for very small particles (electrons, protons) — negligible for macroscopic objects.

Ch 12

Atoms

Key Definitions

Bohr's Model: Electrons orbit nucleus in stationary orbits with fixed energy. Energy emitted/absorbed as photon when electron transitions: E = hν.

Ionisation Energy: Energy needed to remove an electron from the ground state to infinity. For hydrogen: 13.6 eV.

Spectral Series: Groups of lines in hydrogen spectrum. Lyman (UV), Balmer (visible), Paschen (infrared) etc.

Key Points to Remember

→Rutherford's model: nucleus is positively charged, small, and dense. Electrons orbit around it.
→Bohr's postulate: angular momentum L = nh/(2π) = nℏ.
→Radius of nth orbit: rₙ = n² × a₀ (a₀ = 0.529 Å for hydrogen).
→Energy of nth level: Eₙ = −13.6/n² eV.
→Rydberg formula: 1/λ = R(1/n₁² − 1/n₂²). R = 1.097 × 10⁷ m⁻¹.
→Balmer series: transitions to n=2. First line is H_α (656 nm, red).

Formulas & Equations

rₙ = 0.529n² Å

Eₙ = −13.6/n² eV

1/λ = R(1/n₁² − 1/n₂²)

mvr = nℏ (Bohr's condition)

Exam Tips

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Rutherford's model failed: accelerating electron should radiate energy and spiral in — but atoms are stable.

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Bohr's model works only for hydrogen and hydrogen-like ions (He⁺, Li²⁺).

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Excitation energy: energy to go from ground state to excited state (less than ionisation energy).

Ch 13

Nuclei

Key Definitions

Binding Energy: Energy equivalent to mass defect: B.E. = Δm × c². Measures stability of nucleus. Higher BE/nucleon = more stable.

Half Life: Time in which half of a radioactive sample decays. T₁/₂ = 0.693/λ. Independent of amount of substance.

Mass Defect: Difference between sum of masses of nucleons and actual nuclear mass: Δm = Zm_p + (A−Z)m_n − M.

Key Points to Remember

→Nuclear force: strongest fundamental force. Short range (up to ~3 fm), charge independent.
→Radioactive decay law: N = N₀e^(−λt).
→Alpha decay: emits ₂He⁴ — Z decreases by 2, A decreases by 4.
→Beta⁻ decay: n → p + e⁻ + ν̄ — Z increases by 1, A unchanged.
→Gamma decay: nucleus transitions to lower energy state — no change in Z or A.
→Nuclear fission: heavy nucleus splits into smaller nuclei releasing energy. Basis of nuclear reactor.
→Nuclear fusion: lighter nuclei combine — sun's energy source. Higher energy density than fission.

Formulas & Equations

N = N₀e^(−λt)

T₁/₂ = 0.693/λ

B.E. = Δm × 931.5 MeV/u

R = R₀A^(1/3) (nuclear radius)

Exam Tips

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BE/nucleon graph: Fe-56 has highest BE/nucleon — most stable nucleus.

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Fission: energy released because BE/nucleon of products > BE/nucleon of reactant.

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Activity A = λN = 0.693N/T₁/₂.

Ch 14

Semiconductor Electronics

Key Definitions

Intrinsic Semiconductor: Pure semiconductor with equal numbers of electrons and holes. Conductivity increases with temperature.

p-n Junction: Interface between p-type and n-type semiconductors. Depletion layer formed at junction. Forward bias reduces, reverse bias increases barrier.

Transistor: Three-terminal device (emitter, base, collector). NPN or PNP. Used as amplifier or switch.

Key Points to Remember

→Energy bands: valence band (filled), conduction band (empty), and energy gap between them.
→Conductor: zero or overlapping gap. Semiconductor: small gap (~1 eV). Insulator: large gap (>3 eV).
→n-type: doped with group 15 element (extra electron). p-type: doped with group 13 (hole).
→Forward bias: current flows. Reverse bias: only tiny leakage current flows.
→Half wave rectifier: one diode. Full wave rectifier (bridge): 4 diodes. Output is pulsating DC.
→Logic gates: AND, OR, NOT. NAND and NOR are universal gates (any circuit can be made).

Formulas & Equations

β = I_C/I_B (transistor current gain)

I_E = I_B + I_C

Truth table for NAND: 0+0→1, 0+1→1, 1+0→1, 1+1→0

Exam Tips

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Transistor as amplifier: small base current controls large collector current.

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Universal gates: NAND and NOR — any logical operation can be done using only these.

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Zener diode: always reverse biased — used as voltage regulator.

Frequently Asked Questions

Are these notes based on 2025-26 CBSE syllabus for Class 12 Physics?

Yes. All chapter notes here are based on the latest 2025-26 CBSE syllabus for Class 12 Physics. Deleted topics are clearly marked so you focus only on what will be tested in your board exam.

How to study Class 12 Physics notes effectively for board exams?

Read each chapter's notes once to build understanding. Then close the notes and try to recall every key point, definition, and formula from memory. Anything you miss is your weak area — revisit only those points. This active recall method takes less time and retains far more than re-reading.

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