Physics
Fleming's Left & Right Hand Rules — LEFT for motor (Force), RIGHT for generator (Induced current). Thumb=Force/Motion, First finger=Field, seCond finger=Current. Remember: "moLor Left, geneRatoR Right."
Amplitude Modulation Band Math — For AM radio, bandwidth = 2×message frequency. Side bands at fc±fm. Modulation index μ = Am/Ac; μ≤1 prevents distortion. Power in side bands = (μ²/2)Pc.
Series vs Parallel Resistance/Capacitance Flip — Resistors in series ADD; capacitors in series use reciprocal sum (1/Ceq = 1/C₁+1/C₂). In parallel, it flips: resistors use reciprocal, capacitors ADD directly. Opposite behaviors, easy to confuse.
Photoelectric Equation Anchor — KEmax = hν - φ (work function). Stopping potential: eV₀ = KEmax. Below threshold frequency ν₀ = φ/h, NO emission regardless of intensity. Intensity affects current, NOT electron energy.
de Broglie Wavelength Shortcuts — λ = h/p = h/mv. For electrons accelerated through V volts: λ = 12.27/√V Ångströms (derive from ½mv² = eV). Heavier particle = shorter wavelength at same speed.
Bohr Radius & Energy Series — rn = 0.529n²/Z Ångströms (n=1,2,3...). En = -13.6Z²/n² eV. For hydrogen Z=1: r₁=0.529Å, E₁=-13.6eV. Energy released in transition: ΔE = 13.6(1/n₁² - 1/n₂²) eV.
Self-Inductance Flux Rule — ε = -L(dI/dt). Energy stored = ½LI². For solenoid L = μ₀n²Al (n=turns/length, A=area). Inductor opposes CHANGE in current, acts like inertia for electricity.
Escape Velocity Quick Formula — ve = √(2gR) = 11.2 km/s for Earth (g=10 m/s², R=6400 km). Independent of projectile mass. Derive from KE = PE: ½mv² = GMm/R. Orbital velocity = ve/√2.
Chemistry
Lucas Test Timing — 1° alcohols: no turbidity at room temp. 2° alcohols: turbidity in 5 minutes. 3° alcohols: immediate turbidity (ZnCl₂/HCl). Remember "1-Never, 2-Five, 3-Instant" for alcohol classification.
Aldehyde vs Ketone Tests — Aldehydes: Tollen's (silver mirror), Fehling's (red ppt), both POSITIVE. Ketones: NEGATIVE for both (except α-hydroxy ketones). Mnemonic: "AldeHYDE seeks SILVER lining."
Carbylamine Reaction — Primary amines ONLY react with CHCl₃ + alc. KOH to give foul-smelling isocyanide (RNC). 2° and 3° amines: NO reaction. Diagnostic test: "Carbylamine = 1° amine."
Hinsberg Reagent Pattern — Benzenesulfonyl chloride (C₆H₅SO₂Cl): 1° amine gives soluble product in KOH, 2° gives insoluble ppt, 3° doesn't react. "One dissolves, Two precipitates, Three stays away."
Azimuthal Quantum Number Shapes — l=0(s, sphere), l=1(p, dumbbell), l=2(d, double-dumbbell/cloverleaf), l=3(f, complex). For nth shell, l = 0 to (n-1). Remember: pherical eanut ouble lowery.