CBSE Class 12 Physics: Important Formulas for All Chapters (2025–2026 Board Exam Guide)

Excelling in CBSE Class 12 Physics for the 2025–2026 board exams requires a structured command over derivations, definitions, and numerical problem-solving. Physics theory and numerical problems in the Class 12 CBSE curriculum are deeply interconnected through fundamental mathematical relationships. Having a comprehensive, chapter-wise formula sheet allows you to quickly recall equations, identify variables, apply correct SI units, and avoid sign-convention errors during high-stakes exams.

This master formula repository covers every unit in the NCERT syllabus—from Electrostatics to Semiconductor Electronics—alongside real-world physical applications, key CBSE board exam questions with detailed model solutions, and strategic revision techniques.

Key Concepts & Chapter-Wise Formula Breakdown

Unit 1: Electrostatics (Chapters 1 & 2)

Electrostatics governs the behavior of stationary electric charges, electrostatic forces, fields, potentials, and charge storage systems like capacitors.

Coulomb's Law: F = (1 / 4πε₀) × (|q₁q₂| / r²), where 1 / 4πε₀ = 9 × 10⁹ N·m²/C² in free space.
Electric Field Intensity: Point charge field is E = (1 / 4πε₀) × (q / r²). Axial field of a dipole is E_axial = (1 / 4πε₀) × (2p / r³) (for r >> a), and equatorial field is E_equatorial = (1 / 4πε₀) × (p / r³).
Torque and Potential Energy of a Dipole: Torque τ→ = p→ × E→ = pE sin θ; Potential energy U = - p→ · E→ = -pE cos θ.
Gauss's Law & Applications: Total electric flux through a closed surface is Φ = ∮ E→ · dA→ = q_enclosed / ε₀.
- Infinitely long straight charged wire: E = λ / (2πε₀r) (where λ is linear charge density).
- Infinite thin planar sheet: E = σ / (2ε₀) (where σ is surface charge density).
- Thin spherical conducting shell: E = (1 / 4πε₀) × (Q / r²) for r ≥ R, and E = 0 inside (r < R).
Electrostatic Potential & Capacitance: Potential V = (1 / 4πε₀) × (q / r). Relationship with field: E = - dV/dr.
Capacitors: Capacitance C = Q / V. Parallel plate capacitor: C = ε₀A / d (with dielectric slab of constant K, C = Kε₀A / d).
Energy Stored in a Capacitor: U = (1/2)CV² = Q² / (2C) = (1/2)QV. Energy density in electric field: u_E = (1/2)ε₀E².

Real-World Application: Capacitors provide instantaneous power delivery in electronic camera flashes and defibrillators where high electrical energy must be discharged in milliseconds.

Unit 2: Current Electricity (Chapter 3)

Current electricity deals with the continuous flow of charges through conducting materials, terminal voltages, and resistive networks.

Electric Current & Drift Velocity: I = n·A·e·v_d, where drift velocity v_d = (eE / m)τ.
Ohm's Law & Resistivity: V = IR; R = ρL / A, with resistivity ρ = m / (n·e²τ). Electrical conductivity σ = 1 / ρ = n·e²τ / m.
Temperature Dependence: R_T = R₀[1 + α(T - T₀)] (where α is the temperature coefficient of resistance).
Cell EMF, Terminal Voltage & Internal Resistance: During discharging: V = E - Ir; internal resistance r = R[(E / V) - 1].
Kirchhoff's Rules:
1. Junction Rule (KCL): Σ I_in = Σ I_out (Conservation of Charge).
2. Loop Rule (KVL): Σ ΔV = 0 around any closed loop (Conservation of Energy).
Balanced Wheatstone Bridge: P / Q = R / S when galvanometer current I_g = 0.

Unit 3: Magnetic Effects of Current and Magnetism (Chapters 4 & 5)

Moving charges generate magnetic fields, which in turn exert forces on other moving charges and current-carrying conductors.

Biot-Savart Law: dB→ = (μ₀ / 4π) × (I dl→ × r̂) / r².
Magnetic Field Calculations:
- Center of circular loop of N turns: B = (μ₀ N I) / (2R).
- Axis of circular loop: B = (μ₀ N I R²) / [2(R² + x²)^(3/2)].
- Long straight conductor: B = (μ₀ I) / (2πr).
- Inside ideal solenoid: B = μ₀ n I (where n = N / L).
Lorentz Force & Current Elements: F→ = q(E→ + v→ × B→). Magnetic force on wire: F→ = I(L→ × B→) = I L B sin θ.
Force Between Parallel Currents: F / L = (μ₀ I₁ I₂) / (2πd) (Attractive for like current directions; repulsive for opposite).
Galvanometer Conversion:
- To Ammeter: Shunt resistor in parallel, S = (I_g × G) / (I - I_g).
- To Voltmeter: Series multiplier resistor, R = (V / I_g) - G.

Unit 4: Electromagnetic Induction & Alternating Current (Chapters 6 & 7)

Time-varying magnetic fields generate electromotive forces, establishing the operational basis for electrical generators and transformers.

Faraday's Law & Lenz's Law: Induced EMF ε = -N(dΦ_B / dt), where magnetic flux Φ_B = B→ · A→ = BA cos θ.
Motional EMF: ε = B·l·v for a conductor of length l moving perpendicularly through uniform field B at velocity v.
Self & Mutual Inductance: ε = -L(dI / dt); solenoid self-inductance L = μ₀ n² A l. Energy stored in inductor: U = (1/2)L I².
AC Root-Mean-Square Values: V_rms = V₀ / √2 ≈ 0.707 V₀, I_rms = I₀ / √2 ≈ 0.707 I₀.
Reactance & Impedance in Series LCR Circuit:
- Inductive Reactance: X_L = ωL = 2πfL.
- Capacitive Reactance: X_C = 1 / (ωC) = 1 / (2πfC).
- Total Impedance: Z = √[R² + (X_L - X_C)²].
- Resonant Frequency: f_r = 1 / [2π√(LC)].
- Quality Factor (Q-factor): Q = (ω_r L) / R = (1 / R)√(L / C).
- Average Power: P_avg = V_rms × I_rms × cos φ (Power factor cos φ = R / Z).
Transformer Ratio: V_s / V_p = N_s / N_p = I_p / I_s = k (for an ideal lossless transformer).

Unit 5: Electromagnetic Waves (Chapter 8)

Displacement Current: I_d = ε₀(dΦ_E / dt).
Speed of EM Waves in Vacuum: c = 1 / √(μ₀ε₀) = E₀ / B₀ ≈ 3 × 10⁸ m/s.
Total Average Energy Density: u_avg = (1/2)ε₀E_rms² + (1/2)(B_rms² / μ₀) = ε₀E_rms².

Unit 6: Optics (Chapters 9 & 10)

Optics encompasses geometric ray propagation (reflection, refraction, lenses, optical instruments) and wave phenomenon (interference, diffraction).

Mirror & Lens Equations:
- Spherical Mirrors: (1 / f) = (1 / v) + (1 / u); Magnification m = -v / u = (f - v) / f.
- Spherical Refracting Surface: (n₂ / v) - (n₁ / u) = (n₂ - n₁) / R.
- Lens Maker's Formula: 1 / f = (n₂₁ - 1)[(1 / R₁) - (1 / R₂)].
- Thin Lens Formula: (1 / f) = (1 / v) - (1 / u); Magnification m = v / u; Power P = 1 / f(in meters).
Total Internal Reflection & Prism: Critical angle sin i_c = 1 / μ. Prism refractive index μ = sin[(A + D_m) / 2] / sin(A / 2).
Optical Instruments:
- Compound Microscope: m = -(L / f_o)[1 + (D / f_e)] (at near point D = 25 cm); m = -(L / f_o)(D / f_e) (at infinity).
- Astronomical Telescope: Magnification at normal adjustment m = -f_o / f_e, with tube length L = f_o + f_e.
Wave Optics (Interference & Diffraction):
- Young's Double Slit Fringe Width: β = λD / d.
- Position of n-th bright fringe: y_n = nλD / d; n-th dark fringe: y_n = (2n - 1)λD / (2d).
- Single Slit Diffraction Minima: a sin θ = nλ; Angular width of central maxima: 2θ = 2λ / a.

Unit 7 & 8: Modern Physics (Chapters 11, 12 & 13)

Photoelectric Effect: Photon energy E = hν = hc / λ. Einstein's equation: K_max = hν - Φ₀ = e V₀.
de Broglie Wavelength: λ = h / p = h / (mv) = h / √(2mE). For an electron accelerated through potential V: λ = 1.227 / √V nm.
Bohr Model of Hydrogen Atom:
- Quantization condition: m v r = n h / (2π).
- Radius of n-th orbit: r_n = 0.529 × (n² / Z) Å.
- Total Energy: E_n = -13.6 × (Z² / n²) eV.
- Rydberg Formula: 1 / λ = R_H Z² [(1 / n₁²) - (1 / n₂²)].
Nuclear Physics: Nuclear radius R = R₀ A^(1/3) (where R₀ ≈ 1.2 × 10⁻¹⁵ m). Mass defect binding energy: E_b = Δm × 931.5 MeV.

Unit 9: Electronic Devices (Chapter 14)

Semiconductor Carrier Concentration: Mass-action law n_e × n_h = n_i².
Electrical Conductivity: σ = e(n_e μ_e + n_h μ_h).
Dynamic Diode Resistance: r_d = ΔV / ΔI.

Important CBSE Questions with Answers

Below are high-frequency questions extracted directly from official CBSE Class 12 Physics question banks, complete with exact marking-scheme answers.

1. Define electric flux. Write its SI unit.

Answer: Electric flux (Φ) is defined as the total number of electric field lines crossing a given surface area normally. Mathematically, it is the surface integral of the electric field over a closed or open surface:

Φ = ∮ E→ · dA→ = E A cos θ

where θ is the angle between the electric field vector E→ and the area vector A→.
SI Unit: Newton-meter squared per Coulomb (N·m²/C) or Volt-meter (V·m).

2. State Coulomb's Law. Write its vector form.

Answer: Coulomb's Law states that the electrostatic force of attraction or repulsion between two stationary point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them, acting along the line joining the two charges:

F = (1 / 4πε₀) × (|q₁q₂| / r²)

Vector Form: The force exerted on charge q₁ by charge q₂ is given by:

F→₁₂ = (1 / 4πε₀) × [(q₁ q₂) / r²] r̂₂₁ = -(F→₂₁)

where r̂₂₁ is the unit vector pointing from q₂ to q₁.

3. What is an equipotential surface? List its properties.

Answer: An equipotential surface is any surface that has the same electric potential at every point on it (V = \text{constant}).

Key Properties:

Zero Work Done: No work is done in moving a test charge between any two points on an equipotential surface (W = q₀ ΔV = 0).
Perpendicular Electric Field: The electric field lines are always mutually perpendicular to the equipotential surface at every point (E→ ⊥ \text{surface}).
Non-Intersecting: Two equipotential surfaces can never intersect each other; otherwise, there would be two different potentials at the point of intersection.
Field Strength Indicator: Equipotential surfaces are spaced closer together in regions of strong electric fields and farther apart in weaker fields (since E = - dV/dr).

4. Define drift velocity. How is it related to electric current?

Answer: Drift velocity (v_d) is defined as the average velocity with which free electrons in a conductor get drifted toward the positive terminal under the influence of an externally applied electric field.

Relation with Electric Current:

I = n × A × e × v_d

where n is the free electron number density (electrons/m³), A is the cross-sectional area of the conductor, e is the elementary electron charge (1.6 × 10⁻¹⁹ C), and v_d is the drift velocity.

5. State Kirchhoff's laws for electrical circuits.

Answer:

Kirchhoff's First Law (Junction Rule / KCL): The algebraic sum of all electric currents entering and leaving any junction in an electrical circuit is equal to zero (Σ I = 0). It is based on the Law of Conservation of Electric Charge.
Kirchhoff's Second Law (Loop Rule / KVL): In any closed loop of an electrical network, the algebraic sum of changes in potential (including EMFs and potential drops across resistors) around the loop is zero (Σ ΔV = 0 or Σ E = Σ IR). It is based on the Law of Conservation of Energy.

6. What is total internal reflection? State the conditions for it to occur.

Answer: Total Internal Reflection (TIR) is the optical phenomenon in which a ray of light traveling from an optically denser medium toward an optically rarer medium is completely reflected back into the denser medium at the interface without any refraction.

Necessary Conditions for TIR:

The light ray must travel from an optically denser medium to an optically rarer medium.
The angle of incidence in the denser medium must be strictly greater than the critical angle (i > i_c) for the given pair of media, where sin i_c = 1 / μ.

7. What is the electric field at the surface of a charged spherical conductor of radius R and charge Q?

Answer: The electric field at the surface of a charged spherical conductor carrying charge Q and radius R is given by:

E = (1 / 4πε₀) × (Q / R²) = σ / ε₀

For any point outside or on the surface of a conducting sphere (r ≥ R), the entire charge Q behaves electrostatically as though it were concentrated at the geometric center of the sphere. Inside the conductor (r < R), the electric field is strictly zero (E = 0).

8. Two point charges +2 μC and -2 μC are placed 5 cm apart. What is the electric dipole moment?

Answer:

Given data:

Magnitude of charge: q = 2 μC = 2 × 10⁻⁶ C
Separation distance: 2a = 5 cm = 0.05 m = 5 × 10⁻² m

The electric dipole moment p→ is calculated as:

p = q × (2a) = (2 × 10⁻⁶ C) × (0.05 m) = 1.0 × 10⁻⁷ C·m

Direction: Along the dipole axis directed from the negative charge (-2 μC) to the positive charge (+2 μC).

How to Prepare for CBSE Class 12 Physics Formulas & Numericals

Mastering Class 12 Physics formulas requires more than rote memorization; it demands structured application techniques:

Maintain a Derivation-Linked Formula Notebook: Whenever you write an equation, trace its origin (e.g., how the Biot-Savart law yields the circular loop formula). Understanding variable dependencies prevents common algebraic mistakes.
Standardize SI Units and Dimensional Analysis: Always check your final formula dimensions during substitutions. Quantities like electric flux (V·m), magnetic flux (Weber), and capacitance (Farad) frequently trigger unit conversion errors in multi-step questions.
Master Vector Formulations and Sign Conventions: Electrostatics, magnetism, and ray optics heavily rely on Cartesian sign rules. Ensure you assign correct signs for focal lengths (negative for concave, positive for convex) and directional unit vectors.
Practice Timed Chapter-Wise Numericals: Solve at least 10–15 diverse numerical problems per chapter under timed conditions to reinforce equation recall.

Where to Practice More

Consistent, exam-pattern practice is the key to scoring 70/70 in your CBSE Class 12 Physics theory paper. You can explore curated question sets, chapter-wise previous years' questions (PYQs), and full-length simulated board papers on Theorify QPTool. Access tailored assessments on the QPTool Class 12 Physics Practice Hub and test your speed with real exam-style mock tests on Theorify Question Paper Generator today.

CBSE Class 12 Important Formulas for Physics (All Chapters)