Ohm's Law & Power Formulas
Ohm's Law: V = I × R | I = V / R | R = V / I. These three relationships are the foundation of all electrical calculations. Voltage (V) in volts, Current (I) in amps, Resistance (R) in ohms.
Power (Watt's Law): P = V × I | P = I² × R | P = V² / R. Power (P) in watts. These formulas apply to DC circuits and purely resistive AC circuits.
Three-Phase Power: P = V_LL × I_L × √3 × PF (line values) | P = 3 × V_Ph × I_Ph × PF (phase values). Where √3 = 1.732, V_LL = line-to-line voltage, I_L = line current, PF = power factor.
Power Triangle: Apparent Power (kVA) = √(kW² + kVAR²). Power Factor = kW / kVA = cos θ. Reactive Power (kVAR) = kVA × sin θ.
NEC Conductor Sizing
Branch circuit conductors: minimum ampacity ≥ 125% of continuous load + 100% of non-continuous load (NEC 210.19(A)).
Motor conductors: minimum ampacity ≥ 125% of motor FLC from Table 430.248/250 (NEC 430.22).
Feeder for multiple motors: 125% of largest motor FLC + sum of all other motor FLCs (NEC 430.24).
Voltage drop: VD = 2 × L × I × R / 1000 (single-phase) | VD = √3 × L × I × R / 1000 (three-phase). Target ≤ 3% branch, ≤ 5% total.
Overcurrent Protection
Standard breaker sizes: 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100, 110, 125, 150, 175, 200A (NEC 240.6(A)).
Small conductor limits: 14 AWG = 15A max, 12 AWG = 20A max, 10 AWG = 30A max (NEC 240.4(D)).
Motor SCGF (inverse-time breaker): max 250% of FLC. If motor won't start, may increase to 400% (NEC 430.52).
Motor SCGF (dual-element fuse): max 175% of FLC. May increase to 225% (NEC 430.52).
Transformer protection: >9A primary → max 125%. ≤9A → max 167%. ≤2A → max 300% (NEC Table 450.3(B)).
Conduit Fill & Box Fill
Conduit fill: 1 conductor = 53%, 2 conductors = 31%, 3+ conductors = 40% of conduit area.
Nipple exception: conduits ≤ 24 inches may be filled to 60%.
Box fill (NEC 314.16(B)): each 14 AWG conductor = 2.0 in³, 12 AWG = 2.25 in³, 10 AWG = 2.5 in³, 8 AWG = 3.0 in³, 6 AWG = 5.0 in³.
Box fill additions: clamps = 1 × largest conductor volume, fixture studs = 1 × largest, devices = 2 × largest, all grounds = 1 × largest.
Residential Load Calculations
General lighting: 3 VA/ft² × square footage.
Small appliance circuits: 2 × 1,500 VA = 3,000 VA minimum.
Laundry circuit: 1 × 1,500 VA.
Demand factors (Table 220.42): first 3,000 VA at 100%, remainder at 35%.
Range: Table 220.55 — single range ≤ 12 kW → use 8 kW.
Dryer: 5,000 VA or nameplate, whichever is larger.
HVAC: use the larger of heating or cooling load (NEC 220.60).
Service sizing: total demand VA ÷ 240V = minimum service amps.
Quick Reference Values
1 HP = 746 watts. 1 ton (HVAC) ≈ 12,000 BTU/hr ≈ 3.517 kW.
Transformer primary-secondary current: I₁/I₂ = V₂/V₁ = N₂/N₁ (inverse voltage ratio).
Three-phase line vs phase: V_LL = V_Ph × √3 (wye). I_L = I_Ph (wye). V_LL = V_Ph (delta). I_L = I_Ph × √3 (delta).
Efficiency: η = (output power / input power) × 100%. Motor input = HP × 746 / η.
Temperature conversion: °F = (°C × 9/5) + 32. °C = (°F - 32) × 5/9.