Electrical Formulas Reference

V = I × R (Voltage = Current × Resistance)

I = V ÷ R (Current = Voltage ÷ Resistance)

R = V ÷ I (Resistance = Voltage ÷ Current)

KCL: ΣI_in = ΣI_out (Current Law)

KVL: ΣV = 0 (Voltage Law)

Sum of currents in = Sum of currents out

P = V × I (Power = Voltage × Current)

P = I² × R (Power = Current² × Resistance)

P = V² ÷ R (Power = Voltage² ÷ Resistance)

P = V × I × cos(θ) (Real Power)

Q = V × I × sin(θ) (Reactive Power)

S = V × I (Apparent Power)

S² = P² + Q²

PF = P ÷ S (Power Factor)

PF = cos(θ)

θ = arccos(PF)

P = √3 × V_L × I_L × cos(θ)

P = 3 × V_ph × I_ph × cos(θ)

Where V_L = Line voltage, I_L = Line current

Wye: V_L = √3 × V_ph, I_L = I_ph

Delta: V_L = V_ph, I_L = √3 × I_ph

VD = 2 × K × I × L ÷ CM

VD% = (VD ÷ V_applied) × 100

K = 12.9 (copper), 21.2 (aluminum)

L = Length (feet), CM = Circular mils

VD = 1.732 × K × I × L ÷ CM

VD% = (VD ÷ V_line) × 100

NEC limits: 3% feeders, 5% total

R = ρ × L ÷ A

ρ = Resistivity (ohm-cm)

L = Length (cm)

A = Cross-sectional area (cm²)

CM = d² (d = diameter in mils)

1 mil = 0.001 inch

MCM = CM ÷ 1000

HP = (T × RPM) ÷ 5252

kW = HP × 0.746

T = Torque (lb-ft)

1φ: I = (HP × 746) ÷ (V × eff × PF)

3φ: I = (HP × 746) ÷ (√3 × V × eff × PF)

Efficiency = P_out ÷ P_in

P_out = HP × 746 watts

V_p ÷ V_s = N_p ÷ N_s

I_p ÷ I_s = N_s ÷ N_p

p = primary, s = secondary, N = turns

1φ: I = kVA × 1000 ÷ V

3φ: I = kVA × 1000 ÷ (√3 × V)

Fill% = (Total Wire Area ÷ Conduit Area) × 100

NEC Limits:

1 wire: 53%, 2 wires: 31%, 3+ wires: 40%

Area = π × (d ÷ 2)²

d = Overall wire diameter (including insulation)

Use NEC Chapter 9 tables for exact values

R = (ρ ÷ 2πL) × ln(4L ÷ a)

ρ = Soil resistivity (ohm-meters)

L = Rod length (meters)

a = Rod radius (meters)

R_total = R_single ÷ (n × η)

n = Number of rods

η = Efficiency factor (0.6-0.9)

NEC: Maximum 25 ohms

X_C = 1 ÷ (2πfC)

f = Frequency (Hz)

C = Capacitance (Farads)

Q_C = P × (tan(θ₁) - tan(θ₂))

C = Q_C ÷ (2πfV²)

θ₁ = Original angle, θ₂ = Desired angle

E = ½CV² (Energy stored)

I = C × (dV/dt) (Charging current)

Ah = (Load × Hours) ÷ DOD

Wh = Ah × Voltage

DOD = Depth of Discharge (0.5-0.8)

Add 20% safety margin

Series: V_total = V₁ + V₂ + ...

Parallel: Ah_total = Ah₁ + Ah₂ + ...

Runtime = Ah ÷ Load (A)

X_L = 2πfL

f = Frequency (Hz)

L = Inductance (Henries)

Z = √(R² + (X_L - X_C)²)

θ = arctan((X_L - X_C) ÷ R)

f_r = 1 ÷ (2π√(LC))

At resonance: X_L = X_C

E = Φ ÷ A (Illuminance)

Φ = I × Ω (Luminous flux)

E = Lux, Φ = Lumens, A = Area (m²)

I = Luminous intensity (candelas)

Efficacy = Lumens ÷ Watts

Total Lumens = E × Area

Number of fixtures = Total Lumens ÷ Fixture Lumens

kWh = kW × hours

Cost = kWh × Rate ($/kWh)

Monthly kWh = Daily kWh × 30

Watts = Volts × Amps × PF

VA = Volts × Amps

kVA = VA ÷ 1000

E = 4.184 × C_f × E_n × (t ÷ 0.2) × (610^x ÷ D²)

E = Incident energy (cal/cm²)

D = Working distance (mm)

t = Arc duration (seconds)

PPE Categories:

Cat 1: 4 cal/cm², Cat 2: 8 cal/cm²

Cat 3: 25 cal/cm², Cat 4: 40 cal/cm²

Flash protection boundary calculation required