Physics
AC Phase Rule (XL–XC) — In series LCR: voltage leads current when XL > XC (inductive), lags when XC > XL (capacitive). Remember "CIVIL": in C (capacitor) I leads V, in L (inductor) V leads I.
Transformer Turns Ratio — Np/Ns = Vp/Vs = Is/Ip. Trick: "Voltage follows Turns, Current inverses" – step-up doubles voltage, halves current (power stays constant in ideal transformer).
Bohr Radius Formula — rₙ = 0.529n²/Z Ångstroms. Remember "0.529" as "May 29" (5/29) for ground-state hydrogen radius; scales with n² and inversely with atomic number Z.
Balmer Series Wavelength — Visible hydrogen lines: 656nm (red), 486nm (cyan), 434nm (blue), 410nm (violet). Mnemonic: "6-5, 4-8, 4-3, 4-1" – first digit descends, gives visible spectrum order.
Binding Energy per Nucleon Peak — Maximum at Fe-56 (Iron, mass number 56). Remember "Iron is the most stable" – fusion releases energy below Fe, fission above Fe.
Radioactive Decay N=N₀e⁻ᵏᵗ — After n half-lives, N = N₀/(2ⁿ). Quick check: 10 half-lives ≈ 1000-fold reduction (2¹⁰=1024), useful for carbon-dating problems.
Metre Bridge Balance Condition — (R₁/R₂) = (l₁/l₂) where l₁+l₂=100cm. At balance, resistances are in same ratio as wire lengths; swap to verify if l₁ → (100−l₁).
Series-Parallel Resistor Shortcut — For two resistors: Series = R₁+R₂; Parallel = (R₁×R₂)/(R₁+R₂). Remember "Product over Sum" for parallel only when n=2.
Kirchhoff's Current Law (KCL) — "Junction income = junction expense." Sum of currents entering = sum leaving any node; assign + to incoming, − to outgoing.
De Broglie Wavelength λ=h/p — For electron accelerated through V volts: λ = 12.27/√V Ångstroms. Remember "12.27" as dozen-and-quarter for quick numerical solving.
Photoelectric Work Function — KEmax = hν − φ. If frequency below threshold (hν < φ), zero electrons emitted regardless of intensity; intensity only affects photocurrent above threshold.
Chemistry
Quantum Number Limits — For n: l = 0 to (n−1); for l: m = −l to +l; s = ±½. Mnemonic: "Never Let Monkeys Scream" – hierarchy n→l→m→s.
Aufbau Order (1s to 4s) — Use (n+l) rule: fill lowest (n+l) first; if equal, lower n first. Quick: 1s 2s 2p 3s 3p 4s 3d 4p (4s fills before 3d because 4+0 < 3+2).
Hund's Rule Reminder — Electrons fill degenerate orbitals singly (parallel spins) before pairing. "" – passengers occupy empty seats before sharing.