NEB Class 12 Physics cheat sheet

Equations of motion for constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as; each assumes a is uniform and motion is along a straight line.

Projectile motion splits into independent components: horizontal velocity constant at u·cosθ; vertical motion under g with time of flight T = 2u·sinθ/g and range R = u²·sin2θ/g (level ground).

Newton's second law in vector form: F_net = dp/dt = ma when mass is constant; impulse J = ∫F dt = Δp.

Circular motion: centripetal acceleration a = v²/r = ω²r; for a banked road without friction, tanθ = v²/(rg).

Work–energy theorem: W_net = ΔK = ½mv² − ½mu²; a conservative force has zero work over any closed path and a potential energy U with F = −dU/dx.

Conservation of linear momentum applies when net external force is zero; in elastic collisions both momentum and kinetic energy are conserved, in perfectly inelastic collisions only momentum.

Moment of inertia depends on axis: I = Σmr²; parallel-axis theorem I = I_cm + Md², and rolling without slipping gives K = ½Mv² + ½Iω².

Angular momentum L = Iω is conserved when net external torque is zero; torque τ = dL/dt = Iα for a rigid body about a fixed axis.

Gravitation: g = GM/R² at the surface, orbital speed v = √(GM/r), escape speed v_e = √(2GM/R) = √2·v_orbital at the surface.

First law: ΔU = Q − W, with W = ∫P dV the work done by the gas; sign of W flips if the convention W is work done on the gas.

Isothermal work for an ideal gas: W = nRT ln(V₂/V₁); adiabatic relation PV^γ = constant with γ = C_p/C_v, and W = (P₁V₁ − P₂V₂)/(γ − 1).

For an ideal gas C_p − C_v = R; monatomic γ = 5/3, diatomic (rigid) γ = 7/5.

Efficiency of a Carnot engine: η = 1 − T_c/T_h (temperatures in kelvin); no engine between the same two reservoirs can exceed it.

Second law statements: Kelvin–Planck (no cyclic engine converts heat entirely to work) and Clausius (no device moves heat from cold to hot with no work input).

Entropy change for a reversible process: ΔS = ∫dQ_rev/T; for an isolated system ΔS ≥ 0, with equality only for reversible processes.

Kinetic theory: PV = ⅓Nm(v_rms)²; v_rms = √(3RT/M), and mean kinetic energy per molecule = (3/2)kT for a monatomic gas.

Calorimetry with no phase change: Q = mcΔT; during melting or boiling at constant temperature Q = mL, where L is the specific latent heat.

Thermal conduction steady state: H = kA(T₁ − T₂)/L; Stefan's law for a black body: P = σAT⁴, net loss P = σA(T⁴ − T_s⁴).

Mirror and thin-lens formula: 1/v − 1/u = 1/f for mirrors (Cartesian sign convention) and 1/v − 1/u = 1/f for lenses; magnification m = v/u.

Snell's law: n₁sinθ₁ = n₂sinθ₂; refractive index n = c/v, and critical angle for total internal reflection satisfies sinθ_c = n₂/n₁ (n₁ > n₂).

Lens maker's formula: 1/f = (n − 1)(1/R₁ − 1/R₂); power P = 1/f in dioptres when f is in metres, and powers add for thin lenses in contact.

Young's double slit: fringe spacing β = λD/d; bright fringes at path difference nλ, dark at (n + ½)λ.

Single-slit diffraction minima at d·sinθ = nλ; the central maximum is twice as wide as the secondary maxima.

Diffraction grating: d·sinθ = nλ gives principal maxima; resolving power of a grating R = λ/Δλ = nN.

Malus's law: intensity through an analyser I = I₀cos²θ; Brewster's angle satisfies tanθ_B = n₂/n₁, giving fully polarised reflected light.

Rayleigh criterion for a circular aperture: limiting angle θ = 1.22λ/D; a compound microscope's magnifying power M = m_o × m_e.

Coulomb's law: F = (1/4πε₀)q₁q₂/r², with 1/4πε₀ ≈ 9 × 10⁹ N·m²/C²; electric field of a point charge E = kQ/r².

Gauss's law: Φ = ∮E·dA = q_enclosed/ε₀; field inside a conductor in electrostatic equilibrium is zero and charge resides on the surface.

Capacitance: C = Q/V; parallel plate C = ε₀A/d (ε₀ε_r A/d with a dielectric); series 1/C = Σ1/Cᵢ, parallel C = ΣCᵢ.

Energy stored in a capacitor U = ½CV² = Q²/2C; energy density in an electric field u = ½ε₀E².

Ohm's law V = IR with R = ρL/A; for cells in series EMFs add, and internal resistance gives terminal voltage V = ε − Ir.

Kirchhoff's rules: junction rule ΣI = 0 (charge conservation) and loop rule ΣV = 0 (energy conservation); Wheatstone bridge balances when P/Q = R/S.

Biot–Savart and Ampere: long straight wire B = μ₀I/(2πr); centre of a circular loop B = μ₀I/(2R); solenoid B = μ₀nI; force per length between parallel wires = μ₀I₁I₂/(2πd).

Magnetic force on a moving charge F = qv × B (radius r = mv/qB) and on a current-carrying wire F = BIL·sinθ; a current loop has torque τ = NIAB·sinθ.

Faraday's law: ε = −dΦ/dt with Φ = BA·cosθ; Lenz's law fixes direction by opposing the change in flux; self-induced EMF ε = −L·dI/dt.

Photoelectric effect: hf = φ + K_max, with threshold frequency f₀ = φ/h and stopping potential eV₀ = K_max; saturation current depends on intensity, not frequency.

Photon relations: E = hf = hc/λ; h ≈ 6.63 × 10⁻³⁴ J·s, and 1 eV = 1.6 × 10⁻¹⁹ J.

de Broglie wavelength λ = h/p = h/(mv); for an electron accelerated through V volts, λ ≈ 12.27/√V Å.

Bohr model: E_n = −13.6/n² eV for hydrogen; angular momentum L = nh/2π; spectral lines follow 1/λ = R(1/n₁² − 1/n₂²) with R ≈ 1.097 × 10⁷ m⁻¹.

Heisenberg uncertainty principle: Δx·Δp ≥ ħ/2 (ħ = h/2π), a consequence of wave–particle duality rather than instrument limits.

Mass–energy equivalence E = mc²; rest energy of 1 u is about 931.5 MeV, used to convert mass defect to binding energy.

Nuclear binding energy per nucleon peaks near iron-56 (about 8.8 MeV), so fusion of light nuclei and fission of heavy nuclei both release energy.

Radioactive decay law N = N₀e^(−λt); half-life t½ = ln2/λ ≈ 0.693/λ; activity A = λN is measured in becquerel (1 Bq = 1 decay/s).

Alpha decay reduces mass number by 4 and atomic number by 2; beta-minus decay raises Z by 1 with A unchanged; gamma emission changes neither A nor Z.

In a nuclear reaction, mass number and atomic number are conserved separately; Q-value = (mass of reactants − mass of products) × c², positive for exothermic reactions.

Semiconductors: n-type is doped with pentavalent donors (electrons majority), p-type with trivalent acceptors (holes majority); the p-n junction has a depletion region and a built-in potential barrier.

Forward bias narrows the depletion layer and lowers the barrier, giving exponential current; reverse bias widens it, so only a small leakage current flows until breakdown.

Half-wave rectifier output has ripple frequency equal to the input; a full-wave rectifier doubles it, and a filter capacitor smooths the ripple.

Transistor as amplifier: current gain β = I_C/I_B, and I_E = I_B + I_C; for a common-emitter amplifier, voltage gain is negative, so output is 180° out of phase with input.

Logic gates: OR gives Y = A + B, AND gives Y = A·B, NOT gives Y = Ā; NAND and NOR are universal gates from which all others can be built.

Zener diode in reverse breakdown holds a nearly constant voltage and is used as a voltage regulator; an LED emits light when forward biased.

Truth-table rule: a two-input XOR gives 1 only when inputs differ; a half adder uses XOR for sum and AND for carry.