Physics — Class 12 (CBSE)

Board: CBSE | Class: 12 | Subject: Physics (NCERT Part I & II) Class 12 Physics is critical for Board exams (70 marks theory), JEE, and NEET. Chapters span electrostatics, electromagnetism, optics, modern physics, and semiconductors.

Overview

Exam Pattern: Theory — 70 marks | Practical — 30 marks

Unit	Chapters	Marks
Electrostatics	Ch 1–2	15
Current Electricity	Ch 3	7
Magnetic Effects + Magnetism	Ch 4–5	16
EMI + AC	Ch 6–7	10
EM Waves	Ch 8	3
Optics	Ch 9–10	14
Dual Nature of Matter	Ch 11	4
Atoms + Nuclei	Ch 12–13	8
Semiconductor Electronics	Ch 14	7

Unit 1: Electrostatics

Electric Charges and Fields

Coulomb's Law

F = kq₁q₂/r²    k = 1/(4πε₀) = 9 × 10⁹ N·m²/C²
ε₀ = 8.854 × 10⁻¹² C²/N·m²

Electric Field

E = F/q₀ = kQ/r²    (point charge)

Field lines originate at positive charges, terminate at negative charges
Field lines never intersect; density ∝ field strength

Electric Flux and Gauss's Law

φ = ∮ E·dA = Q_enclosed/ε₀

Applications: field due to infinite plane, sphere, cylindrical conductor

Electric Dipole - Dipole moment: p = q × 2a (C·m) - Field on axial point: E = 2kp/r³ - Field on equatorial point: E = kp/r³ - Torque: τ = p × E = pE sinθ

Electrostatic Potential and Capacitance

Electric Potential

V = kQ/r    (potential due to point charge)
V = W/q₀    (work done per unit charge)
E = -dV/dr  (relation between E and V)

Capacitors

C = Q/V     C = ε₀A/d    (parallel plate capacitor)

Configuration	Formula
Series	1/C = 1/C₁ + 1/C₂ + ...
Parallel	C = C₁ + C₂ + ...
With dielectric	C = Kε₀A/d (K = dielectric constant)

Energy stored in capacitor:

U = ½CV² = Q²/2C = QV/2

Unit 2: Current Electricity

Ohm's Law and Resistance

V = IR    R = ρL/A    ρ = resistivity

Temperature dependence: ρ = ρ₀(1 + αΔT)

Kirchhoff's Laws - KCL (Junction Rule): Sum of currents at a junction = 0 (charge conservation) - KVL (Loop Rule): Sum of EMFs = Sum of IR drops around a loop (energy conservation)

Important Circuits - Wheatstone bridge: Balanced when P/Q = R/S; null deflection in galvanometer - Metre bridge: R/S = l₁/(100-l₁) - Potentiometer: Used to measure EMF precisely (no current drawn)

Cell — EMF and Internal Resistance

V = E - Ir    (during discharge)
Terminal voltage < EMF during discharge; > EMF during charging

Unit 3: Magnetic Effects of Current and Magnetism

Biot-Savart Law

dB = (μ₀/4π) × (I dl sinθ)/r²
μ₀ = 4π × 10⁻⁷ T·m/A

Magnetic field due to: - Long straight wire: B = μ₀I/2πr - Circular loop (at centre): B = μ₀I/2R - Solenoid: B = μ₀nI (n = turns per unit length) - Toroid: B = μ₀NI/2πr

Ampere's Circuital Law

∮ B·dl = μ₀I_enclosed

Force on Current-Carrying Conductor

F = IL × B = BIL sinθ

Force between two parallel conductors:

F/L = μ₀I₁I₂/2πd

Parallel currents attract; antiparallel currents repel. Definition of 1 Ampere based on this.

Moving Charges in Magnetic Field

F = qv × B = qvB sinθ    (Lorentz force)

Circular motion: r = mv/qB; f = qB/2πm (cyclotron frequency)

Magnetism and Matter

Type	Susceptibility χ	Examples
Diamagnetic	Small, negative	Bismuth, copper, water
Paramagnetic	Small, positive	Aluminium, oxygen
Ferromagnetic	Large, positive	Iron, nickel, cobalt

Curie's Law: χ ∝ 1/T (paramagnetic)
Curie Temperature: Above this, ferromagnetic → paramagnetic

Unit 4: Electromagnetic Induction and Alternating Currents

Faraday's Laws

EMF is induced whenever magnetic flux through a circuit changes
Magnitude of induced EMF: ε = -dφ/dt

Lenz's Law: Induced current opposes the change causing it (conservation of energy).

Mutual and Self Inductance

M = φ₂₁/I₁      Self inductance: φ = LI
ε = -M(dI₁/dt)    ε = -L(dI/dt)

Energy stored in inductor: U = ½LI²

Alternating Current Circuits

V = V₀ sinωt      I = I₀ sin(ωt ± φ)
V_rms = V₀/√2     I_rms = I₀/√2

Element	Reactance/Impedance	Phase
Resistor (R)	Z = R	V and I in phase
Inductor (L)	X_L = ωL	V leads I by 90°
Capacitor (C)	X_C = 1/ωC	I leads V by 90°
Series LCR	Z = √(R² + (X_L-X_C)²)	tan φ = (X_L-X_C)/R

Resonance: X_L = X_C → ω₀ = 1/√(LC) → Z = R (minimum); current maximum

Power in AC: P = V_rms × I_rms × cos φ (cos φ = power factor)

Transformer

V_s/V_p = N_s/N_p = I_p/I_s

Efficiency = P_output/P_input × 100%
Step-up: N_s > N_p; Step-down: N_s < N_p
Power loss in transmission: minimized by high-voltage (low-current) transmission

Unit 5: Electromagnetic Waves

Maxwell's Equations — predict electromagnetic waves with speed c = 1/√(μ₀ε₀) = 3 × 10⁸ m/s

Electromagnetic Spectrum (increasing wavelength):

Gamma → X-rays → UV → Visible → Infrared → Microwaves → Radio waves

All EM waves travel at c in vacuum; differ only in frequency/wavelength.

Properties: Transverse waves; carry energy and momentum; do not require medium

Unit 6: Optics

Ray Optics

Mirror and Lens Formulas (same as Class 10 but extended) - Lens maker's equation: 1/f = (n-1)(1/R₁ - 1/R₂) - Combination of lenses in contact: 1/f = 1/f₁ + 1/f₂ - Total Internal Reflection: when θ_i > θ_c where sin θ_c = 1/n - Optical fibres use TIR for data transmission

Prism: δ = (i₁ + i₂) - A; at minimum deviation: n = sin(A+δ_m)/2 / sin(A/2)

Optical Instruments: | Instrument | Magnification | |---|---| | Simple microscope | m = 1 + D/f | | Compound microscope | m = m_o × m_e = -L/f_o × (1 + D/f_e) | | Astronomical telescope | m = -f_o/f_e |

Wave Optics

Huygens' Principle: Every point on a wavefront acts as a secondary source of wavelets.

Young's Double Slit Experiment (YDSE)

Fringe width β = λD/d
Position of bright fringe: y_n = nλD/d
Position of dark fringe: y_n = (2n-1)λD/2d

Diffraction (Single slit): - Central maximum width = 2λD/a - First minimum at: a sinθ = λ

Polarisation: - Light polarised by reflection at Brewster's angle: tan θ_B = n - Malus' Law: I = I₀ cos²θ (intensity through analyser)

Unit 7: Dual Nature of Radiation and Matter

Photoelectric Effect

Einstein's Equation:

KE_max = hf - φ = hf - hf₀

h = 6.626 × 10⁻³⁴ J·s (Planck's constant)
φ = work function = energy to remove electron from surface
Stopping potential: eV₀ = KE_max
No effect of intensity on KE_max; only frequency matters

De Broglie Wavelength (Wave-Particle Duality)

λ = h/p = h/mv

For accelerated electron: λ = h/√(2meV)

Davisson-Germer Experiment — confirmed wave nature of electrons

Unit 8: Atoms and Nuclei

Bohr's Model of Hydrogen Atom

rₙ = 0.529 × n² Å    (radius of nth orbit)
Eₙ = -13.6/n² eV     (energy of nth orbit)

Ground state (n=1): E = −13.6 eV; radius = 0.529 Å
Spectral series: Lyman (UV), Balmer (visible), Paschen (IR), Brackett, Pfund

Frequency of emitted radiation:

hf = Eₙ₂ - Eₙ₁ = 13.6(1/n₁² - 1/n₂²) eV

Nuclear Physics

Composition: - Nucleus = Protons (Z) + Neutrons (N); mass number A = Z + N - Isotopes: same Z, different A - Nuclear size: R = R₀ A^(1/3) where R₀ = 1.2 × 10⁻¹⁵ m

Mass Defect and Binding Energy:

Δm = [Zm_p + Nm_n] - M_nucleus
BE = Δm × c²    c = 3 × 10⁸ m/s
1 u = 931.5 MeV/c²

Higher BE/nucleon → more stable nucleus; Iron-56 most stable

Radioactive Decay:

N = N₀ e^(-λt)    t₁/₂ = 0.693/λ    T_avg = 1/λ

Alpha decay: A decreases by 4, Z decreases by 2
Beta decay: A unchanged; β⁻: Z increases by 1; β⁺: Z decreases by 1
Gamma decay: No change in A or Z; energy released as photon

Unit 9: Semiconductor Electronics

Energy Bands

Material	Band gap
Conductor	Overlapping conduction and valence bands
Semiconductor	Small gap (~1 eV)
Insulator	Large gap (>3 eV)

p-n Junction Diode

Forward bias: Depletion layer reduces; current flows (above ~0.7 V for Si)
Reverse bias: Depletion layer increases; very small reverse current

Half-wave rectifier: One diode; only positive half of AC utilised Full-wave rectifier: Two diodes (centre tap) or four diodes (bridge); both halves utilised

Zener Diode: Works in breakdown region; used as voltage regulator

Transistors

BJT types: n-p-n and p-n-p
Configurations: Common base, common emitter (most used), common collector
CE configuration:
Current gain: β = I_C/I_B
Voltage gain: A_V = β × R_C/R_i
Applications: Amplifier, switch, oscillator

Logic Gates

Gate	Symbol	Output
AND	A·B	1 only when both inputs 1
OR	A+B	1 when at least one input 1
NOT	Ā	Inverts input
NAND	NOT-AND	Universal gate
NOR	NOT-OR	Universal gate
XOR	A⊕B	1 when inputs differ

De Morgan's Theorems:

(A·B)' = A' + B'
(A+B)' = A'·B'

Key Constants — Class 12

Constant	Value
h (Planck)	6.626 × 10⁻³⁴ J·s
e (electron charge)	1.6 × 10⁻¹⁹ C
m_e (electron mass)	9.1 × 10⁻³¹ kg
μ₀	4π × 10⁻⁷ T·m/A
ε₀	8.85 × 10⁻¹² C²/N·m²
k = 1/4πε₀	9 × 10⁹ N·m²/C²
c (speed of light)	3 × 10⁸ m/s
1 eV	1.6 × 10⁻¹⁹ J
1 u (atomic mass unit)	1.66 × 10⁻²⁷ kg = 931.5 MeV/c²

Board Exam Tips

Electrostatics + Current Electricity = 22 marks — master these first
Always draw neat, labelled diagrams for optics and circuits
For numerical problems: write formula → substitute with units → calculate
Derivations commonly asked: Torque on dipole, Biot-Savart, Faraday's law, Einstein's photoelectric equation, Bohr's radius, half-life
Logic gate truth tables must be memorised
YDSE and diffraction problems appear every year