ESAA Intermediate Level Exam cheat sheet

Three-phase real power P = √3 × V_LL × I_L × power factor; for single-phase P = V × I × PF.

Apparent power S (VA) = P + jQ; reactive power Q = √3 × V_LL × I_L × sin θ, positive for inductive loads.

Per-unit method: Z_pu = Z_actual / Z_base, where Z_base = V_base² / S_base; base change formula Z_pu,new = Z_pu,old × (S_new/S_old) × (V_old/V_new)².

Delta-connected load: phase voltage equals line voltage, line current = √3 × phase current. Wye-connected load: phase current equals line current, line voltage = √3 × phase voltage.

Transformer turns ratio a = N1/N2 = V1/V2; reflected impedance Z_primary = a² × Z_secondary.

Voltage drop on a feeder ≈ √3 × I × (R cos θ + X sin θ) for three-phase; keep drop within 3% (branch) and 5% total per NEC 210.19 informational notes.

Short-circuit current from a source: I_sc = V / Z_source; transformer I_sc,secondary ≈ I_FLA / Z_pu.

Power factor correction kVAR = P × (tan θ_initial − tan θ_target); capacitors do not reduce real power, only reactive demand.

Symmetrical components: any unbalanced three-phase set decomposes into positive, negative, and zero sequences; zero-sequence currents require a neutral or ground return path.

Synchronous speed N_s = 120 × f / P (rpm); slip s = (N_s − N_r)/N_s, typically 1–5% at full load for induction motors.

NEMA Design B is the general-purpose industrial motor: locked-rotor current ≈ 6× FLA, breakdown torque ≈ 200% rated, slip < 5%.

NEMA frame sizes encode face-to-face dimensions; frame number × 4 = shaft height in sixteenths of an inch (e.g., 184T → 4.5 in).

Motor FLA from NEC Table 430.250 is used for branch-circuit sizing; nameplate FLA is used for overload protection (NEC 430.32).

Insulation class B = 130 °C, F = 155 °C, H = 180 °C; Class F with 1.15 service factor is the common industrial combination.

Torque (lb-ft) = 5252 × HP / rpm; motor current is approximately proportional to load torque below breakdown.

DC motor speed ≈ (V − I_a R_a)/kΦ; shunt motor is nearly constant speed, series motor has high starting torque and must never run unloaded.

Inverter-duty motors require insulation rated for PWM voltage spikes and often a shaft grounding ring to prevent bearing currents.

NEMA contactor sizing uses AC-3 for squirrel-cage motor starting; IEC utilization categories: AC-1 resistive, AC-3 motor starting, AC-4 plugging/jogging.

Overload relay class number = trip time in seconds at 6× FLA from cold; Class 10 is standard, Class 20 for high-inertia loads.

VFD V/f control holds V/f constant to keep flux constant; below base speed torque is constant, above base speed power is constant (field weakening).

PWM carrier frequency: higher carrier reduces audible noise but increases switching loss, common-mode current, and motor heating.

VFD acceleration time must exceed the motor's accelerating torque capability; DC injection braking is limited (typically 3–5 s) to avoid overheating.

Line reactors (typically 3–5% impedance) reduce VFD input harmonics and protect the drive from transients; harmonic limits per IEEE 519.

VFD output cable: use shielded VFD cable, limit distance per manufacturer, and never install a contactor or disconnect between drive and motor while running.

Safe torque off (STO) removes gate pulses without contactor; it is not equivalent to a lockout/tagout isolation.

4–20 mA loop: 4 mA = 0% and 20 mA = 100% of span; live zero at 4 mA allows detection of broken wires.

Ohm's law for loops: maximum loop resistance = (supply voltage − 12 V) / 0.020 A for a 4–20 mA transmitter.

RTD (Pt100): 100 Ω at 0 °C, ≈ 0.385 Ω/°C; 3-wire and 4-wire connections cancel lead resistance.

Thermocouple types: K (chromel-alumel) most common general purpose; J (iron-constantan) not for oxidizing atmospheres; use reference junction compensation.

Orifice plate flow: Q ∝ √ΔP; a 25% flow requires 6.25% of full-scale differential pressure.

Gauge vs absolute vs differential pressure: gauge reads relative to atmosphere, absolute relative to vacuum, differential is the difference between two ports.

Level by differential pressure: ΔP = ρ × g × h; interface and density changes shift zero and require compensation.

HART superimposes a ±0.5 mA FSK digital signal on the 4–20 mA analog current; loop must have ≥ 230 Ω for communication.

PLC scan cycle: input scan → logic solve → output update → housekeeping; scan time is dominated by program size and instruction mix.

Ladder logic: XIC (examine if closed), XIO (examine if open), OTE (output energize), OTL/OTU (latch/unlatch), TON/TOF/RTO timers, CTU/CTD counters.

A TON timer's accumulated value resets when its rung goes false; an RTO retains accumulated value until a separate reset.

Analog input scaling: engineering units = ((raw − raw_min)/(raw_max − raw_min)) × (EU_max − EU_min) + EU_min.

Sinking vs sourcing: a sinking input module provides the common return; a sourcing output module supplies +24 V to the load.

PID equation: output = Kp·e + Ki·∫e dt + Kd·de/dt; derivative acts on error or PV (derivative-on-PV avoids derivative kick).

Safety PLCs and standard PLCs must be separate; safety functions require certified hardware and are rated by SIL (IEC 61508/61511) or PL (ISO 13849).

Industrial networks: EtherNet/IP and PROFINET are Ethernet-based; Modbus RTU is RS-485 serial; DeviceNet and Profibus DP are fieldbus.

NFPA 70E arc flash PPE categories: Category 1 (4 cal/cm²), 2 (8), 3 (25), 4 (40); use incident-energy analysis when available.

Arc flash boundary: distance at which incident energy equals 1.2 cal/cm² (the second-degree burn threshold).

Approach boundaries per NFPA 70E: limited (shock protection), restricted (qualified only), and arc flash boundary.

Lockout/tagout per OSHA 1910.147 requires energy isolation, verification of zero energy, and a lock per worker.

Body current thresholds: 1 mA perception, 10 mA let-go, 30 mA respiratory tetanus, 100–300 mA ventricular fibrillation.

Ground-fault circuit interrupters trip at 4–6 mA; equipment protective devices (GFPE) trip at 30 mA for personnel protection at higher settings.

Bonding and grounding: equipment grounding conductor carries fault current; earth ground is not a substitute for the EGC.

Test before touch: verify a meter on a known live source, test the circuit, then re-verify on the known source.

NEC Article 430 covers motors; 430.52 sets branch-circuit short-circuit and ground-fault protection at 250% of FLA for inverse-time breakers (up to 400% if needed).

NEC 430.32 overload protection: 125% of motor nameplate FLA for motors with 1.15 service factor, 115% otherwise.

NEC Table 310.16 ampacities apply to not more than three current-carrying conductors in a raceway at 30 °C ambient; apply correction factors for temperature and conduit fill.

NEC 250.122 equipment grounding conductor sizing is based on the overcurrent device rating, not the conductor ampacity.

NEC 210.8 requires GFCI protection for 125–250 V receptacles in bathrooms, kitchens, outdoors, garages, and similar locations.

NEC 500/505 hazardous locations: Class I gases/vapors, Class II dusts, Class III fibers; Division 1 vs 2, or Zones 0/1/2 (gas) and 20/21/22 (dust).

NEMA enclosure types: Type 1 indoor general, Type 4/4X watertight (X = corrosion resistant), Type 7/9 hazardous gas/dust.

IEEE 519 limits harmonic current distortion at the point of common coupling; IEEE 1584 provides arc flash incident-energy calculations.

Half-splitting: measure at the midpoint of a signal chain to halve the search area; continue until the faulty component is isolated.

Motor insulation resistance: minimum acceptable ≈ 1 MΩ per kV of rated voltage plus 1 MΩ; Polarization Index (10 min / 1 min) > 2.0 is good.

Vibration analysis: 1× running speed = unbalance; 2× = misalignment; high-frequency broadband = bearing defect; bearing defect frequencies BPFO/BPFI/BSF/FTF.

Infrared thermography detects loose connections and overloaded conductors; compare phase-to-phase and ambient-referenced temperatures.

Thermography delta-T guides: 1–3 °C possible deficiency, 4–15 °C probable, >15 °C major, >40 °C critical.

Predictive maintenance uses condition monitoring (vibration, oil analysis, thermography, MCA) to schedule work before failure.

Reliability metrics: MTBF = total operating time / number of failures; availability = MTBF / (MTBF + MTTR).

Root cause analysis tools: 5 Whys, fishbone (Ishikawa), and fault tree analysis; always verify with physical evidence.