# Voltage Drop in Electric Circuits

## Ohm's law and voltage drop in an electric circuit

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 = (11ohm- 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 | Metricmm^{2} | ||

Single-phase | 3-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 |