Resistance of Circular Wires


What is wire?

A wire is a single, usually cylindrical, flexible strand or rod of metal. Wires are used to bear mechanical loads or electricity and telecommunications signals. Wire is commonly formed by drawing the metal through a hole in a die or draw plate. Wire gauges come in various standard sizes, as expressed in terms of a gauge number. The term wire is also used more loosely to refer to a bundle of such strands, as in "multi-stranded wire", which is more correctly termed a wire rope in mechanics, or a cable in electricity.
Wire comes in solid core, stranded, or braided forms. Although usually circular in cross-section, wire can be made in square, hexagonal, flattened rectangular, or other cross-sections, either for decorative purposes, or for technical purposes such as high-efficiency voice coils in loudspeakers.
The resistance of any material is due primarily to four factors:
  • 1. Material
  • 2. Length
  • 3. Cross-sectional area
  • 4. Temperature of the material
The atomic structure determines how easily a free electron will pass through a material. The longer the path through which the free electron must pass, the greater is the resistance factor. Free electrons pass more easily through conductors with larger cross-sectional areas. In addition, the higher the temperature of the conductive materials, the greater is the internal vibration and motion of the components that make up the atomic structure of the wire, and the more difficult it is for the free electrons to find a path through the material.
The first three elements are related by the following basic equation for resistance:
$$\bbox[10px,border:1px solid grey]{R = \rho {L \over A}}\, \text{(ohm)} \, \tag{1}$$
$\rho = \text{CM-Ω/ft at T=20 ℃}$
$L= \text{Length(feet)}$
$A= \text{Area (in circular mils (CM))}$
The material is identified by a factor called the resistivity, which uses the Greek letter rho ($\rho$) as its symbol and is measured in CM-Ω/ft. Its value at a temperature of 20℃ (room temperature = 68℉) is provided in Table (1) for a variety of common materials.
Table No.1
It is important to realize at this point that since the resistivity is provided at a particular temperature, Eq. (1) is applicable only at room temperature. The effect of higher and lower temperatures is considered in next section.
The higher the resistivity, the greater is the resistance of a conductor.
The longer the conductor, the greater is the resistance.
The greater the area of a conductor, the less is the resistance.

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