VOLTAGE DROP EQUATIONS
Voltage Drop Equations
Voltage Drop = √3 I ( R Cos θ + X Sin θ) L
3∅
Voltage Drop = 21 ( R Cos θ + X Sin θ) L
1∅
Voltage Drop = in volts (V)
I = Current in amperes
R= Conductive resistance in ohms/ 1000 ft.
X= Conductor inductive reactance in ohms/1000 ft.
L= one way length of circuit ( source to load) in thousands of feet (K ft.)
Z = Complex impedance ohms/ 1000 ft. obtain from Tables.
θ = Phase angle of load
Cos θ = Power Factor: Motors see 6-5, 6-6, .6-.8 is usual see 5-1 to 5-8 for more power factor calculations,
also 8-2
Given voltage drop, find wire size
Voltage Drop 3∅ = √3 I (Z) L
Z = Voltage Drop = Vd
√3 I L √3 IL
Voltage Drop 1 ∅= 21 (Z) L
Z = Voltage Drop = Vd
2 I L 2 IL
Procedure (Example)
1. Assume a voltage drop, say 2 %, Base voltage 230V, 1∅ vd = .02(230)
2. Current and distance must be known I= 30A, L= .56K ft. .56Kft.Power factor must be known. P.F. =
.85
3. Solve for Z:Z = Vd/ 2 IL= 4.8V/2 (30A) (.5Kft) = 16Ω/ Kft
4. Look up Z in tables at 16Ω/ Kft, 85 P.F. Copper direct burial in nonmagnetic conduit. Always use wire
with next smaller impedance Z per 1,000 feet than that calculated.
6/14/02 Chapter 8: Voltage Drop Equations 1/5
