How to use this list#
- Check the syllabus wording first. CBSE's 2026-27 Physics curriculum marks some topics as "qualitative treatment only" or "no derivation, formulae only". Those are listed separately below, so you do not waste time on them.
- Learn each derivation as a story: the set-up (diagram and assumptions), the physics law you start from, the key steps, and the final result in a box.
- Practise writing, not reading. Write each derivation from memory at least twice before the exam, then check it against your NCERT textbook.
- Use the official sample paper. The 2026-27 CBSE Physics sample paper and marking scheme show how derivation-type answers are marked step by step. See our CBSE sample paper guide.
CBSE Class 12 Physics 2026-27 at a glance#
The 2026-27 curriculum has nine units and 14 chapters. The theory paper is 70 marks and the practical component is 30 marks. The official 2026-27 sample paper has 33 questions in five sections (A to E), is 3 hours long, and does not allow calculators.
| Units | Theory marks |
|---|---|
| I Electrostatics and II Current Electricity | 16 |
| III Magnetic Effects of Current and Magnetism and IV EMI and Alternating Currents | 17 |
| V Electromagnetic Waves and VI Optics | 18 |
| VII Dual Nature of Radiation and Matter and VIII Atoms and Nuclei | 12 |
| IX Electronic Devices | 7 |
| Total | 70 |
Derivations by chapter#
Formulas are written as plain text. ε₀ is the permittivity of free space, μ₀ the permeability of free space, and k = 1/(4πε₀).
Chapter 1: Electric Charges and Fields
- Electric field on the axial line of a dipole: E = k · 2pr/(r² − a²)², which becomes E = k · 2p/r³ for r ≫ a, along the direction of p.
- Electric field on the equatorial line of a dipole: E = k · p/(r² + a²)^(3/2), which becomes E = k · p/r³ for r ≫ a, opposite to p.
- Torque on a dipole in a uniform field: τ = pE sin θ (vector form τ = p × E); net force is zero.
- Gauss's law, infinitely long straight wire: E = λ/(2πε₀r).
- Gauss's law, infinite plane sheet: E = σ/(2ε₀).
- Gauss's law, thin spherical shell: E = k · q/r² outside (r > R) and E = 0 inside (r < R).
Chapter 2: Electrostatic Potential and Capacitance
- Potential due to a point charge: V = k · q/r.
- Potential due to a dipole: V = k · p cos θ/r² (for r ≫ a); zero on the equatorial line.
- Potential due to a system of charges: V = k · Σ(qᵢ/rᵢ), by superposition.
- Relation between field and potential: E = −dV/dr.
- Potential energy of two point charges: U = k · q₁q₂/r₁₂.
- Potential energy of a dipole in a uniform field: U = −pE cos θ.
- Capacitance of a parallel-plate capacitor: C = ε₀A/d; with a dielectric of constant K filling the gap, C = Kε₀A/d.
- Capacitors in series and parallel: 1/C = 1/C₁ + 1/C₂ + … (series); C = C₁ + C₂ + … (parallel).
Chapter 3: Current Electricity
- Current and drift velocity: I = neAv_d.
- Drift velocity and resistivity: v_d = eEτ/m, which leads to ρ = m/(ne²τ) and Ohm's law from first principles.
- Mobility: μ = v_d/E = eτ/m.
- Terminal voltage and internal resistance: V = ε − Ir.
- Cells in series: ε_eq = ε₁ + ε₂ and r_eq = r₁ + r₂.
- Cells in parallel: ε_eq = (ε₁r₂ + ε₂r₁)/(r₁ + r₂) and r_eq = r₁r₂/(r₁ + r₂).
- Balance condition of a Wheatstone bridge using Kirchhoff's rules: P/Q = R/S.
Chapter 4: Moving Charges and Magnetism
- Biot–Savart law, field on the axis of a circular loop: B = μ₀IR²/[2(x² + R²)^(3/2)]; at the centre (x = 0), B = μ₀NI/(2R) for N turns.
- Ampere's circuital law, infinitely long straight wire: B = μ₀I/(2πr).
- Charged particle in a uniform magnetic field: F = q(v × B); circular path of radius r = mv/(qB) when v is perpendicular to B.
- Force on a current-carrying conductor: F = I(l × B), magnitude F = IlB sin θ.
- Force between two parallel currents: force per unit length f = μ₀I₁I₂/(2πd); this defines the ampere.
- Torque on a current loop in a uniform field: τ = NIAB sin θ = mB sin θ, with magnetic moment m = NIA.
- Moving coil galvanometer: current sensitivity = φ/I = NAB/k (k is the torsional constant).
- Conversion to an ammeter: shunt S = I_g G/(I − I_g), in parallel.
- Conversion to a voltmeter: series resistance R = V/I_g − G.
The straight solenoid is "qualitative treatment only" in the 2026-27 syllabus.
Chapter 5: Magnetism and Matter
The 2026-27 syllabus treats the bar magnet as an equivalent solenoid, the field of a magnetic dipole along and perpendicular to its axis, and the torque on a magnetic dipole as qualitative treatment only. Focus on explanations, field-line diagrams and the properties of para-, dia- and ferromagnetic materials rather than derivations.
Chapter 6: Electromagnetic Induction
- Faraday's law with Lenz's law: ε = −dΦ/dt (for N turns, ε = −N dΦ/dt).
- Motional emf in a rod moving in a uniform field: ε = Blv.
- Self-inductance of a long solenoid: L = μ₀n²Al (n turns per unit length, area A, length l).
- Mutual inductance of two long coaxial solenoids: M = μ₀n₁n₂πr₁²l.
Chapter 7: Alternating Current
- RMS value of alternating current: I_rms = I₀/√2 (and V_rms = V₀/√2).
- AC through a resistor, an inductor and a capacitor: current in phase with voltage (R); lags by π/2 with X_L = ωL (L); leads by π/2 with X_C = 1/(ωC) (C).
- Series LCR circuit using phasors: Z = √[R² + (X_L − X_C)²] and tan φ = (X_L − X_C)/R.
- Resonance: ω₀ = 1/√(LC), when X_L = X_C and Z = R.
- Average power: P = V_rms I_rms cos φ; power factor cos φ = R/Z; wattless current when φ = 90°.
- AC generator: ε = NBAω sin ωt.
- Ideal transformer: V_s/V_p = N_s/N_p = I_p/I_s.
Chapter 8: Electromagnetic Waves
Displacement current is a "basic idea", and the transverse nature of EM waves is "qualitative idea only" in the 2026-27 syllabus. Learn the characteristics of EM waves and the order and uses of the electromagnetic spectrum, from radio waves to gamma rays.
Chapter 9: Ray Optics and Optical Instruments
- Mirror formula: 1/v + 1/u = 1/f, with f = R/2.
- Refraction at a spherical surface: n₂/v − n₁/u = (n₂ − n₁)/R.
- Lens maker's formula: 1/f = (n₂₁ − 1)(1/R₁ − 1/R₂).
- Thin lens formula: 1/v − 1/u = 1/f, with magnification m = v/u.
- Thin lenses in contact: 1/f = 1/f₁ + 1/f₂, so P = P₁ + P₂.
- Refraction through a prism: A + δ = i + e, and at minimum deviation n = sin[(A + D_m)/2]/sin(A/2).
- Critical angle: sin i_c = 1/n (for light going from a medium of index n to air).
- Compound microscope: magnifying power m = (L/f_o)(D/f_e) with the final image at infinity.
- Astronomical telescope: magnifying power m = f_o/f_e in normal adjustment.
Chapter 10: Wave Optics
- Laws of reflection using Huygens' principle: angle of incidence = angle of reflection.
- Snell's law using Huygens' principle: sin i/sin r = v₁/v₂ = n₂/n₁.
The fringe width in Young's double slit experiment, β = λD/d, is "no derivation, final expression only" in the 2026-27 syllabus, and the width of the central maximum in single-slit diffraction is "qualitative treatment only".
Chapter 11: Dual Nature of Radiation and Matter
- Einstein's photoelectric equation: K_max = hν − φ₀, so eV₀ = hν − φ₀ and threshold frequency ν₀ = φ₀/h.
- de Broglie wavelength: λ = h/p = h/(mv).
- Electron accelerated through a potential V: λ = h/√(2meV), which gives λ ≈ 1.227/√V nm.
Chapter 12: Atoms
- Bohr model, radius of the nth orbit: rₙ = n²h²ε₀/(πme²).
- Velocity of the electron in the nth orbit: vₙ = e²/(2ε₀nh).
- Energy of the electron in the nth orbit: Eₙ = −me⁴/(8ε₀²n²h²) = −13.6/n² eV.
Hydrogen line spectra are "qualitative treatment only" in the 2026-27 syllabus.
Chapter 13: Nuclei
- Size of the nucleus: R = R₀A^(1/3), which shows that nuclear density does not depend on mass number A.
- Mass defect and binding energy: Δm = [Zm_p + (A − Z)m_n] − M, and E_b = Δm c²; binding energy per nucleon = E_b/A.
Chapter 14: Semiconductor Electronics
There is no algebraic derivation here. Be ready to explain the formation of the depletion layer, the I–V characteristics of a p-n junction diode in forward and reverse bias, and the diode as a rectifier with circuit diagrams and input and output waveforms. Energy bands are "qualitative ideas only".
Formula only or qualitative in 2026-27#
| Topic | What the 2026-27 syllabus says |
|---|---|
| Energy stored in a capacitor | No derivation, formulae only (U = Q²/2C = ½CV²) |
| Straight solenoid | Qualitative treatment only |
| Bar magnet as solenoid, dipole field, torque on a magnetic dipole | Qualitative treatment only |
| Transverse nature of EM waves | Qualitative idea only |
| Fringe width in YDSE | No derivation, final expression only |
| Width of central maximum (single slit) | Qualitative treatment only |
| Hydrogen line spectra | Qualitative treatment only |
| Energy bands | Qualitative ideas only |
Topics such as the potentiometer, cyclotron and the radioactive decay law do not appear in the 2026-27 theory syllabus, so derivations based on them are not needed for the board exam. (The metre bridge appears only in the practical list.)
Core derivations to revise first#
CBSE does not publish how often each derivation is asked. Rather than guess, revise first the derivations that sit at the centre of each unit and are named directly in the syllabus.
| Unit | Revise first |
|---|---|
| Electrostatics | Dipole field (axial and equatorial), Gauss's law for wire, sheet and shell, parallel-plate capacitor with dielectric |
| Current Electricity | I = neAv_d and ρ = m/ne²τ, Wheatstone bridge balance |
| Magnetism | Field on the axis of a circular loop, torque on a current loop, galvanometer to ammeter and voltmeter |
| EMI and AC | Self-inductance of a solenoid, LCR impedance and resonance, AC generator emf |
| Optics | Lens maker's formula, prism formula, microscope and telescope magnifying power, Snell's law from Huygens' principle |
| Modern Physics | Bohr radius, velocity and energy; photoelectric equation; de Broglie wavelength for an accelerated electron |
The official 2026-27 sample paper itself includes derivation-type parts. Look at it and its marking scheme to see the level of detail expected.
Tips for writing derivations in the exam#
- Start with a labelled diagram. Mark distances, angles, directions and the charge or current. A diagram often carries marks of its own.
- State the law you begin from. For example, "Using Gauss's law, ∮E · dA = q/ε₀".
- Write assumptions. "For a short dipole, r ≫ a", or "for a thin lens".
- Keep steps short and in order. Each new line should follow from the one before it.
- Box the final result and write the direction for vector quantities.
- Check units and limits. Does B at the centre of the loop match x = 0 in the axial formula? Does the dipole field fall as 1/r³?
- Use the time for the marks. A 5-mark question with a derivation expects more steps than a 2-mark one; follow the marking scheme pattern.
Related reading#
Class 12 is easier when Class 10 basics are strong. Our notes of Electricity Class 10 CBSE revise Ohm's law and circuits, and our CBSE Class 10 preparation plan shows how to structure the last 60 days before a board exam; the same approach works for Class 12. If you are also preparing for engineering entrance exams, see how to prepare for JEE Main 2027. For doubts on any derivation, join a live class with a teacher.