Resistivity

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Electrical resistivity (also known as resistivity, specific electrical resistance, or volume resistivity) is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre [Ω m].

Contents

Definitions

Electrical resistivity ρ (Greek: rho) is defined by,

where

Most resistors and conductors have a uniform cross section with a uniform flow of electric current and are made of one material. (See the diagram to the right.) In this case, the above definition of ρ leads to:

where

Finally, electrical resistivity is also defined as the inverse of the conductivity σ (sigma), of the material, or

Explanation

The reason resistivity has the dimension units of ohm-metres can be seen by transposing the definition to make resistance the subject:

The resistance of a given sample will increase with the length, but decrease with greater cross sectional area. Resistance is measured in ohms. Length over area has units of 1/distance. To end up with ohms, resistivity must be in the units of "ohms × distance" (SI ohm-metre, US ohm-inch).

In a hydraulic analogy, increasing the diameter of a pipe reduces its resistance to flow, and increasing the length increases resistance to flow (and pressure drop for a given flow).

Table of resistivities

This table shows the resistivity and temperature coefficient of various materials at 20 °C (68 °F)

*The numbers in this column increase or decrease the significand portion of the resistivity. For example, at 30 °C (303 K), the resistivity of silver is 1.65×10−8. This is calculated as Δρ = α ΔT ρo where ρo is the resistivity at 20 °C (in this case) and α is the temperature coefficient.

The effective temperature coefficient varies with temperature and purity level of the material. The 20 °C value is only an approximation when used at other temperatures. For example, the coefficient becomes lower at higher temperatures for copper, and the value 0.00427 is commonly specified at 0 °C. For further reading: http://library.bldrdoc.gov/docs/nbshb100.pdf.

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