Class 12 Physics — Complete Notes and CBSE PYQs

Unit 1: Electrostatics

Coulomb's Law

Force between two point charges: F = kq₁q₂/r² where k = 9×10⁹ Nm²/C²

Electric Field: E = F/q = kQ/r² (field due to point charge)

• Direction: away from positive charge, towards negative
• Unit: N/C or V/m

Electric Field Lines Rules:

• Start from positive, end at negative charge
• Never cross each other
• Denser lines = stronger field
• Perpendicular to conductor surface

Gauss's Law: ΦE = q_enclosed/ε₀

• Sphere: E = q/(4πε₀r²) = kq/r²
• Infinite line charge: E = λ/(2πε₀r)
• Infinite plane: E = σ/(2ε₀)

Electric Potential and Capacitance

Potential: V = W/q = kQ/r (unit: Volt) Relation: E = -dV/dr (E is negative gradient of V)

Capacitance: C = Q/V (unit: Farad) Parallel plate capacitor: C = ε₀A/d With dielectric: C = Kε₀A/d (K = dielectric constant)

Series: 1/C = 1/C₁ + 1/C₂ Parallel: C = C₁ + C₂

Energy stored: U = ½CV² = Q²/2C = ½QV

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Unit 2: Current Electricity

Ohm's Law: V = IR, J = σE (microscopic form) Resistivity: ρ = RA/L; varies with temperature: ρₜ = ρ₀(1 + αt)

Kirchhoff's Laws:

• KCL (Junction Rule): Sum of currents at junction = 0 (charge conservation)
• KVL (Loop Rule): Sum of EMFs = Sum of potential drops (energy conservation)

Wheatstone Bridge: P/Q = R/S (balanced condition) Meter Bridge: R/S = l/(100-l)

EMF and Internal Resistance: Terminal voltage V = E - Ir (discharging), V = E + Ir (charging)

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Unit 3 & 4: Magnetism and Electromagnetic Induction

Biot-Savart Law: dB = μ₀/4π × Idl sinθ/r² Magnetic field due to long wire: B = μ₀I/2πr Solenoid: B = μ₀nI (n = turns per unit length)

Force on current-carrying conductor: F = BIL sinθ Torque on current loop: τ = NIAB sinθ = MB sinθ

Faraday's Laws:

1. EMF induced whenever magnetic flux changes
2. Magnitude of EMF: ε = -dΦ/dt (Lenz's law: negative sign)

Self-Inductance: ε = -L(dI/dt), Energy = ½LI² Mutual Inductance: ε₂ = -M(dI₁/dt)

Transformer: V₁/V₂ = N₁/N₂ = I₂/I₁

• Step-up: N₂ > N₁, V₂ > V₁
• Step-down: N₂ < N₁, V₂ < V₁

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Unit 6: Optics

Snell's Law: n₁sinθ₁ = n₂sinθ₂ Total Internal Reflection: when θ > critical angle (sinθc = n₂/n₁) Applications: optical fibre, diamond, mirage

Lenses:

• Lens maker's equation: 1/f = (μ-1)[1/R₁ - 1/R₂]
• Power: P = 1/f (diopters)
• Two lenses in contact: P = P₁ + P₂

Waveoptics:

• Young's Double Slit: fringe width β = λD/d
• Constructive: path diff = nλ
• Destructive: path diff = (2n-1)λ/2

Diffraction: single slit, first minima at sinθ = λ/a

Polarization: only transverse waves can be polarized Malus's law: I = I₀cos²θ

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Unit 9: Atoms, Nuclei, and Semiconductors

Bohr's Model:

• Electron in nth orbit: rₙ = n²a₀ (a₀ = 0.529 Å)
• Energy: Eₙ = -13.6/n² eV
• Frequency: ν = (E₂-E₁)/h

Radioactivity:

• Alpha (α): He nucleus, stopped by paper
• Beta (β): electron, stopped by aluminum
• Gamma (γ): EM radiation, stopped by lead

Half-life: t₁/₂ = 0.693/λ Decay law: N = N₀e^(-λt)

Semiconductors:

| Feature | Intrinsic | n-type | p-type | |---|---|---|---| | Dopant | None | Pentavalent (P, As) | Trivalent (Al, B) | | Majority carriers | holes = electrons | Electrons | Holes | | Minority carriers | — | Holes | Electrons |

p-n Junction:

• Forward bias: decreases barrier, current flows
• Reverse bias: increases barrier, very small current
• Breakdown voltage: Zener diode application

Rectifier: Half-wave (one diode) or Full-wave (4 diodes/bridge) Transistor: NPN or PNP; current amplifier

• Common emitter: voltage gain = β × Rc/Ri

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Solved CBSE PYQs

Q1 (2023): Two charges 4μC and -4μC are 20cm apart. Find electric field at midpoint. Both fields point in same direction at midpoint (both towards -charge). E_each = kQ/r² = 9×10⁹ × 4×10⁻⁶ / (0.1)² = 3.6×10⁶ N/C E_total = 7.2×10⁶ N/C

Q2 (2023): An ac source 200V, 50Hz is connected to 20Ω resistor. Find rms current. I_rms = V_rms/R = 200/20 = 10 A

Q3 (2022): In Young's experiment, fringe width is 0.5mm. If distance is doubled, new fringe width? β = λD/d → β is proportional to D → new β = 1.0 mm

Q4 (2024): Find the de Broglie wavelength of electron with KE = 100eV. λ = h/√(2mE) = 6.63×10⁻³⁴/√(2 × 9.1×10⁻³¹ × 100×1.6×10⁻¹⁹) ≈ 1.23 Å

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Quick Revision Checklist

• Coulomb's law and Gauss's law applications
• Capacitance: series/parallel, energy stored
• Kirchhoff's laws: KCL and KVL
• Faraday's and Lenz's law
• Transformer equation: V₁/V₂ = N₁/N₂
• Lens formula, lensmaker's equation
• Bohr's model: rₙ = n²a₀, Eₙ = -13.6/n² eV
• Radioactive decay: N = N₀e^(-λt)
• n-type vs p-type semiconductor
• p-n junction: forward/reverse bias