06 February, 2007

Resistivity and Conductivity

Resistivity and Conductivity :
Resistivity is the electrical resistance offered by a homogeneous unit cube of material to the flow of a direct current of uniform density between opposite faces of the cube. Also called specific resistance, it is an intrinsic, bulk (not thin-film) property of a material. Resistivity is usually determined by calculation from the measurement of electrical resistance of samples having a known length and uniform cross section according to the following equation where ? is the resistivity, R the measured resistance, A the cross-sectional area, and l the length. In the mks system (SI), the unit of resistivity is the ohm-meter. Therefore, in the equation below, resistance is expressed in ohms, and the sample dimensions in meters.

Resistivity is also temperature dependent.Resistivity increases by about 0.4%/K at room temperature and is nearly proportional to the absolute temperature over wide temperature ranges.The room-temperature resistivity of pure metals extends from approximately 1.5 × 10^-8 ohm-meter for silver, the best conductor, to 135 × 10^-8 ohm-meter for manganese, the poorest pure metallic conductor. Most metallic alloys also fall within the same range. Insulators have resistivities within the approximate range of 10^8 to 10^16 ohm-meters. The resistivity of semiconductor materials, such as silicon and germanium, depends not only on the basic material but to a considerable extent on the type and amount of impurities in the base material. Large variations result from small changes in composition, particularly at very low concentrations of impurities. Values typically range from 10^-4 to 10^5 ohm-meters.

Conductivity :
Electrical conductivity is a measure of a material's ability to conduct an electric current. When an electric potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current. The conductivity σ is defined as the ratio of the current density J to the electic field strength E:

Conductivity is the reciprocal (inverse) of electrical resistivity and has the SI units of siemens per metre (S·m-1) i.e. if the electrical conductance between opposite faces of a 1-metre cube of material is 1 siemens then the material's electrical conductivity is 1 siemens per metre. Elecrical conductivity is commonly represented by the Greek letter σ, but κ or γ are also occasionally used.

Classification of materials by conductivity :

  • A conductor such as a metal has high conductivity.
  • An insulator like glass or a vacuum has low conductivity.
  • The conductivity of a semiconductor is generally intermediate, but varies widely under different conditions, such as exposure of the material to electric fields or specific frequencies of light, and, most important, with temperature.
Temperature Dependence :
Electrical conductivity is more or less strongly dependent on temperature. In metals, electrical conductivity decreases with increasing temperature, whereas in semiconductors, electrical conductivity increases with increasing temperature. Over a limited temperature range, the electrical conductivity can be approximated as being directly proportional to temperature. In order to compare electrical conductivity measurements at different temperatures, they need to be standardized to a common temperature. This dependence is often expressed as a slope in the conductivity-vs-temperature graph, and can be used:

where
σT′ is the electrical conductivity at a common temperature, T′
σT is the electrical conductivity at a measured temperature, T
α is the temperature compensation slope of the material,
T is the measured temperature,
T′ is the common temperature.

The temperature compensation slope for most naturally occurring waters is about 2 %/°C, however it can range between (1 to 3) %/°C. This slope is influenced by the geochemistry, and can be easily determined in a laboratory.

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