For comparison of the resistance and the size of one conductor with another, some convenient unit must be established. This unit is the mil-foot (mil-ft). a conductor will have this unit size if it has a diameter of one mil (0.001 inches) and is one foot long.

The circular mil (c mil) is the standard unit of wire cross-sectional area. Because the diameter of round conductors is usually only a small fraction of an inch, it is convenient to express them in mils, equal to 1/1000 of an inch, to avoid the use of decimals.

For example, the diameter of a conductor is expressed as 25 mils rather than 0.025 in. a circular mil is the area of a circle having a diameter of one mil, as illustrated in figure 1.

Fig.1: Circular Mil

The area is circular mils of a round conductor is obtained by squaring the diameter measured in mils. This rule is an engineering agreement dating back many decades and is not related to the area of a circle being equal 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 shown in figure 2, is actually a unit of volume. It is one foot long and has a cross-sectional area of one circular mil. Because it is considered a unit conductor, the circular mil-foot is useful in making comparisons between conductors made of different metals. For example, a comparison of the resistivity of various types of conductors may be made by determining the resistance of a circular mil-foot of each of the conductors.

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.ohms per unit length per unit area, that is, per circular mil-foot.

Specific resistance or resistivity is the resistance in ohms offered by unit volume (the circular mil-foot) of a material to the flow of electric current.

A substance that has high resistivity will have low conductivity and vice versa. For example, the **specific resistance of copper** is $10.4\text{ }{}^{\Omega }/{}_{mil-ft}$ . in other words, a copper wire 1 c.mil in cross-sectional area and 1 foot long has 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.

The resistance of a conductor of a uniform cross-sectional area is directly proportional to length and inversely proportional to cross-sectional area. Thus, if the length of a particular conductor were unchanged but its cross-sectional are doubled, the resistance would be reduced by one-half.

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 (AWG)**

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

Wires are manufactured in sizes numbered according to the American wire gauge (AWG). Some of these numbers appear in Table 1. Notice that the wire diameters become smaller as the gauge numbers increase. In typical applications, where the current is mill amperes, a #22 number wire would be sued. 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 separately 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 3 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 4 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 insulations. 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.