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Electrical resistivity and conductivity

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 ohmmetre [Î©m]. It is commonly represented by the Greek letterÏ� (rho).

Electrical conductivity or specific conductance is the reciprocal quantity, and measures a material's ability to conduct an electric current. It is commonly represented by the Greek letter Ïƒ, but Îº (esp. in electrical engineering) or Î³ are also occasionally used. Its SI unit is siemens per metre (SÂ·m-1) and CGSE unit is inverse second (sâ€“1):

\sigma = {1\over\rho}.

## Definitions

Electrical resistivity Ï� (Greek: rho) is defined by,

\rho={E \over J} \,\!

where

Ï� is the static resistivity (measured in ohm-metres, Î©-m)
E is the magnitude of the electric field (measured in volts per metre, V/m);
J is the magnitude of the current density (measured in amperes per square metre, A/mÂ²).

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 Ï� leads to:

\rho = R \frac{A}{\ell}, \,\!

where

R is the electrical resistance of a uniform specimen of the material (measured in ohms, Î©)
\ell is the length of the piece of material (measured inmetres, m)
A is the cross-sectional area of the specimen (measured in square metres, mÂ²).

## Explanation

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

R = \rho \frac{\ell}{A} \,\!

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 Ã— 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).

## Resistivity of various materials

• A conductor such as a metal has high conductivity and a low resistivity.
• An insulator like glass has low conductivity and a high resistivity.
• 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 and composition of the semiconductor material.

The degree of doping in semiconductors makes a large difference in conductivity. To a point, more doping leads to higher conductivity. The conductivity of a solution of water is highly dependent on its concentration of dissolved salts, and other chemical species that ionize in the solution. Electrical conductivity of water samples is used as an indicator of how salt-free, ion-free, or impurity-free the sample is; the purer the water, the lower the conductivity (the higher the resistivity). Conductivity measurements in water are often reported as specific conductance, the conductivity of the water at 25&nbsp;Â°C. An EC meter is normally used to measure conductivity in a solution.

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

The effective temperature coefficient varies with temperature and purity level of the material. The 20&nbsp;Â°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&nbsp;Â°C. For further reading: http://library.bldrdoc.gov/docs/nbshb100.pdf.

The extremely low resistivity (high conductivity) of silver is characteristic of metals. George Gamow tidily summed up the nature of the metals' dealings with electrons in his science-popularizing book, One, Two, Three...Infinity (1947): "The metallic substa

Thermal conductivity

In physics, thermal conductivity, k, is the property of a material describing its ability to conduct heat. It appears primarily in Fourier's Law for heat conduction. Thermal conductivity is measured in watts per kelvin-metre (WÂ·Kâˆ’1Â·mâˆ’1, i.e. W/(KÂ·m). Multiplied by a temperature difference (in kelvins, K) and an area (in square metres, m2), and divided by a thickness (in metres, m), the thermal conductivity predicts the rate of energy loss (in watts, W) through a piece of material. In the window building industry "thermal conductivity" is expressed as the [http://www.energystar.gov/index.cfm?c=windows_doors.pr_ind_tested U-Factor] measures the rate of heat transfer and tells you how well the window insulates. U-factor values generally range from 0.15 to 1.25 and are measured in Btu per hour - square foot - degree Fahrenheit (ie. Btu/hÂ·ftÂ²Â·Â°F). The lower the U-factor, the better the window insulates.

The reciprocal of thermal conductivity is thermal resistivity.

## Measurement

There are a number of ways to measure thermal conductivity. Each of these is suitable for a limited range of materials, depending on the thermal properties and the medium temperature. There is a distinction between steady-state and transient techniques.

In general, steady-state techniques are useful when the temperature of the material does not change with time. This makes the signal analysis straightforward (steady state implies constant signals). The disadvantage is that a well-engineered experimental setup is usually needed. The Divided Bar (various types) is the most common device used for consolidated rock samples.

The transient techniques perform a measurement during the process of heating up. Their advantage is quicker measurements. Transient methods are usually carried out by needle probes.

### Standards

• IEEE Standard 442-1981, "IEEE guide for soil thermal resistivity measurements", ISBN 0-7381-0794-8. See also soil thermal properties. [http://ieeexplore.ieee.org/servlet/opac?punumber=2543]
• IEEE Standard 98-2002, "Standard for the Preparation of Test Procedures for the Thermal Evaluation of Solid Electrical Insulating Materials", ISBN 0-7381-3277-2 [http://ieeexplore.ieee.org/servlet/opac?punumber=7893]
• ASTM Standard D5334-08, "Standard Test Method for Determination of Thermal Conductivity of Soil and Soft Rock by Thermal Needle Probe Procedure"
• ASTM Standard D5470-06, "Standard Test Method for Thermal Transmission Properties of Thermally Conductive Electrical Insulation Materials" [http://www.astm.org/cgi-bin/SoftCart.exe/DATABASE.CART/REDLINE_PAGES/D5470.htm?E+mystore]
• ASTM Standard E1225-04, "Standard Test Method for Thermal Conductivity of Solids by Means of the Guarded-Comparative-Longitudinal Heat Flow Technique" [http://www.astm.org/cgi-bin/SoftCart.exe/DATABASE.CART/REDLINE_PAGES/E1225.htm?L+mystore+wnox2486+1189558298]
• ASTM Standard D5930-01, "Standard Test Method for Thermal Conductivity of Plastics by Means of a Transient Line-Source Technique" [http://www.astm.org/cgi-bin/SoftCart.exe/STORE/filtrexx40.cgi?U+mystore+wnox2486+-L+THERMAL:CONDUCTIVITY+/usr6/htdocs/astm.org/DATABASE.CART/REDLINE_PAGES/D5930.htm]
• ASTM Standard D2717-95, "Standard Test Method for Thermal Conductivity of Liquids" [http://www.astm.org/cgi-bin/SoftCart.exe/DATABASE.CART/REDLINE_PAGES/D2717.htm?L+mystore+wnox2486+1189564966]
• ISO 22007-2:2008 "Plastics -- Determination of thermal conductivity and thermal diffusivity -- Part 2: Transient plane heat source (hot disc) method" [http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=40683]
• Note: What is called the k-value of construction materials (e.g. window glass) in the U.S., is called Î»-value in Europe. What is called U-value (= the inverse of R-value) in the U.S., used to be called k-value in Europe, but is now also called U-value in Europe.

## Definitions

The reciprocal of thermal conductivity is thermal resistivity, usually measured in kelvin-metres per watt (KÂ·mÂ·Wâˆ’1). When dealing with a known amount of material, its thermal conductance and the reciprocal property, thermal resistance, can be described. Unfortunately, there are differing definitions for these terms.

### Conductance

For general scientific use, thermal conductance is the quantity of heat that passes in unit time through a plate of particular area and thickness when its opposite faces differ in temperature by one kelvin. For a plate of thermal conductivity k, area A and thickness L this is kA/L, measured in WÂ·Kâˆ’1 (equivalent to: W/Â°C). Thermal conductivity and conductance are analogous to electrical conductivity (AÂ·mâˆ’1Â·Vâˆ’1) and electrical conductance (AÂ·Vâˆ’1).

There is also a measure known as heat transfer coefficient: the quantity of heat that passes in unit time through unit area of a plate of particular thickness when its opposite faces differ in temperature by one kelvin. The reciprocal is thermal insulance. In summary:

• thermal conductance = kA/L, measured in WÂ·Kâˆ’1
• thermal resistance = L/(kA), measured in KÂ·Wâˆ’1 (equivalent to: Â°C/W)
• heat transfer coefficient = k/L, measured in WÂ·Kâˆ’1Â·mâˆ’2
• thermal insulance = L/k, measured in KÂ·mÂ²Â·Wâˆ’1.

The heat transfer coefficient is also known as thermal admittance

### Resistance

When thermal resistances occur in series, they are additive. So when heat flows through two components each with a resistance of 1 Â°C/W, the total resistance is 2 Â°C/W.

A common engineering design problem involves the selection of an appropriate sized heat sink for a given heat source. Working in units of thermal resistance greatly simplifies the design calculation. The following formula can be used to estimate the performance:

R_{hs} = \frac {\Delta T}{P_{th}} - R_s

where:

• Rhs is the maximum thermal resistance of the heat sink to ambient, in Â°C/W
• \Delta T is the temperature difference (temperature drop), in Â°C
• Pth is the thermal power (heat flow), in watts
• Rs is the thermal resistance of the heat source, in Â°C/W

For example, if a component produces 100 W of heat, and has a thermal resistance of 0.5 Â°C/W, what is the maximum thermal resistance of the heat sink? Sup

Question:I can't find out how to make an electrical conductivity apparatus. Can someone please give a detailed description or link to a good site.

Answers:Check out this diagram. http://www.uq.edu.au/_School_Science_Lessons/3.59ch.GIF Use graphite pencils for the electrodes. Sharpen each end to provide a place to attach the alligator clips. Use a flashlight lamp and the correct number of cells for the lamp.

Question:For a project, I need to find the thermal AND electrical conductivity level for several elements. How can I tell this? And/Or where can I look to find it? I have had trouble finding it online and its not in my textbook. Also, how to I find the level of reactivity? Lastly, the Ion Charge?? Please Help!!

Answers:just search online for "resistivity table", that is more useful. conductivity is just 1/resistivity. and search for "thermal conductivity table" to get the thermal numbers. here are the ones I have. resistivity Ag 15.9e-9 -m resistivity Cu 17.2e-9 -m or 17.2e-6 ohm-mm resistivity Au 22.14e-9 -m resistivity Al 28.2e-9 -m resistivity brass 35e-9 -m resistivity W 56e-9 -m resistivity Zn 68e-9 -m resistivity Fe 100e-9 -m resistivity Pt 105e-9 -m resistivity Nichrome 150e-8 -m thermal conductivity, all in W/mK Silver429 W/mK Copper401 Gold310 Aluminum 250 Beryllium218 Magnesium156 Zinc Zn116 Brass109 Nickel91 Iron80 Platinum70 Tin Sn67 Steel 46 Lead 35 Antimony18.5 Stainless Steel16 Mercury8 .

Question:Describe one method you could choose to determine the electrical conductivity of a length of 25mm diameter aluminium bar.

Answers:Put my Fluke 87 on MHO's and measure it then divided by 1000.

Question:I understand that quartz is used in the manufacture of semiconductors. How is this mineral able to conduct electricity? I think it is both covalently and ionically bonded. I am new to this stuff and cannot see if it is solid how electricity is able to be conducted

Answers:I answered the other one let me delve into it more... first, quartz can conduct actually, if you've ever owmed a quartz watch or heard of a cesium clock.... If you pass DC voltage into a crystal the crystal....well it gets pissed and vibrates....the output current from the crystal has a AC signature at a known frequency. YOu can then amplify it and pass it through frequency dividers to get 1 hzt, or 5Mhz etc. In wafers, they don't work the same way, the Si doesn't conduct....it's the "board" in which conductive materals are placed to form the logic circuit, but it's all on the surface. Hope this clears it up, chemicals like gemanium, carbon, do all the work, then when the the wafer has all it's channels done it becomes a "back end wafer" and metals are deposited on it to finish up at the very top.