Definition of Electrical Resistivity

Electrical resistivity ρ (Greek: rho) is defined by, where ρ is the static resistivity (measured in ohm-metres, Ω-m) E is the magnitude of the electric field (measured in volts per metre, V/m);AZ70XX J is the magnitude of the current density (measured in amperes per square metre, A/m²). Many 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: AZ70XX where R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ω) is the length of the piece of material (measured in metres, m)AZV99 A is the cross-sectional area of the specimen (measured in square metres, m²). 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 low-noise amplifier or pre-amp the noise characteristics of a resistor may be an issue. In a hydraulic analogy, increasing the cross-sectional area of a pipe reduces its resistance to flow, AZV99and increasing the length increases resistance to flow (and pressure drop for a given flow). Practical resistors include a series inductance and a small parallel capacitance; these specifications can be important in high-frequency applications.
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