Electric Circuits Voltage Drop

Voltage drop in an electric circuit can be calculated using Ohm's law as

U = R I (1)

where

U = voltage drop (volts, V)

R = electrical resistance in the electric circuit (ohms, Ω)

I = current (amps, A)

Example - Voltage Drop

Voltage drop in a 100 ft power line:

• 2 x 100 ft
• #10 copper
• electrical resistance 1.02 Ω /1000 ft
• current 10 amps

The electric resistance in the circuit can be calculated

R = (1.02 Ω/1000 ft) (100 ft) 2

= 0.204 Ω

The voltage drop in the circuit can be calculated with (1)

U = ( 0.204 Ω ) (10 amps)

= 2.04 volts

Circular mils and Voltage drop

Voltage drop can also be calculated using mils like

U = K P L I / A                       (2)

where

K = specific resistivity ( Ω - circular mils/foot)

P = phase constant = 2 (for single phase) = 1.732 (for three phase)

L =  wire length (ft)

A = wire area ( circular mils )

Specific electric resistivity for different types of wire materials

• Solid Copper, K = 11 (temp 77 ^oF - 121 ^oF), K = 12 (temp 122 ^oF - 167 ^oF)
• Solid Aluminum, K = 18 (temp 77 ^oF - 121 ^oF), K = 20 (temp 122 ^oF - 167 ^oF)
• Stranded Copper, K = 11 (temp 77 ^oF - 121 ^oF), K = 12 (temp 122 ^oF - 167 ^oF)
• Stranded Aluminum, K = 19 (temp 77 ^oF - 121 ^oF), K = 20 (temp 122 ^oF - 167 ^oF)

Example - Specific resistivity and Voltage Drop

With values from the example above the voltage drop can be calculated as

U = (11 ohm - circular mils/foot) 2 (100 ft) (10 A) / (10400 mils)

= 2.11 V

Copper Conductor - Voltage Drop Table

The voltage drop in a copper conductor can be estimated with

U = f I L                          (3)

where

f = factor from table below

I = current (amps)

L = conductor length (ft)

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm