In short: Derivations carry 20–24 marks out of 70 in the CBSE Class 12 Physics theory paper. We analyzed board papers from 2019–2026 and identified the 20 derivations that appear most frequently. For each one, you get the chapter, marks allotted, frequency, and a step-by-step breakdown showing exactly where the examiner awards each mark. Master these 20 and you lock in nearly a third of the paper.
How Derivations Are Marked in CBSE Physics
CBSE provides an official marking scheme to examiners. Each derivation is broken into discrete steps, and marks are awarded step-by-step — not for the final result alone. This means:
- A 3-mark derivation typically has 3 distinct marking points
- A 5-mark derivation has 5 marking points (sometimes 4 steps + 1 diagram)
- A correct diagram with labelling often carries 1 mark by itself
- Writing the correct starting formula earns 0.5–1 mark even if you go wrong afterward
The CBSE marking scheme guide explains how examiners use this step system across all subjects. For physics specifically, derivations and numericals together dominate the paper — see the full chapter-wise weightage.
The 20 Must-Know Derivations
Overview Table
| # | Derivation | Chapter | Marks | Frequency |
|---|---|---|---|---|
| 1 | Electric field due to an electric dipole (axial + equatorial) | Electrostatics (Ch 1) | 5 | Every year |
| 2 | Gauss's law application — infinite plane sheet of charge | Electrostatics (Ch 1) | 3 | Every year |
| 3 | Gauss's law application — uniformly charged sphere | Electrostatics (Ch 1) | 3 | Most years |
| 4 | Capacitance of parallel plate capacitor (with and without dielectric) | Electrostatics (Ch 2) | 3 | Every year |
| 5 | Wheatstone bridge (balanced condition) | Current Electricity (Ch 3) | 3 | Every year |
| 6 | Meter bridge / Potentiometer principle | Current Electricity (Ch 3) | 3 | Every year |
| 7 | Force on a current-carrying conductor in magnetic field | Magnetism (Ch 4) | 3 | Most years |
| 8 | Magnetic field on the axis of a circular current loop | Magnetism (Ch 4) | 5 | Every year |
| 9 | Force between two parallel current-carrying conductors | Magnetism (Ch 4) | 3 | Most years |
| 10 | Motional EMF (EMF induced in a rod moving in magnetic field) | EMI (Ch 6) | 3 | Every year |
| 11 | Self-inductance of a solenoid | EMI (Ch 6) | 3 | Most years |
| 12 | Impedance and phase angle in LCR series circuit | AC (Ch 7) | 5 | Regular |
| 13 | Resonance condition in LCR circuit | AC (Ch 7) | 3 | Most years |
| 14 | Lens maker's formula | Ray Optics (Ch 9) | 5 | Every year |
| 15 | Refraction at a single spherical surface | Ray Optics (Ch 9) | 3 | Regular |
| 16 | Young's double slit experiment — fringe width derivation | Wave Optics (Ch 10) | 5 | Every year |
| 17 | Bohr model — radius of nth orbit | Atoms (Ch 12) | 3 | Every year |
| 18 | Bohr model — energy of nth orbit | Atoms (Ch 12) | 3 | Every year |
| 19 | Einstein's photoelectric equation | Dual Nature (Ch 11) | 3 | Every year |
| 20 | Relation between de Broglie wavelength and kinetic energy | Dual Nature (Ch 11) | 3 | Regular |
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Detailed Step-by-Step Marking Breakdown
1. Electric Field Due to an Electric Dipole (5 marks)
Chapter: Electrostatics (Ch 1) | Frequency: Every year
(a) On Axial Line:
| Step | What to Write | Marks |
|---|---|---|
| 1 | Diagram: dipole with charges +q and −q separated by 2a, point P at distance r on axis | 1 |
| 2 | E₊ = kq/(r−a)² toward right; E₋ = kq/(r+a)² toward left | 1 |
| 3 | E_axial = E₊ − E₋ = kq[(r+a)² − (r−a)²] / [(r−a)(r+a)]² | 0.5 |
| 4 | Simplify: E_axial = kq(4ar) / (r² − a²)² | 0.5 |
| 5 | For r >> a: E_axial = 2kp/r³ (where p = q × 2a) | 1 |
| 6 | Direction: along the dipole moment (from −q to +q) | — |
(b) On Equatorial Line (if asked as part of 5-mark):
| Step | What to Write | Marks |
|---|---|---|
| 1 | Components: E_net = 2E cosθ (vertical components cancel) | 0.5 |
| 2 | E_eq = 2 × [kq/(r² + a²)] × [a/√(r² + a²)] = kp/(r² + a²)^(3/2) | 0.5 |
| 3 | For r >> a: E_eq = kp/r³, direction opposite to dipole moment | — |
2. Gauss's Law — Infinite Plane Sheet of Charge (3 marks)
Chapter: Electrostatics (Ch 1) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | Diagram: infinite plane sheet with surface charge density σ, Gaussian surface as a cylinder with flat faces parallel to sheet | 1 |
| 2 | Apply Gauss's law: ∮E⃗·dA⃗ = q_enc/ε₀. Flux through curved surface = 0 (E ⊥ to dA). Flux through two flat faces = 2EA | 1 |
| 3 | q_enc = σA. So 2EA = σA/ε₀ → E = σ/2ε₀ (independent of distance) | 1 |
3. Gauss's Law — Uniformly Charged Sphere (3 marks)
Chapter: Electrostatics (Ch 1) | Frequency: Most years
| Step | What to Write | Marks |
|---|---|---|
| 1 | Diagram: sphere of radius R, total charge Q, Gaussian spherical surface at r > R | 0.5 |
| 2 | For r > R: ∮E⃗·dA⃗ = Q/ε₀ → E(4πr²) = Q/ε₀ → E = Q/(4πε₀r²) (behaves as point charge) | 1 |
| 3 | For r < R: q_enc = Q(r³/R³); E(4πr²) = Qr³/(ε₀R³) → E = Qr/(4πε₀R³) (linear with r) | 1 |
| 4 | At surface (r = R): E = Q/(4πε₀R²) | 0.5 |
4. Capacitance of Parallel Plate Capacitor (3 marks)
Chapter: Electrostatics (Ch 2) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | E between plates = σ/ε₀ = Q/(Aε₀) | 0.5 |
| 2 | V = Ed = Qd/(Aε₀) | 1 |
| 3 | C = Q/V = ε₀A/d | 0.5 |
| 4 | With dielectric (K): C' = Kε₀A/d = KC | 1 |
5. Wheatstone Bridge — Balanced Condition (3 marks)
Chapter: Current Electricity (Ch 3) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | Diagram: four resistances P, Q, R, S in diamond/bridge configuration with galvanometer G between B and D | 1 |
| 2 | At balance, I_G = 0. Apply Kirchhoff's loop rule to loops ABDA and BCDB. I₁P = I₂R and I₁Q = I₂S | 1 |
| 3 | Divide: P/Q = R/S — the balanced condition | 1 |
6. Potentiometer — Principle and EMF Comparison (3 marks)
Chapter: Current Electricity (Ch 3) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | Principle: potential drop across a uniform wire is proportional to length. V ∝ l, so V = φl (where φ = potential gradient) | 1 |
| 2 | For cell 1: E₁ = φl₁; For cell 2: E₂ = φl₂ (at null point, no current through galvanometer) | 1 |
| 3 | E₁/E₂ = l₁/l₂ | 1 |
7. Force on Current-Carrying Conductor in Magnetic Field (3 marks)
Chapter: Magnetism (Ch 4) | Frequency: Most years
| Step | What to Write | Marks |
|---|---|---|
| 1 | Force on single charge: F = qv⃗ × B⃗. In conductor, n charges per unit volume, area A, length l | 1 |
| 2 | Total charge = nAl × q. Drift velocity = v_d. F = nAlq × v_d × B sinθ | 1 |
| 3 | Since I = nAqv_d → F = BIl sinθ or F⃗ = Il⃗ × B⃗ | 1 |
8. Magnetic Field on Axis of Circular Current Loop (5 marks)
Chapter: Magnetism (Ch 4) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | Diagram: circular loop of radius R carrying current I, point P on axis at distance x | 1 |
| 2 | dB due to element dl: dB = μ₀Idl/(4π(R² + x²)) (by Biot-Savart law) | 1 |
| 3 | Component along axis: dB_x = dB × cosα = dB × R/√(R² + x²) | 1 |
| 4 | Integrate: B_x = ∮dB_x = μ₀IR²/[2(R² + x²)^(3/2)] | 1 |
| 5 | At centre (x = 0): B = μ₀I/2R | 1 |
9. Force Between Two Parallel Current-Carrying Conductors (3 marks)
Chapter: Magnetism (Ch 4) | Frequency: Most years
| Step | What to Write | Marks |
|---|---|---|
| 1 | Magnetic field due to conductor 1 at conductor 2: B₁ = μ₀I₁/(2πd) | 1 |
| 2 | Force on length l of conductor 2: F = B₁I₂l = μ₀I₁I₂l/(2πd) | 1 |
| 3 | Force per unit length: F/l = μ₀I₁I₂/(2πd). Same direction → attractive; opposite → repulsive. Definition of 1 Ampere. | 1 |
10. Motional EMF (3 marks)
Chapter: EMI (Ch 6) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | Conductor of length l moves with velocity v in field B (all mutually perpendicular). Force on charge q: F = qvB | 1 |
| 2 | Work done to move charge from one end to other: W = Fl = qvBl | 1 |
| 3 | EMF = W/q = ε = Bvl | 1 |
11. Self-Inductance of a Solenoid (3 marks)
Chapter: EMI (Ch 6) | Frequency: Most years
| Step | What to Write | Marks |
|---|---|---|
| 1 | Magnetic field inside solenoid: B = μ₀nI (n = N/l turns per unit length) | 1 |
| 2 | Total flux linkage: Φ = NBA = N(μ₀nI)A = μ₀n²lAI (since N = nl) | 1 |
| 3 | L = Φ/I = μ₀n²lA = μ₀N²A/l | 1 |
12. LCR Series Circuit — Impedance (5 marks)
Chapter: AC (Ch 7) | Frequency: Regular
| Step | What to Write | Marks |
|---|---|---|
| 1 | Phasor diagram: V_R along I, V_L leads I by 90°, V_C lags I by 90° | 1 |
| 2 | V² = V_R² + (V_L − V_C)² | 1 |
| 3 | V = I√[R² + (X_L − X_C)²] where X_L = ωL, X_C = 1/ωC | 1 |
| 4 | Z = √[R² + (ωL − 1/ωC)²] | 1 |
| 5 | Phase angle: tan φ = (X_L − X_C)/R | 1 |
13. Resonance in LCR Circuit (3 marks)
Chapter: AC (Ch 7) | Frequency: Most years
| Step | What to Write | Marks |
|---|---|---|
| 1 | At resonance: X_L = X_C → ωL = 1/ωC | 1 |
| 2 | ω² = 1/LC → ω₀ = 1/√(LC) → f₀ = 1/(2π√LC) | 1 |
| 3 | At resonance: Z = R (minimum impedance), I = V/R (maximum current) | 1 |
14. Lens Maker's Formula (5 marks)
Chapter: Ray Optics (Ch 9) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | Consider refraction at first surface (radius R₁): n₁/v' − n₁/u = (n₂ − n₁)/R₁ ... (Wait — using standard sign convention) For surface 1: μ₁/u + μ₂/v₁ formulation | 1 |
| 2 | Refraction at surface 1 (air to lens): n₂/v₁ − n₁/u = (n₂ − n₁)/R₁ | 1 |
| 3 | Refraction at surface 2 (lens to air): n₁/v − n₂/v₁ = (n₁ − n₂)/R₂ | 1 |
| 4 | Add both equations: n₁/v − n₁/u = (n₂ − n₁)[1/R₁ − 1/R₂] | 1 |
| 5 | Divide by n₁: 1/f = (n₂₁ − 1)[1/R₁ − 1/R₂] where n₂₁ = n₂/n₁ | 1 |
15. Refraction at Single Spherical Surface (3 marks)
Chapter: Ray Optics (Ch 9) | Frequency: Regular
| Step | What to Write | Marks |
|---|---|---|
| 1 | Diagram with object O in medium 1 (n₁), refraction at convex surface of radius R, image at I in medium 2 (n₂) | 1 |
| 2 | Using Snell's law for small angles: n₁ sinα ≈ n₁α, and geometric relations with angles | 1 |
| 3 | n₂/v − n₁/u = (n₂ − n₁)/R | 1 |
16. Young's Double Slit — Fringe Width (5 marks)
Chapter: Wave Optics (Ch 10) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | Diagram: two slits S₁ and S₂ separated by d, screen at distance D, point P at distance y from centre | 1 |
| 2 | Path difference: Δ = S₂P − S₁P = yd/D (for D >> d and D >> y) | 1 |
| 3 | For bright fringe: yd/D = nλ → y_n = nλD/d | 1 |
| 4 | Fringe width: β = y_(n+1) − y_n = λD/d | 1 |
| 5 | For dark fringe: yd/D = (2n+1)λ/2 → same fringe spacing β = λD/d | 1 |
17. Bohr Model — Radius of nth Orbit (3 marks)
Chapter: Atoms (Ch 12) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | Centripetal force = Coulomb force: mv²/r = kZe²/r² | 1 |
| 2 | Bohr's quantization: mvr = nh/2π → v = nh/(2πmr) | 1 |
| 3 | Substitute v in step 1: r_n = n²h²/(4π²mkZe²) = n²a₀/Z where a₀ = 0.529 Å | 1 |
18. Bohr Model — Energy of nth Orbit (3 marks)
Chapter: Atoms (Ch 12) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | KE = ½mv² = kZe²/(2r); PE = −kZe²/r | 1 |
| 2 | Total energy: E = KE + PE = −kZe²/(2r) | 1 |
| 3 | Substitute r_n: E_n = −13.6 Z²/n² eV (negative sign shows bound state) | 1 |
19. Einstein's Photoelectric Equation (3 marks)
Chapter: Dual Nature (Ch 11) | Frequency: Every year
| Step | What to Write | Marks |
|---|---|---|
| 1 | Photon energy: E = hν. Work function: φ₀ = hν₀ (minimum energy to eject electron) | 1 |
| 2 | Energy conservation: hν = φ₀ + KE_max | 1 |
| 3 | KE_max = hν − φ₀ = h(ν − ν₀); or ½mv²_max = hν − φ₀. Stopping potential: eV₀ = hν − φ₀ | 1 |
20. De Broglie Wavelength and Kinetic Energy (3 marks)
Chapter: Dual Nature (Ch 11) | Frequency: Regular
| Step | What to Write | Marks |
|---|---|---|
| 1 | De Broglie relation: λ = h/p = h/(mv) | 1 |
| 2 | Kinetic energy: KE = ½mv² → v = √(2KE/m) → p = mv = √(2mKE) | 1 |
| 3 | λ = h/√(2mKE). For electron accelerated through V volts: KE = eV → λ = h/√(2meV) = 12.27/√V Å | 1 |
Derivation Revision Strategy for the Last 30 Days
| Week | Focus | Derivations |
|---|---|---|
| Week 1 | Electrostatics + Current Electricity | #1–6 (6 derivations) |
| Week 2 | Magnetism + EMI + AC | #7–13 (7 derivations) |
| Week 3 | Optics (Ray + Wave) | #14–16 (3 derivations) |
| Week 4 | Modern Physics + Full revision | #17–20, then all 20 from memory |
For a comprehensive day-by-day plan, see the board exam time management strategy.
How to Write Derivations in the Exam
- Always start with a labelled diagram — it carries 1 mark for 5-mark derivations
- State the starting law or principle — "Applying Gauss's law..." or "By Biot-Savart law..."
- Show every algebraic step — skipping steps loses marks
- Box or underline the final formula — helps examiner locate your answer
- Write the conditions/assumptions — "for r >> a" or "at resonance"
Learn more about answer writing techniques in the answer sheet writing guide.
Frequently Asked Questions
How many marks do derivations carry in CBSE Class 12 Physics?
Derivations typically carry 20–24 marks out of 70 in the theory paper. The 2026 paper had about 22 marks of direct derivation questions. Additionally, numericals often require derivation formulas as starting points, so indirectly derivations influence another 10–15 marks.
Which derivation is asked every single year without fail?
Based on papers from 2019–2026, these appear every year: electric field due to dipole, Gauss's law for plane sheet, parallel plate capacitor, Wheatstone bridge, potentiometer, motional EMF, lens maker's formula, Young's double slit fringe width, Bohr model radius, and Einstein's photoelectric equation.
Should I memorize derivations or understand them?
Both. Understanding the physics lets you reconstruct a derivation even if you forget a step. But the exam is timed, so you need to write them fast — which requires practice. Write each derivation at least 5 times before the exam. Time yourself: a 3-mark derivation should take 4–5 minutes, a 5-mark one should take 7–8 minutes.
What if I forget a step in the middle of a derivation?
Write whatever you remember. The CBSE marking scheme awards marks for each correct step independently. If you skip step 2 but write steps 1, 3, 4, and 5 correctly, you lose only 1 mark instead of all 5. Never leave a derivation blank.
Do I need to draw diagrams for derivation questions?
Yes. For most 5-mark derivation questions, the diagram carries 1 mark. Even for 3-mark questions, a clear labelled diagram shows the examiner you understand the setup and may earn you benefit of doubt on borderline answers.
Are derivations from deleted syllabus topics still asked?
No. CBSE strictly follows the reduced syllabus. Check the CBSE deleted syllabus 2027 to confirm which derivations are out of scope. For 2027, topics like communication systems and some advanced electromagnetic wave derivations are not in the exam.
Related Guides
- CBSE Class 12 Physics Chapter Wise Marks Weightage 2027
- CBSE Class 12 Maths Chapter Wise Marks Weightage 2027
- How to Study Physics Numericals Without Fear
- Board Exam Answer Sheet — Write for Maximum Marks 2027
- CBSE Class 12 Physics Sample Paper 2027 Analysis
- Board Exam Time Management — 3 Hour Strategy 2027
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