Class 12 Physics Formula Sheet (PDF) — All Important Formulas Free
Free class 12 physics formula sheet — all 93 key formulas on one page, downloadable as PDF for fast revision before CBSE board exams. No signup.
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Comprehensive formula sheet for CBSE Class 12 Physics. Covers electrostatics, magnetism, optics, modern physics, and semiconductors. All SI units.
Electrostatics
| Formula | Expression |
|---|---|
| Coulomb's Law | F = kq₁q₂/r² = (1/(4πε₀))(q₁q₂/r²) — k ≈ 9×10⁹ N⋅m²/C², ε₀ = 8.85×10⁻¹² F/m |
| Electric Field | E = F/q = kQ/r² (point charge) — E in N/C. Direction: away from +ve, toward -ve charge |
| Electric Potential | V = kQ/r, V = W/q (work per unit charge) — V in volts (J/C). Potential energy U = qV = kQq/r |
| Electric Dipole Moment | p = qd (magnitude) — q = charge magnitude, d = separation. Direction from -ve to +ve charge |
| Dipole Potential | V = (kp cos θ)/r² = (1/(4πε₀))(p⃗·r̂)/r² — θ = angle from dipole axis. V depends on angle and distance |
| Dipole Torque in Field | τ = pE sin θ = p⃗ × E⃗ — τ rotates dipole to align with field |
| Dipole in Uniform Field | U = -pE cos θ = -p⃗·E⃗ — Minimum (stable) when aligned with field |
Capacitance & Dielectrics
| Formula | Expression |
|---|---|
| Capacitance Definition | C = Q/V — C in farads (F). Charge stored per volt applied |
| Parallel Plate Capacitor | C = ε₀εᵣA/d — A = plate area, d = separation, εᵣ = dielectric constant (≥1) |
| Cylindrical Capacitor | C = (2πε₀l)/(ln(b/a)) — l = length, a = inner radius, b = outer radius |
| Spherical Capacitor | C = 4πε₀ab/(b-a) (isolated sphere: C = 4πε₀a) — a = inner radius, b = outer radius |
| Energy Stored in Capacitor | U = (1/2)QV = (1/2)CV² = Q²/(2C) — U in joules. Energy stored in electric field |
| Capacitors in Series | 1/C_total = 1/C₁ + 1/C₂ + ..., Q = same on all — V divides: smallest V on largest C |
| Capacitors in Parallel | C_total = C₁ + C₂ + ..., V = same on all — Charge divides: most charge on largest C |
| Dielectric Constant | K = C/C₀ = E₀/E — C₀ = capacitance without dielectric, E₀ = field without |
| Polarization | P = ε₀(K-1)E = ε₀χE — P = polarization, χ = electric susceptibility |
Current Electricity
| Formula | Expression |
|---|---|
| Electric Current | I = dQ/dt = nAeVd — I in amperes (A). Vd = drift velocity |
| Ohm's Law (Microscopic) | J = σE — J = current density (A/m²), σ = conductivity (Ω⁻¹m⁻¹) |
| Resistance | R = ρL/A = L/(σA) — ρ = resistivity (Ω⋅m), L = length, A = cross-section |
| Temperature Coefficient | R(T) = R₀[1 + α(T - T₀)] — α = temperature coefficient (K⁻¹). R changes with temperature |
| EMF & Internal Resistance | I = ε/(R + r), V = ε - Ir — ε = EMF (V), r = internal resistance, R = external load |
| Power & Energy | P = VI = I²R = V²/R, E = Pt — P in watts, E in joules. Heat dissipated = I²Rt |
| Resistivity vs Conductivity | σ = 1/ρ, R = ρL/A, G = σA/L — G = conductance (siemens, S). σ in (Ω⋅m)⁻¹ |
| Drift Velocity | Vd = (eE/m)τ = (I/(nAe)) — τ = relaxation time. Very slow (~mm/s) but current fast |
Moving Charges & Magnetism
| Formula | Expression |
|---|---|
| Lorentz Force | F = q(E + v × B) — F on charge q moving with velocity v in fields E and B |
| Magnetic Force on Current | F = IL × B = BIL sin θ — L = length vector, θ = angle. F perpendicular to both L and B |
| Magnetic Field (Straight Wire) | B = (μ₀I)/(2πr) — μ₀ = 4π×10⁻⁷ T⋅m/A. Field circular around wire |
| Magnetic Field (Circular Loop) | B = (μ₀I)/(2R) (at center) — R = radius. Field along axis: B = (μ₀IR²)/(2(R²+x²)^(3/2)) |
| Magnetic Dipole Moment | m = IA (magnitude) — I = current, A = area of loop. Direction: right-hand rule |
| Torque on Magnetic Dipole | τ = m × B = mB sin θ — θ = angle between m and B. Torque aligns dipole with field |
| Ampere's Law | ∮B⃗·dl⃗ = μ₀I_enclosed — Line integral of B around closed loop = μ₀ times enclosed current |
| Radius of Circular Motion (Charged Particle) | r = mv/(qB) = (m/(qB))√(2KE) — Particle moves in circle perpendicular to B |
| Hall Effect | V_H = (BI)/(ned) — Hall voltage V_H across conductor. n = charge carrier density |
Electromagnetic Induction
| Formula | Expression |
|---|---|
| Faraday's Law | ε = -dΦ/dt — ε = induced EMF, Φ = magnetic flux (Wb). Negative sign = Lenz's law |
| Magnetic Flux | Φ = B⃗·A⃗ = BA cos θ — Φ in weber (Wb). θ = angle between B and normal to area |
| Motional EMF | ε = BLv — L = length of conductor, v = velocity perpendicular to B |
| Induced EMF in Rotating Coil | ε = NABω sin(ωt + φ) — N = turns, A = area, ω = angular velocity. AC generator equation |
| Self-Inductance | L = Φ/I = μ₀N²A/l — L in henry (H). Flux per unit current through coil |
| Mutual Inductance | M = k√(L₁L₂) — k = coupling coefficient (0 ≤ k ≤ 1). Flux in one affects the other |
| Energy in Inductor | U = (1/2)LI² — Energy stored in magnetic field. Analogous to (1/2)CV² for capacitor |
| LR Circuit (Growing Current) | I = (ε/R)(1 - e^(-Rt/L)) — I grows exponentially with time constant τ = L/R |
| LC Circuit Oscillation | I = I₀ sin(ωt + φ), ω = 1/√(LC) — Energy oscillates between inductor and capacitor |
Alternating Current (AC)
| Formula | Expression |
|---|---|
| AC Voltage & Current | V = V₀ sin(ωt + φ), I = I₀ sin(ωt) — V₀, I₀ = peak values. RMS values: V_rms = V₀/√2, I_rms = I₀/√2 |
| Impedance | Z = √(R² + (X_L - X_C)²) — Z in ohms. X_L = inductive, X_C = capacitive reactance |
| Inductive Reactance | X_L = ωL = 2πfL — X_L in ohms. Increases with frequency |
| Capacitive Reactance | X_C = 1/(ωC) = 1/(2πfC) — X_C in ohms. Decreases with frequency |
| Power in AC Circuit | P = VI cos φ = I²_rms × R — cos φ = power factor. Only resistor dissipates power |
| Resonance Frequency | f₀ = 1/(2π√(LC)) — At resonance X_L = X_C, Z = R (minimum) |
| Quality Factor | Q = (ωL)/R = 1/(R√(C/L)) — Q = sharpness of resonance. Higher Q = narrower peak |
| Transformer Equation | V_p/V_s = N_p/N_s = I_s/I_p — Ideal transformer: V_p×I_p = V_s×I_s (power conserved) |
Electromagnetic Waves & Ray Optics
| Formula | Expression |
|---|---|
| EM Wave Speed | c = 1/√(μ₀ε₀) = 3×10⁸ m/s — c = speed of light in vacuum. Same for all EM waves |
| EM Wave Relation | E₀/B₀ = c, E = cB — Electric and magnetic fields perpendicular, in phase |
| Energy Density | u = (ε₀E²)/2 = B²/(2μ₀) — Energy per unit volume in EM field |
| Poynting Vector | S = (1/μ₀)E⃗ × B⃗, I = ⟨S⟩ = (E₀B₀)/(2μ₀) — S = energy flux (W/m²). ⟨S⟩ = time-averaged intensity |
| Radiation Pressure | P = I/c — Pressure exerted by EM radiation on absorbing surface |
| Snell's Law | n₁ sin θ₁ = n₂ sin θ₂ — n = refractive index. Different for different media |
| Critical Angle & Total Internal Reflection | sin θc = n₂/n₁ (when n₁ > n₂) — Total reflection occurs when θ > θc |
| Lens Maker's Formula | 1/f = (n-1)[1/R₁ - 1/R₂] — n = refractive index, R = radius of curvature |
| Magnification | m = -v/u (mirror), m = v/u (lens) — Negative = inverted, positive = erect |
Wave Optics
| Formula | Expression |
|---|---|
| Young's Double Slit | λ = (ax)/D — a = slit separation, x = fringe width, D = screen distance |
| Interference Condition | Bright: Δx = nλ, Dark: Δx = (n+½)λ — Δx = path difference. n = 0, 1, 2, ... |
| Diffraction (Single Slit) | Minima: b sin θ = nλ — b = slit width. n = 1, 2, 3, ... (n ≠ 0) |
| Diffraction Grating | d sin θ = nλ — d = grating spacing. Bright fringes when condition satisfied |
| Resolving Power | R = λ/Δλ = nN (for grating) — n = order, N = total number of slits. Ability to separate close wavelengths |
| Rayleigh Criterion | θ = 1.22(λ/D) — D = aperture diameter. Minimum resolvable angle |
| Fraunhofer vs Fresnel | Fraunhofer: θ ≈ λ/a, Fresnel: complex — Fraunhofer = far field (∞ or lens), Fresnel = near field |
| Polarization by Malus Law | I = I₀ cos² θ — θ = angle between polarizers. Intensity decreases |
Dual Nature & Photoelectric Effect
| Formula | Expression |
|---|---|
| Photon Energy | E = hf = hc/λ — h = 6.63×10⁻³⁴ J⋅s. Energy of single photon |
| Photoelectric Effect | hf = φ + KE_max = φ + eVs — φ = work function, Vs = stopping potential |
| Threshold Frequency | f₀ = φ/h, λ₀ = hc/φ — Minimum frequency/maximum wavelength to emit electrons |
| de Broglie Wavelength | λ = h/p = h/(mv) — All particles have wave nature. p = momentum |
| Bohr Model (Hydrogen) | r_n = (0.53×10⁻¹⁰ m)n²/Z = n²a₀/Z — a₀ = Bohr radius. r_n ∝ n². E_n = -13.6 eV/n² (hydrogen) |
| Energy Levels | ΔE = E_n - E_m = 13.6(1/n² - 1/m²) eV — Negative = energy released (emission), positive = absorbed |
| Ionization Energy | IE = 13.6 eV (hydrogen from n=1) — Energy to remove electron from ground state |
| Compton Scattering | λ' - λ = (h/(m_e c))(1 - cos θ) — λc = h/(m_e c) = 2.43×10⁻¹² m (Compton wavelength) |
Atoms & Nuclei
| Formula | Expression |
|---|---|
| Nuclear Mass Defect | Δm = (Zmp + Nmn) - m_nucleus — Mass lost converted to binding energy (Einstein: E = Δmc²) |
| Binding Energy | BE = Δmc² = [Zmp + Nmn - m_nucleus]c² — Energy holding nucleus together. BE/A = binding energy per nucleon |
| Radioactive Decay | N(t) = N₀ e^(-λt), λ = ln(2)/T₁/₂ — λ = decay constant, T₁/₂ = half-life. Exponential decay |
| Activity | A = λN = dN/dt — A in decays/second (Bq). A₀ = λN₀ initially |
| Alpha Decay | ^A_Z X → ^(A-4)_(Z-2) Y + ^4_2 He — Emits ⁴He nucleus. Z decreases by 2, A by 4 |
| Beta Decay | ^A_Z X → ^A_(Z+1) Y + e⁻ + ν̄_e — β⁻ decay: electron + antineutrino. Increases Z by 1 |
| Gamma Decay | ^A_Z X* → ^A_Z X + γ — High-energy photon. A and Z unchanged |
| Mass-Energy Equivalence | E = mc² — m = 1 u = 1.66×10⁻²⁷ kg = 931.5 MeV/c² |
| Q-value of Decay | Q = (m_initial - m_final)c² — Q > 0 = exothermic (spontaneous), Q < 0 = endothermic |
Semiconductors & Electronics
| Formula | Expression |
|---|---|
| Bandgap Energy | Eg = hf = hc/λ — Energy difference between conduction and valence bands |
| Intrinsic Semiconductor | ni = √(Nc Nv) exp(-Eg/(2kT)) — ni = intrinsic carrier concentration. Doubles ~every 5°C |
| Conductivity | σ = (q/kT)(ne μe + nh μh) — ne, nh = electron/hole concentrations, μ = mobility |
| Drift Velocity in Semiconductor | vd = μ_n E (electrons), vd = μ_p E (holes) — μ = mobility (cm²/V⋅s). Typical: ~1000 for e⁻, ~400 for h⁺ |
| PN Junction (Forward Bias) | I = I₀[exp(qV/kT) - 1] — I₀ = reverse saturation current. Exponential rise with V |
| Depletion Width | w = √((2ε₀εᵣ(V_bi - V))/(q)(N_A + N_D)/(N_A N_D)) — V_bi = built-in voltage. w decreases with forward bias |
| Zener Breakdown | V_z = breakdown voltage (typical 5-10 V) — Sharp increase in reverse current. Used in voltage regulation |
| Transistor (BJT) Beta | β = I_C/I_B — Current gain. Typical β = 100-300. I_C = β×I_B |
| MOSFET Drain Current | I_D = (μ_n C_ox / 2)(W/L)(V_GS - V_T)² — Saturation region. W/L = aspect ratio, V_T = threshold voltage |
FAQs
What's the key difference between series and parallel capacitors?
Series: 1/C_total = 1/C₁ + 1/C₂ (charge Q same on all). Parallel: C_total = C₁ + C₂ (voltage V same on all). Series capacitors act like smaller C total; parallel act like larger.
How do I solve AC circuit problems with impedance?
Calculate X_L = ωL and X_C = 1/(ωC). Find Z = √(R² + (X_L - X_C)²). Current I = V/Z. Power P = VI cos φ where cos φ = R/Z. At resonance X_L = X_C, so Z = R (minimum).
When solving optics problems, how do I choose between geometric and wave models?
Use geometric optics (ray model) for mirrors, lenses, refraction when object/image size >> wavelength. Use wave optics (diffraction, interference) when dealing with slits, gratings, or when wavelength is comparable to aperture. Dual nature: all light has both, choose convenient model.