LEW cheat sheet

Ohm's law: V = I × R; power P = V × I = I²R = V²/R. In AC, use RMS values for these relations.

Series circuit: same current everywhere, resistances add, voltages divide in proportion to resistance. Parallel: same voltage, conductances add, currents divide inversely with resistance.

Three-phase power: P = √3 × V_LL × I × PF for balanced loads; single-phase P = V × I × PF. Reactive power Q = √3 × V_LL × I × sin θ.

Impedance Z = R + jX; |Z| = √(R² + X²), phase angle θ = arctan(X/R). Inductive reactance X_L = 2πfL; capacitive X_C = 1/(2πfC).

Resonance occurs where X_L = X_C, giving f_r = 1/(2π√(LC)); impedance is minimum (series) or maximum (parallel) at resonance.

Wye (star) connection: V_line = √3 × V_phase, I_line = I_phase. Delta: V_line = V_phase, I_line = √3 × I_phase.

Per-unit method: divide actual quantities by base values; base impedance Z_base = V_base² / S_base. Per-unit simplifies multi-voltage transformer networks.

Kirchhoff's laws: KCL - sum of currents at a node equals zero; KVL - sum of voltages around a closed loop equals zero. Use superposition or Thevenin for linear networks.

Conductor ampacity depends on insulation temperature rating, ambient temperature correction, and conduit fill adjustment (NEC Table 310.15 series).

Conduit fill limits: 1 conductor 53%, 2 conductors 31%, 3 or more 40% of interior cross-sectional area (NEC Chapter 9).

Box fill is calculated from conductor volume allowances plus devices, clamps, and grounds; see NEC Table 314.16(B) for cubic-inch allowances per conductor size.

Bending radius: for cable, not less than 5× diameter for ≤1 in and 10× for larger; conduit bends typically 6× trade diameter for one-shot and 4× for field bends (verify with NEC 344/352).

Support intervals: rigid metal conduit every 10 ft and within 3 ft of boxes; EMT every 10 ft and within 3 ft; cable types per NEC 334.30 (typically 4.5 ft).

Conductor color code (NEC 310.110): grounded conductor white/gray, equipment grounding conductor green or green with yellow stripe, ungrounded typically black/red/blue.

Expansion fittings are required where raceway crosses building expansion joints or where thermal expansion exceeds design limits; PVC needs expansion fittings per temperature change.

Wet locations require conductors and fittings listed for wet use; NM cable is prohibited in wet locations and in most commercial occupancies per NEC 334.12.

Standard OCPD sizes (NEC 240.6): 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100, 110, 125, 150, 175, 200, 225, 250, 300, 350, 400 A, etc.

Next-size-up rule (NEC 240.4(B)) applies only when the ampacity does not correspond to a standard size, the next size does not exceed 800 A, and the load does not exceed the conductor ampacity.

Ground-fault protection for equipment (GFPE) at 1,000 A or more, 480Y/277 V services is required per NEC 230.95; trip threshold typically 1,200 A maximum with a delay.

Equipment grounding conductor sizing is based on the OCPD rating (NEC Table 250.122); it may need upsizing if conductors are increased for voltage drop.

Grounding electrode system: metal water pipe (10 ft contact), metal frame of building, concrete-encased electrode (20 ft of ½ in rebar or 4 AWG bare copper in 2 in concrete), ground ring, and rod/pipe electrodes.

Bonding jumpers around water meters, insulating joints, and flexible connections must maintain continuity; bonding to gas piping is prohibited except as allowed by NEC 250.104(B).

GFCI protects people (5 mA trip threshold typical); AFCI protects against parallel and series arcing; both have specific required locations per NEC 210.8 and 210.12.

Selective coordination requires time-current curves to overlap so downstream OCPDs trip first; study curves and settings for adjustable trip units.

Motor full-load current comes from NEC Tables 430.247–430.250 (by horsepower and voltage), not from nameplate current, for sizing branch-circuit conductors and overloads.

Branch-circuit short-circuit and ground-fault protection (NEC Table 430.52): inverse-time breaker typically 250% of FLC; dual-element fuse 175%; non-time-delay fuse 300%.

Overload protection is sized to nameplate current: typically 125% for continuous-duty motors with service factor ≤1.15, or 115% with higher service factor (NEC 430.32).

Motor disconnecting means must be within sight of the controller and motor, or capable of being locked open (NEC 430.102).

NEMA starter sizes correlate with horsepower at 460 V: Size 0 ≈ 5 hp, Size 1 ≈ 10 hp, Size 2 ≈ 25 hp, Size 3 ≈ 50 hp; verify with the manufacturer's table.

Across-the-line starting draws 6–8× FLC; reduced-voltage, wye-delta, soft-start, and VFD methods reduce inrush. VFDs require shielded cable and proper grounding to control EMI.

Control circuits are typically 120 V AC or 24 V DC; a holding contact (seal-in) maintains the coil circuit after the start pushbutton is released.

Motor rotation reversal: swap any two of the three supply leads for a three-phase motor; for a single-phase motor, reverse the start winding leads.

Transformer turns ratio: V_primary/V_secondary = N_primary/N_secondary; current ratio is inverse; apparent power is conserved (ignoring losses).

Delta-wye transformers provide a neutral and a 30° phase shift; paralleling transformers requires matched voltage ratio, polarity, impedance, and phase sequence.

Transformer protection: primary OCPD typically 125% of primary FLA for continuous rating (NEC 450.3); secondary protection may be required when the primary device exceeds certain thresholds.

Voltage drop approximation: VD = (2 × K × I × L) / CM for single-phase; use √3 factor for three-phase. K ≈ 12.9 for copper, 21.2 for aluminum (ohm-cmil/ft).

Power factor correction capacitors reduce reactive current; place them at the load to avoid leading power factor and overvoltage during light load.

Harmonics from VFDs and switching supplies cause neutral overheating (triplen harmonics add in the neutral) and transformer derating; use K-rated transformers.

Short-circuit calculation: use transformer impedance (%Z) with base kVA to find fault current; I_sc ≈ (kVA × 1000) / (√3 × V × %Z/100).

Voltage unbalance causes motor heating; NEMA derates motors when voltage unbalance exceeds 1%; 3.5% unbalance can cause ~25% temperature rise.

NFPA 70E establishes arc-flash and shock protection boundaries: limited approach, restricted approach, and arc-flash boundary, based on voltage and incident energy.

Arc-flash incident energy is expressed in cal/cm²; PPE categories (or arc ratings) are selected to exceed the calculated incident energy at the working distance.

Approach boundaries: for 480 V, the limited approach boundary is typically 10 ft for movable conductors and 3 ft 6 in for fixed; restricted approach is 1 ft (verify with current tables).

Lockout/tagout requires an energy-isolating device, verification of de-energization, and application of locks by each worker; test-before-touch confirms absence of voltage.

NEC Article 90 establishes that the Code is not a design manual or instruction manual; local amendments and the AHJ govern enforcement.

Classified locations are divided into Class I (gases/vapors), Class II (dust), and Class III (fibers/flyings); divisions or zones define the likelihood of hazard.

Temporary wiring, GFCI protection on construction sites, and assured equipment grounding conductor programs are required by OSHA 1926 Subpart K.

Standards hierarchy: NFPA 70 (installation), NFPA 70E (workplace safety), NFPA 70B (maintenance), UL standards (product listing), and NEMA (equipment ratings).

Insulation resistance testing uses a megohmmeter at a test voltage appropriate to the winding (500 V for 480 V equipment, 1,000 V for medium voltage); record values and temperature-correct them.

Continuity and low-resistance testing confirms bonding and equipment grounding paths; a reading above a few tenths of an ohm indicates a poor connection.

A clamp-on ammeter measures load current without breaking the circuit; a split-core or flexible Rogowski coil works for large conductors.

A multimeter's CAT rating (CAT III, CAT IV) must match the environment; CAT IV is required at service entrances and outdoor feeders.

Phase rotation meters verify ABC sequence before connecting motors; a reversed phase causes reverse rotation and potential damage.

Thermographic inspection finds loose connections and overloaded conductors; compare similar phases/loads and investigate temperature differences above ~10 °C.

Troubleshooting sequence: verify the symptom, isolate the circuit, test from the source toward the load, and confirm the repair with a functional test.

Ground-fault loop impedance and breaker trip-time testing verify OCPD performance; a breaker that trips below its rating may indicate a fault or a failing breaker.