Electric Circuits Voltage Drop
Ohm's law and voltage drop in electric circuits.
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 ^{o}F  121 ^{o}F), K = 12 (temp 122 ^{o}F  167 ^{o}F)
 Solid Aluminum, K = 18 (temp 77 ^{o}F  121 ^{o}F), K = 20 (temp 122 ^{o}F  167 ^{o}F)
 Stranded Copper, K = 11 (temp 77 ^{o}F  121 ^{o}F), K = 12 (temp 122 ^{o}F  167 ^{o}F)
 Stranded Aluminum, K = 19 (temp 77 ^{o}F  121 ^{o}F), K = 20 (temp 122 ^{o}F  167 ^{o}F)
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)
Size  Factor  f   

AWG  Metric mm^{2}  
Singlephase  3phase  
14  2.08  0.476  0.42 
12  3.31  0.313  0.26 
10  5.26  0.196  0.17 
8  8.37  0.125  0.11 
6  13.3  0.0833  0.071 
4  21.2  0.0538  0.046 
3  0.0431  0.038  
2  33.6  0.0323  0.028 
1  42.4  0.0323  0.028 
1/0  53.5  0.0269  0.023 
2/0  67.4  0.0222  0.020 
3/0  85.0  0.019  0.016 
4/0  107.2  0.0161  0.014 
250  0.0147  0.013  
300  0.0131  0.011  
350  0.0121  0.011  
400  0.0115  0.009  
500  0.0101  0.009 
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