Class 12 Physics Formula Poster (Printable PDF, Free) — All 93 Formulas

Electrostatics

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)/r²θ = angle from dipole axis. V depends on angle and distance
Dipole Torque in Field: τ = pE sin θ = p⃗ × E⃗τ rotates dipole to align with field
Dipole in Uniform Field: U = -pE cos θ = -p⃗·E⃗Minimum (stable) when aligned with field

Capacitance & Dielectrics

Capacitance Definition: C = Q/VC in farads (F). Charge stored per volt applied
Parallel Plate Capacitor: C = ε₀εᵣA/dA = 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 allV divides: smallest V on largest C
Capacitors in Parallel: C_total = C₁ + C₂ + ..., V = same on allCharge divides: most charge on largest C
Dielectric Constant: K = C/C₀ = E₀/EC₀ = capacitance without dielectric, E₀ = field without
Polarization: P = ε₀(K-1)E = ε₀χEP = polarization, χ = electric susceptibility

Current Electricity

Electric Current: I = dQ/dt = nAeVdI in amperes (A). Vd = drift velocity
Ohm's Law (Microscopic): J = σEJ = 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 - Irε = EMF (V), r = internal resistance, R = external load
Power & Energy: P = VI = I²R = V²/R, E = PtP in watts, E in joules. Heat dissipated = I²Rt
Resistivity vs Conductivity: σ = 1/ρ, R = ρL/A, G = σA/LG = 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

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 θL = 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 θθ = angle between m and B. Torque aligns dipole with field
Ampere's Law: ∮B⃗·dl⃗ = μ₀I_enclosedLine 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

Faraday's Law: ε = -dΦ/dtε = induced EMF, Φ = magnetic flux (Wb). Negative sign = Lenz's law
Magnetic Flux: Φ = B⃗·A⃗ = BA cos θΦ in weber (Wb). θ = angle between B and normal to area
Motional EMF: ε = BLvL = 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/lL 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)LI²Energy 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)

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 = 2πfLX_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 × Rcos 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_pIdeal transformer: V_p×I_p = V_s×I_s (power conserved)

Electromagnetic Waves & Ray Optics

EM Wave Speed: c = 1/√(μ₀ε₀) = 3×10⁸ m/sc = speed of light in vacuum. Same for all EM waves
EM Wave Relation: E₀/B₀ = c, E = cBElectric 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/cPressure exerted by EM radiation on absorbing surface
Snell's Law: n₁ sin θ₁ = n₂ sin θ₂n = 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

Young's Double Slit: λ = (ax)/Da = slit separation, x = fringe width, D = screen distance
Interference Condition: Bright: Δx = nλ, Dark: Δx = (n+½)λΔx = path difference. n = 0, 1, 2, ...
Diffraction (Single Slit): Minima: b sin θ = nλb = slit width. n = 1, 2, 3, ... (n ≠ 0)
Diffraction Grating: d sin θ = nλd = 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: complexFraunhofer = far field (∞ or lens), Fresnel = near field
Polarization by Malus Law: I = I₀ cos² θθ = angle between polarizers. Intensity decreases

Dual Nature & Photoelectric Effect

Photon Energy: E = hf = hc/λh = 6.63×10⁻³⁴ J⋅s. Energy of single photon
Photoelectric Effect: hf = φ + KE_max = φ + eVsφ = work function, Vs = stopping potential
Threshold Frequency: f₀ = φ/h, λ₀ = hc/φMinimum 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/Za₀ = 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) eVNegative = 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

Nuclear Mass Defect: Δm = (Zmp + Nmn) - m_nucleusMass lost converted to binding energy (Einstein: E = Δmc²)
Binding Energy: BE = Δmc² = [Zmp + Nmn - m_nucleus]c²Energy holding nucleus together. BE/A = binding energy per nucleon
Radioactive Decay: N(t) = N₀ e^(-λt), λ = ln(2)/T₁/₂λ = decay constant, T₁/₂ = half-life. Exponential decay
Activity: A = λN = dN/dtA in decays/second (Bq). A₀ = λN₀ initially
Alpha Decay: ^A_Z X → ^(A-4)_(Z-2) Y + ^4_2 HeEmits ⁴He nucleus. Z decreases by 2, A by 4
Beta Decay: ^A_Z X → ^A_(Z+1) Y + e⁻ + ν̄_eβ⁻ decay: electron + antineutrino. Increases Z by 1
Gamma Decay: ^A_Z X* → ^A_Z X + γHigh-energy photon. A and Z unchanged
Mass-Energy Equivalence: E = mc²m = 1 u = 1.66×10⁻²⁷ kg = 931.5 MeV/c²
Q-value of Decay: Q = (m_initial - m_final)c²Q > 0 = exothermic (spontaneous), Q < 0 = endothermic

Semiconductors & Electronics

Bandgap Energy: Eg = hf = hc/λEnergy 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_BCurrent 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)²Saturation region. W/L = aspect ratio, V_T = threshold voltage