Alternating Current
- XL increases, XC decreases — Inductive reactance XL = ωL grows with frequency; capacitive reactance XC = 1/(ωC) shrinks with frequency. Remember: "L loves high ω, C chokes high ω."
- ELI the ICE man — In pure L, current *lags* voltage by 90° (ELI: E before I); in pure C, current *leads* voltage by 90° (ICE: I before E). Phase relations made instant.
- Power factor cosφ = R/Z — In series RLC, cosφ equals resistance over impedance. Zero power dissipated when φ=90° (pure reactive), maximum when φ=0° (pure resistive).
- Resonance ω₀ = 1/√(LC) — At resonance XL = XC, impedance minimum (series) or maximum (parallel). Bandwidth inversely proportional to quality factor Q = ω₀L/R.
Atoms and Nuclei
- Rydberg formula: 1/λ = R(1/n₁² – 1/n₂²) — For hydrogen transitions, R ≈ 1.097×10⁷ m⁻¹. Lyman (n₁=1, UV), Balmer (n₁=2, visible), Paschen (n₁=3, IR). Remember sequence: "L-B-P = 1-2-3."
- Bohr radius scales as n²/Z — Ground-state radius a₀ = 0.529 Å for hydrogen. For level n or nuclear charge Z: rₙ = n²a₀/Z. Energy scales as Z²/n².
- Mass defect → binding energy — ΔE = Δm·c². One atomic mass unit (u) = 931.5 MeV/c². Binding energy per nucleon peaks near Fe-56 (most stable nucleus).
- Radioactive decay: N = N₀e^(–λt) — Half-life t₁/₂ = 0.693/λ. After n half-lives, remaining fraction = (1/2)ⁿ. Activity A = λN, measured in becquerels (disintegrations/sec).
Current Electricity
- Color code: BB ROY of Great Britain has Very Good Wife — Resistor bands: Black Brown Red Orange Yellow Green Blue Violet Grey White = 0–9. Tolerance: Gold ±5%, Silver ±10%.
- Series: currents equal, voltages add — In series, same I throughout; V_total = ΣV; R_eq = ΣR. In parallel: same V, currents add; 1/R_eq = Σ(1/R). "Series adds Rs, parallel adds 1/Rs."
- Wheatstone bridge balance: P/Q = R/S — At null deflection, product of opposite arms equal. Meter bridge: unknown/known = (100–l)/l where l is balance length in cm.
- Kirchhoff mnemonics — KCL: "Current in = Current out" at any junction (conservation of charge). KVL: "Voltage rises = Voltage drops" around any loop (conservation of energy).
Electrostatics
- Gauss's Law: Φ = Q_enclosed/ε₀ — Electric flux through closed surface depends only on charge inside. Symmetry shortcuts: spherical (point/shell), cylindrical (line), planar (sheet).
- Field vs Potential: E = –dV/dr — Field is negative potential gradient. In uniform field, V = Ed. Remember: "Field flows from high to low potential, like water downhill."
- Capacitance combinations reverse resistance rules — Series capacitors: 1/C_eq = Σ(1/C); parallel: C_eq = ΣC. "Capacitors opposite resistors: series adds reciprocals, parallel adds directly."
- Energy in capacitor: U = ½CV² = ½Q²/C = ½QV — All three forms identical. Energy density in field u = ½ε₀E². Dielectric insertion: C multiplied by κ, energy divided by κ at constant Q.
Electromagnetic Induction
- Lenz's Law: "Nature opposes change" — Induced current creates magnetic field opposing the flux change that caused it. Right-hand rule: thumb = field direction, fingers curl = induced current direction.
- Faraday's Law: ε = –dΦ/dt = –d(BA cosθ)/dt — Motional emf ε = Bvl for rod moving perpendicular to field. Coil with N turns: multiply by N. Sign from Lenz's law.
- Self-inductance: ε = –L(dI/dt) — Energy stored U = ½LI². Time constant τ = L/R in LR circuit; current grows as I(t) = I₀(1 – e^(–t/τ)), decays as I₀e^(–t/τ).
- Eddy currents minimized by lamination — Thin insulated sheets perpendicular to flux change reduce circulating currents. Used in transformer cores to minimize I²R power loss.
Electronic Devices
- Diode: "PINE = Positive-In-Negative-Emitter" — Wait, that's BJT. For diode: P-side is anode, N-side is cathode. Forward bias: P positive, N negative; current flows. Reverse bias: blocks current.
- Transistor: "NPN = Not Pointing iN" — Arrow on emitter points out for NPN, in for PNP. Emitter heavily doped, collector lightly doped. Active mode: EB forward, CB reverse biased.
- Logic gates quick recall — AND: both 1 → 1. OR: any 1 → 1. NOT: flips. NAND = universal gate (can build all others). XOR: odd number of 1s → 1.
Electromagnetic Waves
- EM spectrum: "Raging Martians Invaded Venice Using X-ray Guns" — Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma. Frequency increases, wavelength decreases left-to-right.
- Wave speed: c = fλ = 1/√(μ₀ε₀) — In vacuum c = 3×10⁸ m/s. In medium v = c/n where n is refractive index. Energy carried: intensity I ∝ E₀² ∝ B₀².