In order to compare the resistance and conductor sizes with each other, we need to establish a convenient unit. This unit is the mil-foot (mil-ft). A conductor will possess this unit size if having one mil (0.001 inches) diameter and a length of one foot.

The standardized unit for wire cross-sectional area is circular mil. Since the round conductor’s diameter is generally a small fraction of an inch, it is quite handy to demonstrate them in mils, which is equivalent to 1/1000 of an inch, for avoiding the use of decimals.

For instance, the conductor diameter can be stated as 25 mils instead of 0.025 in. A circular mil, in fact, is the area of a circle whose diameter is one mil, as depicted in figure 1.

Fig.1: Circular Mil

The area of a round conductor in circular mils is acquired by squaring up the diameter which is calculated in mils. This convention is an engineering agreement which is in practice for last many decades and is not quite associated to the circle area being equivalent to $\pi {{r}^{2}}$.

Example

What is the circular mil area of a round conductor with a diameter of 25 mils?

Solution

$A={{d}^{2}}={{25}^{2}}=635\text{ c}\text{.mils}$

A circular mil-foot, as demonstrated in figure 2, is, in reality, a volume unit. It holds a one circular mil cross-sectional area and a length of one foot. Since it is conceived a unit conductor, the circular mil-foot is very valuable in order to make comparisons between conductors formed of dissimilar metallic elements. For instance, a resistivity comparison of different conductors’ types can be made by finding out the resistance of a circular mil-foot of each conductor.

Fig.2: Circular Mil-Foot

**Specific Resistance or Resistivity**

The resistance of a conductor expressed in ohms per unit length per unit area, that is, per circular mil-foot.

Specific Resistance can be described as the resistance (calculated in ohms) offered by a unit volume (which is equivalent to the circular mil-foot) of a substance (material) to the electrical current flow. A substance that possesses higher resistivity will offer low conductivity, and vice versa. For instance, the cooper specific resistance is $10.4\text{ }{}^{\Omega }/{}_{mil-ft}$ . Put differently, a copper conductor of the cross-sectional area and a length of 1 foot possesses 10.4 Ω resistance.

A list of specific resistivities of several different types of materials is given in table 1. The values indicated are based on 20 ^{o}C.

Material | Resistivity |
---|---|

Silver | 9.56 |

Copper | 10.4 |

Gold | 14 |

Aluminum | 17 |

Tungsten | 34 |

Brass | 42 |

Iron | 61 |

Nichrome | 675 |

Table 1: Specific Resistivities (${}^{\Omega }/{}_{c.mil-ft}$ at 20 ^{o}C)

## Calculation of Resistance

The relationship of specific resistance, length, and cross-sectional area is given by the following equation:

$R=\rho \frac{L}{A}$

Where

ρ= specific resistance

L= length in feet

A= cross-section area in circular mils

The following example illustrates the use of this formula.

**Example**

Calculate the resistance of a piece of copper wire at 20 ^{o}C if it is 25 ft long and 40 mils in diameter.

**Solution**

$A={{d}^{2}}={{25}^{2}}=1600\text{ c}\text{.mils}$

Substitute in the above mentioned formula, we come up with

$R=10.4*\frac{25}{1600}=0.163\text{ }\Omega $

**American Wire Gauge**

The system of notation for measuring the size of conductors or wires.

Wires are manufactured in sizes numbered according to the American wire gage (AWG). Some of these numbers appear in Table 1. Notice that the wire diameters become smaller as the gage numbers increase. In typical applications, where the current is mill amperes, a #22 number wire would be used. By comparison, a #14 wire is customarily used in residential-lightning circuits and #12 for wall plugs. When any conductor is selected, consideration must be given to the maximum current it can safely carry and the voltage its insulation can stand without breakdown.

Gage number | Diameter (mils) | Circular mil area | Ohms per 1000 ft |
---|---|---|---|

0 | 365 | 133000 | 0.0795 |

0 | 325 | 106000 | 0.1 |

1 | 289 | 83700 | 0.126 |

2 | 258 | 66400 | 0.159 |

3 | 229 | 52600 | 0.201 |

4 | 204 | 41700 | 0.253 |

5 | 182 | 33100 | 0.319 |

6 | 162 | 26300 | 0.403 |

7 | 144 | 20800 | 0.508 |

8 | 128 | 16500 | 0.641 |

9 | 114 | 13100 | 0.808 |

10 | 102 | 10400 | 1.02 |

11 | 91 | 8230 | 1.28 |

12 | 81 | 6530 | 1.62 |

13 | 72 | 5180 | 2.04 |

14 | 64 | 4110 | 2.58 |

15 | 57 | 3260 | 3.25 |

16 | 51 | 2580 | 4.09 |

17 | 45 | 2050 | 5.16 |

18 | 40 | 1620 | 6.51 |

19 | 36 | 1290 | 8.21 |

20 | 32 | 1020 | 10.4 |

21 | 28.5 | 810 | 13.1 |

22 | 25.3 | 642 | 16.5 |

23 | 22.6 | 509 | 20.8 |

24 | 20.1 | 404 | 26.2 |

25 | 17.9 | 320 | 33 |

26 | 15.9 | 254 | 41.6 |

27 | 14.2 | 202 | 52.5 |

28 | 12.6 | 160 | 66.2 |

29 | 11.3 | 127 | 83.4 |

30 | 10 | 101 | 105 |

31 | 8.9 | 79.7 | 133 |

32 | 8 | 63.2 | 167 |

33 | 7.1 | 50.1 | 211 |

34 | 6.3 | 39.8 | 266 |

35 | 5.6 | 31.5 | 335 |

36 | 5 | 25 | 423 |

Table.2: American Wire Gauge (AWG) Wire Sizes

Copper is most frequently used for wire conductors because it has a low resistance per unit length, is less expensive than silver or gold, and is easily solderable. The copper is usually tinned (covered with a thin coating of solder) and may be solid or stranded.

Twin-lead transmission line

A type of transmission line comprised of two parallel conductors covered by a solid insulation.

Coaxial cable

A transmission line in which one conductor is concentric to another and separated by a continuous solid dielectric spacer.

Many electric cables are used in industry to interconnect components. Cables consist of two or more conductors within a common covering. Figure 1 shows a typical 300 Ω twin-lead transmission line, or cable, such as used in TV to connect the antenna to the receiver.

Fig.3: Twin-Lead Transmission Line

The cable shown in figure 2 is a coaxial cable, which is used extensively for conducting high-frequency currents and consists of an inner conductor surrounded by polyethylene or other highly resistive insulation. Over the insulation is a flexible, tinned copper braid, which is in turn enclosed in a vinyl jacket. The inner conductor and braid constitute the two leads.

Fig.4: Coaxial Cable

**Aluminum Conductors**

Although aluminum has only about 60 % of the conductivity of copper, it is much lighter in weight than copper and is now frequently used by the electrical power companies. Because aluminum conductors are not easily soldered, lugs, or terminals, are generally fastened to them by special tools.