CBSE · Class 12
Physics Formulas for Class 12
All important formulas chapter-wise for CBSE Class 12 Physics 2026-27 — from Electrostatics and Magnetism to Optics, Semiconductors and Modern Physics.
For reference only. Always verify formulas and information against your official NCERT textbooks or board-prescribed materials before use in exams. Learnizo does not guarantee absolute accuracy.
Ch 1.Electric Charges and Fields
| Formula / Relation | Expression |
|---|---|
| Coulomb's Law | F = kq₁q₂/r² = q₁q₂ / (4πε₀r²) |
| Electric Field (point charge) | E = kq/r² = q / (4πε₀r²) |
| Electric Flux | Φ = E · A · cos θ = E⃗ · A⃗ |
| Gauss's Law | Φ_net = q_enc / ε₀ |
| Field (infinite line charge) | E = λ / (2πε₀r) |
| Field (infinite plane) | E = σ / (2ε₀) |
| Torque on dipole | τ = pE sin θ = p⃗ × E⃗ |
Ch 2.Electrostatic Potential and Capacitance
| Formula / Relation | Expression |
|---|---|
| Electric Potential (point charge) | V = kq/r |
| Potential Energy (two charges) | U = kq₁q₂/r |
| Work done by electric force | W = q(V_A − V_B) |
| Capacitance | C = Q/V |
| Parallel plate capacitor | C = ε₀A/d |
| Capacitors in series | 1/C_eq = 1/C₁ + 1/C₂ + … |
| Capacitors in parallel | C_eq = C₁ + C₂ + … |
| Energy stored in capacitor | U = ½CV² = ½Q²/C = QV/2 |
| Energy density | u = ½ε₀E² |
Ch 3.Current Electricity
| Formula / Relation | Expression |
|---|---|
| Ohm's Law | V = IR |
| Resistivity-temperature | ρ_T = ρ₀(1 + αΔT) |
| Drift Velocity | v_d = eEτ/m = I/(nAe) |
| Current Density | J = I/A = nev_d = σE |
| Kirchhoff's Voltage Law | ΣV = 0 (around a closed loop) |
| Kirchhoff's Current Law | ΣI_in = ΣI_out (at a node) |
| Wheatstone Bridge (balance) | P/Q = R/S |
| Power | P = IV = I²R = V²/R |
| EMF and Internal Resistance | V = ε − Ir; I = ε/(R + r) |
| Cells in series | ε_eq = ε₁ + ε₂; r_eq = r₁ + r₂ |
| Cells in parallel (equal ε) | ε_eq = ε; r_eq = r/n |
Ch 4.Moving Charges and Magnetism
| Formula / Relation | Expression |
|---|---|
| Lorentz Force | F⃗ = q(E⃗ + v⃗ × B⃗) |
| Force on current-carrying wire | F = BIl sin θ |
| Biot-Savart Law | dB = (μ₀/4π)(I dl sin θ / r²) |
| B at centre of circular loop | B = μ₀I / (2R) |
| Ampere's Law | ∮ B⃗·dl⃗ = μ₀I_enc |
| B inside solenoid | B = μ₀nI |
| B inside toroid | B = μ₀NI / (2πr) |
| Radius of circular motion | r = mv / (qB) |
| Cyclotron Frequency | f = qB / (2πm) |
| Torque on current loop | τ = nIAB sin θ = MB sin θ |
Ch 5.Magnetism and Matter
| Formula / Relation | Expression |
|---|---|
| Magnetic Moment | M = IA (current loop) |
| Bar magnet: field on axial | B = μ₀(2M) / (4πd³) |
| Bar magnet: field on equatorial | B = μ₀M / (4πd³) |
| Magnetic Susceptibility | χ = M_material / H |
| Relative Permeability | μ_r = 1 + χ |
| Curie's Law | χ = C/T |
Ch 6.Electromagnetic Induction
| Formula / Relation | Expression |
|---|---|
| Faraday's Law | ε = −dΦ/dt = −N dΦ/dt (for N turns) |
| Lenz's Law | Induced current opposes the change in flux |
| Motional EMF | ε = Blv |
| Self-Inductance | ε = −L(dI/dt); L = NΦ/I |
| Mutual Inductance | ε₂ = −M(dI₁/dt) |
| Energy in inductor | U = ½LI² |
| Energy density (B field) | u = B²/(2μ₀) |
Ch 7.Alternating Current
| Formula / Relation | Expression |
|---|---|
| RMS values | V_rms = V₀/√2; I_rms = I₀/√2 |
| Inductive Reactance | X_L = ωL = 2πfL |
| Capacitive Reactance | X_C = 1/(ωC) = 1/(2πfC) |
| Impedance (series RLC) | Z = √(R² + (X_L − X_C)²) |
| Resonance Frequency | f₀ = 1/(2π√(LC)) |
| Power Factor | cos φ = R/Z |
| Average Power | P_avg = V_rms · I_rms · cos φ |
| Transformer ratio | V_s/V_p = N_s/N_p = I_p/I_s |
| Quality Factor (Q) | Q = ω₀L/R = 1/(ω₀CR) |
Ch 8.Ray Optics and Optical Instruments
| Formula / Relation | Expression |
|---|---|
| Mirror Formula | 1/f = 1/v + 1/u |
| Magnification (mirror) | m = −v/u = h_i/h_o |
| Snell's Law | n₁ sin θ₁ = n₂ sin θ₂ |
| Critical Angle | sin C = n₂/n₁ (n₁ > n₂) |
| Lens Formula | 1/f = 1/v − 1/u |
| Lensmaker's Equation | 1/f = (n−1)[1/R₁ − 1/R₂] |
| Magnification (lens) | m = v/u |
| Power of lens | P = 1/f (in metres) |
| Lenses in contact | P_total = P₁ + P₂; 1/f_total = 1/f₁ + 1/f₂ |
| Prism: Deviation | δ = (μ − 1)A (for small angle A) |
| Minimum Deviation | μ = sin[(A + D_m)/2] / sin(A/2) |
| Angular Magnification (microscope) | M = L/f_o × D/f_e |
Ch 9.Wave Optics
| Formula / Relation | Expression |
|---|---|
| Constructive Interference (YDSE) | Δ = nλ; y_n = nλD/d |
| Destructive Interference (YDSE) | Δ = (2n−1)λ/2; y_n = (2n−1)λD/(2d) |
| Fringe Width (YDSE) | β = λD/d |
| Single-slit Diffraction (minima) | a sin θ = nλ |
| Brewster's Angle | tan θ_B = n |
| Malus's Law | I = I₀ cos² θ |
Ch 10.Dual Nature of Radiation and Matter
| Formula / Relation | Expression |
|---|---|
| Photon Energy | E = hν = hc/λ |
| Photoelectric Equation | KE_max = hν − φ = eV₀ |
| Threshold Frequency | ν₀ = φ/h |
| de Broglie Wavelength | λ = h/p = h/mv = h/√(2mKE) |
| de Broglie λ for accelerated e⁻ | λ = h/√(2meV) |
Ch 11.Atoms
| Formula / Relation | Expression |
|---|---|
| Bohr: Radius | rₙ = n² × 0.529 Å (for H) |
| Bohr: Energy | Eₙ = −13.6/n² eV (for H) |
| Frequency emitted (Bohr) | ν = (E₂ − E₁)/h = RcZ²(1/n₁² − 1/n₂²) |
| Rydberg Equation | 1/λ = R(1/n₁² − 1/n₂²) |
Ch 12.Nuclei
| Formula / Relation | Expression |
|---|---|
| Nuclear Radius | R = R₀A^(1/3) |
| Mass Defect | Δm = [Zm_p + (A−Z)m_n] − m_nucleus |
| Binding Energy | BE = Δm × c² = Δm × 931.5 MeV/u |
| Radioactive Decay Law | N = N₀e^(−λt) |
| Half-Life | t₁/₂ = 0.693/λ |
| Activity | A = λN = A₀e^(−λt) |
Ch 13.Semiconductor Electronics
| Formula / Relation | Expression |
|---|---|
| Intrinsic carrier concentration | n_i = √(n_e × n_h) |
| Diode: forward bias condition | V_forward > V_threshold (≈ 0.7 V for Si) |
| Transistor: current gain (β) | β = I_C / I_B = α/(1−α) |
| Logic Gates | AND: Y = A·B; OR: Y = A+B; NOT: Y = Ā |
Frequently Asked Questions
Which chapters are most formula-heavy in CBSE Class 12 Physics?
Current Electricity, Alternating Current, Electromagnetic Induction, Ray Optics and Electrostatics carry the most formulas and numericals. Together they account for about 40-45% of the board exam marks. Prioritise these chapters for formula revision.
What is the difference between mirror formula and lens formula?
Mirror formula: 1/f = 1/v + 1/u. Lens formula: 1/f = 1/v − 1/u. The sign difference arises from the sign convention. For mirrors, f = R/2 (positive for concave). For lenses, positive f means converging lens. Both use the same sign convention (distances measured from optical centre/pole, real positive for lenses but incident side negative for mirrors).
How do you remember the YDSE fringe width formula?
β = λD/d — remember 'wavelength times Distance divided by slit distance'. A mnemonic: 'Long Distance, Small Slits give wide fringes.' β increases with λ and D, decreases with d. This formula is used in almost every YDSE numerical.
What is the photoelectric effect formula in simple terms?
KE_max = hν − φ. The incoming photon (energy hν) gives its energy to the electron. The electron uses φ (work function) to escape the metal, and the rest becomes kinetic energy. If hν < φ, no electrons are emitted regardless of intensity.
How is the transformer equation derived?
V_s/V_p = N_s/N_p comes from Faraday's law — the same changing flux links both coils. For an ideal transformer, input power = output power: V_p I_p = V_s I_s, giving V_s/V_p = I_p/I_s. Real transformers have efficiency losses (eddy currents, flux leakage).
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