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Voltage Drop in Electric Circuits

Ohm's law and voltage drop in an electric circuit

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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:

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

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)

SizeFactor
- f -
AWGMetric
mm2
Single-phase3-phase
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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