Electrical resistance, expressed in ohms, is different from resistivity. To understand what resistivity is, it is necessary to relate it to the physical properties of the material.

About specific conductivity and specific resistance

The flow of electrons does not travel unhindered through the material. At a constant temperature, elementary particles swing around a state of rest. In addition, electrons in the conduction band interfere with each other by mutual repulsion due to the same charge. Thus, resistance arises.

Conductivity is an intrinsic characteristic of materials and quantifies the ease with which charges can move when a substance is exposed electric field... Resistivity is the reciprocal and is characterized by the degree of difficulty that electrons encounter in moving around in a material, giving an idea of ​​how good or bad a conductor is.

Important! Specific electrical resistance a high value indicates that the material is poorly conductive, and a low value indicates a good conductive material.

Specific conductivity is denoted by the letter σ and is calculated using the formula:

Resistivity ρ, as a reciprocal, can be found as follows:

In this expression, E is the strength of the generated electric field (V / m), and J is the density of the electric current (A / m²). Then the unit of measurement of ρ will be:

W / mx m² / A = ohm m.

For conductivity σ, the unit in which it is measured is S / m or siemens per meter.

Types of materials

According to the resistivity of materials, they can be classified into several types:

1. Conductors. These include all metals, alloys, solutions dissociated into ions, as well as thermally excited gases, including plasma. Of non-metals, graphite can be cited as an example;
2. Semiconductors, which are actually non-conductive materials, whose crystal lattices are purposefully doped with the inclusion of foreign atoms with more or less bound electrons. As a result, quasi-free excess electrons or holes are formed in the lattice structure, which contribute to the current conductivity;
3. Dissociated dielectrics or insulators are all materials that normal conditions do not have free electrons.

For the transport of electrical energy or in electrical installations for household and industrial purposes, a frequently used material is copper in the form of single-core or multi-core cables. Alternatively, the metal used is aluminum, although the resistivity of copper is 60% of that of aluminum. But it is much lighter than copper, which predetermined its use in power lines of networks. high voltage... Gold is used as a conductor in special-purpose electrical circuits.

Interesting. The electrical conductivity of pure copper was adopted by the International Electrotechnical Commission in 1913 as the standard for this value. By definition, the conductivity of copper measured at 20 ° is 0.58108 S / m. This value is called 100% LACS, and the conductivity of the rest of the materials is expressed as a specific percentage of LACS.

Most metals have a conductivity value of less than 100% LACS. However, there are exceptions such as silver or very high conductivity special copper designated C-103 and C-110, respectively.

Dielectrics do not conduct electricity and are used as insulators. Examples of insulators:

• glass,
• ceramics,
• plastic,
• rubber,
• mica,
• wax,
• paper,
• dry wood,
• porcelain,
• some fats for industrial and electrical use; and bakelite.

The transitions between the three groups are fluid. It is known for sure: there are no absolutely non-conductive media and materials. For example, air is an insulator at room temperature, but in conditions of a strong low frequency signal, it can become a conductor.

Determination of conductivity

If we compare the electrical resistivity various substances, standardized measurement conditions are required:

1. In the case of liquids, poor conductors and insulators, use cube specimens with a rib length of 10 mm;
2. The values ​​of the resistivity of soils and geological formations are determined on cubes with a length of each edge of 1 m;
3. The conductivity of a solution depends on the concentration of its ions. The concentrated solution is less dissociated and has fewer charge carriers, which lowers the conductivity. As the dilution increases, the number of ion pairs increases. The concentration of the solutions is set at 10%;
4. To determine the resistivity of metal conductors, wires of one meter length and a cross-section of 1 mm² are used.

If a material such as a metal can provide free electrons, then when a potential difference is applied, the wire will flow electricity... As the voltage increases, more electrons move through the substance in a unit of time. If all additional parameters (temperature, cross-sectional area, wire length and material) are unchanged, then the ratio of the current strength to the applied voltage is also constant and is called conductivity:

Accordingly, the electrical resistance will be:

The result is obtained in ohms.

In turn, the conductor can be of different lengths, cross-sectional sizes and made of various materials, which determines the value of R. Mathematically, this dependence looks like this:

The material factor takes into account the ρ factor.

From here, you can derive the formula for the resistivity:

If the values ​​of S and l correspond to the given conditions for the comparative calculation of the resistivity, ie 1 mm² and 1 m, then ρ = R. When changing the dimensions of the conductor, the number of ohms also changes.

Resistivity of popular conductors (metals and alloys). Steel resistivity

Resistivity of iron, aluminum and other conductors

The transmission of electricity over long distances requires taking care of minimizing losses resulting from the overcoming of the current resistance of the conductors that make up electric line... Of course, this does not mean that such losses, already occurring specifically in circuits and consumer devices, do not play a role.

Therefore, it is important to know the parameters of all elements and materials used. And not only electrical, but also mechanical. And have some handy reference materials available to compare performance different materials and choose for design and operation exactly what will be optimal in a specific situation. In power transmission lines, where the task is most productive, that is, with high efficiency, to bring energy to the consumer, both the economy of losses and the mechanics of the lines themselves are taken into account. The final economic efficiency of the line depends on the mechanics - that is, the device and the location of the conductors, insulators, supports, step-up / step-down transformers, the weight and strength of all structures, including wires stretched over long distances, as well as the materials chosen for each structural element. , its work and operating costs. In addition, in lines that transmit electricity, there are higher requirements for ensuring the safety of both the lines themselves and everything around them where they pass. And this adds costs to both the provision of electricity wiring and an additional margin of safety for all structures.

For comparison, data are usually presented in a single, comparable form. Often, the epithet “specific” is added to such characteristics, and the values ​​themselves are considered on some standards unified in terms of physical parameters. For example, electrical resistivity is the resistance (ohm) of a conductor made of some kind of metal (copper, aluminum, steel, tungsten, gold) that has a unit length and a unit cross-section in the system of units used (usually in SI). In addition, the temperature is negotiated, since when heated, the resistance of the conductors can behave differently. It is based on normal average operating conditions - at 20 degrees Celsius. And where properties are important when changing the parameters of the medium (temperature, pressure), coefficients are introduced and additional tables and graphs of dependencies are drawn up.

Resistivity types

Since resistance happens:

• active - or ohmic, resistive - resulting from the consumption of electricity for heating a conductor (metal) when an electric current passes through it, and
• reactive - capacitive or inductive, - which comes from the inevitable losses due to the creation of all sorts of changes in the current passing through the conductor of electric fields, then the resistivity of the conductor is of two types:

1. Specific electrical resistance to direct current (having a resistive character) and
2. Specific electrical resistance to alternating current (having a reactive character).

Here, type 2 resistivity is a complex value, it consists of two TP components - active and reactive, since resistive resistance always exists when current flows, regardless of its nature, and reactive resistance occurs only with any change in current in the circuits. In DC circuits, reactance arises only during transient processes, which are associated with turning on the current (changing the current from 0 to rated) or turning off (changing from rated to 0). And they are usually taken into account only when designing overload protection.

In chains alternating current the phenomena associated with reactances are much more diverse. They depend not only on the actual passage of the current through a certain section, but also on the shape of the conductor, and the dependence is not linear.

The fact is that alternating current induces electric field both around the conductor through which it flows, and in the conductor itself. And from this field, eddy currents arise, which give the effect of "pushing" the actual main movement of charges, from the depth of the entire cross-section of the conductor to its surface, the so-called "skin effect" (from skin - skin). It turns out that eddy currents seem to "steal" its cross-section from the conductor. The current flows in a layer close to the surface, the rest of the conductor thickness remains unused, it does not reduce its resistance, and there is simply no point in increasing the conductor thickness. Especially at high frequencies. Therefore, for alternating current, resistances are measured in such conductor cross-sections, where its entire cross-section can be considered near-surface. Such a wire is called thin, its thickness is equal to twice the depth of this surface layer, where eddy currents displace the useful main current flowing in the conductor.

Of course, the effective conduction of alternating current is not exhausted by the reduction in the thickness of the round wires in cross-section. The conductor can be thinned, but at the same time made flat in the form of a tape, then the cross section will be higher than that of a round wire, respectively, and the resistance is lower. In addition, simply increasing the surface area will have the effect of increasing the effective section. The same can be achieved using stranded wire instead of a single-core, moreover, a multi-core is superior in flexibility to a single-core, which is often also valuable. On the other hand, taking into account the skin effect in the wires, it is possible to make the wires composite by making the core of a metal with good strength characteristics, such as steel, but low electrical. In this case, an aluminum braid is made over the steel, which has a lower resistivity.

In addition to the skin effect, the flow of alternating current in conductors is affected by the excitation of eddy currents in the surrounding conductors. Such currents are called induction currents, and they are induced both in metals that do not play the role of wiring (load-bearing structural elements), and in the wires of the entire conducting complex - playing the role of wires of other phases, zero, grounding.

All of these phenomena are found in all structures associated with electricity, this further enhances the importance of having at your disposal a summary of reference information on a variety of materials.

The resistivity for conductors is measured by very sensitive and accurate instruments, since metals with the lowest resistance are selected for wiring - of the order of ohms * 10-6 per meter of length and sq. mm. section. To measure the specific resistance of insulation, devices are needed, on the contrary, having ranges of very large values resistances are usually megohms. It is clear that conductors must conduct well, and insulators must be well insulated.

table

Iron as a conductor in electrical engineering

Iron is the most widespread metal in nature and technology (after hydrogen, which is also a metal). It is the cheapest and has excellent strength characteristics, therefore it is used everywhere as the basis of strength. various designs.

In electrical engineering, iron is used as a conductor in the form of flexible steel wires where physical strength and flexibility are needed, and the required resistance can be achieved due to the appropriate cross-section.

Having a table of specific resistances of various metals and alloys, you can calculate the cross-sections of wires made from different conductors.

As an example, let's try to find the electrically equivalent cross-section of conductors made of different materials: copper, tungsten, nickelin and iron wire. For the initial one, we take an aluminum wire with a cross section of 2.5 mm.

We need the resistance of the wire from all these metals to be equal to the resistance of the original one over a length of 1 m. The resistance of aluminum per 1 m of length and 2.5 mm of cross-section will be equal to

, where R is the resistance, ρ is the resistivity of the metal from the table, S is the cross-sectional area, L is the length.

Substituting the initial values, we get the resistance of a meter piece of aluminum wire in ohms.

Then we solve the formula for S

, we will substitute the values ​​from the table and obtain the cross-sectional areas for different metals.

Since the resistivity in the table is measured on a wire 1 m long, in micro-ohms per 1 mm2 section, we got it in micro-ohms. To get it in ohms, you need to multiply the value by 10-6. But the number of ohms with 6 zeros after the decimal point is not at all necessary for us to receive, since the final result is still found in mm2.

As you can see, the iron resistance is quite large, the wire is thick.

But there are materials that have even more of it, for example, nickeline or constantan.

Similar articles:

domelectrik.ru

Table of electrical resistivity of metals and alloys in electrical engineering

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Resistivity of metals.

Resistivity of alloys.

The values ​​are given at t = 20 ° C. The resistances of the alloys depend on their exact composition. Comments powered by HyperComments

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Specific electrical resistance | The world of welding

Specific electrical resistance of materials

Specific electrical resistance (resistivity) - the ability of a substance to prevent the passage of electric current.

Measurement unit (SI) - Ohm · m; also measured in Ohm cm and Ohm mm2 / m.

Material Temperature, ° С Specific electrical resistance, Ohm m

Metals
Aluminum	20	0.028 10-6
Beryllium	20	0.036 10-6
Phosphorous bronze	20	0.08 10-6
Vanadium	20	0.196 10-6
Tungsten	20	0.055 10-6
Hafnium	20	0.322 10-6
Duralumin	20	0.034 10-6
Iron	20	0.097 10-6
Gold	20	0.024 10-6
Iridium	20	0.063 10-6
Cadmium	20	0.076 10-6
Potassium	20	0.066 10-6
Calcium	20	0.046 10-6
Cobalt	20	0.097 10-6
Silicon	27	0.58 10-4
Brass	20	0.075 10-6
Magnesium	20	0.045 10-6
Manganese	20	0.050 10-6
Copper	20	0.017 10-6
Magnesium	20	0.054 10-6
Molybdenum	20	0.057 10-6
Sodium	20	0.047 10-6
Nickel	20	0.073 10-6
Niobium	20	0.152 10-6
Tin	20	0.113 10-6
Palladium	20	0.107 10-6
Platinum	20	0.110 10-6
Rhodium	20	0.047 10-6
Mercury	20	0.958 10-6
Lead	20	0.221 10-6
Silver	20	0.016 10-6
Steel	20	0.12 10-6
Tantalum	20	0.146 10-6
Titanium	20	0.54 10-6
Chromium	20	0.131 10-6
Zinc	20	0.061 10-6
Zirconium	20	0.45 10-6
Cast iron	20	0.65 10-6
Plastics
Getinax	20	109–1012
Nylon	20	1010–1011
Lavsan	20	1014–1016
Organic glass	20	1011–1013
Styrofoam	20	1011
Polyvinyl chloride	20	1010–1012
Polystyrene	20	1013–1015
Polyethylene	20	1015
Glass fiber laminate	20	1011–1012
Textolite	20	107–1010
Celluloid	20	109
Ebonite	20	1012–1014
Rubber
Rubber	20	1011–1012
Liquids
Transformer oil	20	1010–1013
Gases
Air	0	1015–1018
Tree
Dry wood	20	109–1010
Minerals
Quartz	230	109
Mica	20	1011–1015
Various materials
Glass	20	109–1013

LITERATURE

• Alpha and Omega. Quick reference/ Tallinn: Printest, 1991 - 448 p.
• Handbook of elementary physics / N.N. Koshkin, M.G. Shirkevich. M., Science. 1976.256 s.
• Reference book on welding of non-ferrous metals / S.M. Gurevich. Kiev .: Naukova Dumka. 1990.512 s.

weldworld.ru

Resistivity of metals, electrolytes and substances (Table)

Resistivity of metals and insulators

The reference table gives the values ​​of the resistivity p of some metals and insulators at a temperature of 18-20 ° C, expressed in ohm cm. The value of p for metals depends to a large extent on impurities, the table gives the values ​​of p for chemically pure metals, for insulators they are given approximately. Metals and insulators are listed in the table in order of increasing p values.

Resistivity table of metals

Pure metals	104 ρ (ohm cm)	Pure metals	104 ρ (ohm cm)
Aluminum
Duralumin
		Platinum 2)
		Argentan
Manganese
		Manganin
Tungsten		Constantan
Molybdenum		Wood alloy 3)
		Alloy Rose 4)
Palladium		Fechral 6)

Resistivity table of insulators

Insulators		Insulators
Dry wood
Celluloid
		Rosin
Getinax		Quartz _ | _ axis
Soda glass		Polystyrene
Pyrex glass
Quartz || axes
Fused quartz

Resistivity of pure metals at low temperatures

The table gives the values ​​of the resistivity (in ohm cm) of some pure metals at low temperatures (0 ° C).

The ratio of the resistance Rt / Rq of pure metals at a temperature of T ° K and 273 ° K.

The reference table gives the Rt / Rq ratio of the resistances of pure metals at temperatures T ° K and 273 ° K.

Pure metals
Aluminum
Tungsten
Molybdenum

Resistivity of electrolytes

The table gives the values ​​of the resistivity of electrolytes in ohm · cm at a temperature of 18 ° C. The concentration of solutions with is given in percent, which determine the number of grams of anhydrous salt or acid in 100 g of solution.

Source of information: BRIEF PHYSICAL AND TECHNICAL REFERENCE / Volume 1, - M .: 1960.

infotables.ru

Specific electrical resistance - steel

Page 1

The electrical resistivity of steel increases with increasing temperature, and the greatest changes are observed when heated to the Curie point temperature. After the Curie point, the resistivity value changes insignificantly and remains practically constant at temperatures above 1000 C.

Due to the high electrical resistivity of the steel, these iuKii create a large slowdown in the decay of the flux. In contactors for 100 a, the drop-out time is 0 07 sec, and in contactors 600 a-0 23 sec. In connection with the special requirements for contactors of the KMV series, which are designed to turn on and off the electromagnets of the drives of oil switches, the electromagnetic mechanism of these contactors allows adjustment of the actuation voltage and release voltage by adjusting the force of the return spring and a special tear-off spring. Contactors of the KMV type must operate with a deep voltage dip. Therefore, the minimum pick-up voltage of these contactors can drop down to 65% UH. This low pick-up voltage causes a current to flow through the winding at rated voltage, causing the coil to heat up.

The addition of silicon increases the electrical resistivity of the steel almost proportionally to the silicon content and thereby helps to reduce the eddy current losses that arise in the steel when it is operated in an alternating magnetic field.

The addition of silicon increases the electrical resistivity of the steel, which helps to reduce eddy current losses, but at the same time silicon impairs the mechanical properties of the steel and makes it brittle.

Ohm - mm2 / m - electrical resistivity of steel.

To reduce eddy currents, cores made of steel grades with increased electrical resistivity of steel, containing 0 5 - 4 8% silicon, are used.

For this, a thin screen made of soft magnetic steel was put on a massive rotor made of the optimal CM-19 alloy. The specific electrical resistance of steel differs little from the specific resistance of the alloy, and the cg of steel is about an order of magnitude higher. The thickness of the screen is chosen according to the penetration depth of the first-order tooth harmonics and is equal to d e 0 8 mm. For comparison, there are additional losses, W, at the base squirrel cage rotor and a two-layer rotor with a massive cylinder made of CM-19 alloy and with copper end rings.

The main magnetically conductive material is sheet alloyed electrical steel containing from 2 to 5% silicon. The addition of silicon increases the electrical resistivity of the steel, as a result of which eddy current losses are reduced, the steel becomes resistant to oxidation and aging, but becomes more brittle. V last years cold rolled grain steel with higher magnetic properties in the rolling direction is widely used. To reduce losses from eddy currents, the core of the magnetic circuit is made in the form of a package assembled from sheets of stamped steel.

Electrical steel is a low carbon steel. To improve the magnetic characteristics, silicon is introduced into it, which causes an increase in the electrical resistivity of the steel. This leads to a decrease in eddy current losses.

After machining, the magnetic core is annealed. Since eddy currents in steel participate in the creation of deceleration, one should focus on the value of the specific electrical resistance of steel of the order of Pc (10-15) 10 - 6 ohm cm.In the attracted position of the armature, the magnetic system is quite saturated, therefore the initial induction in various magnetic systems fluctuates within very insignificant limits and for steel grade E VN1 6 - 1 7 hl. The indicated value of the induction maintains the field strength in steel on the order of Yang.

For the manufacture of magnetic systems (magnetic cores) of transformers, special thin-sheet electrical steels are used, which have an increased (up to 5%) silicon content. Silicon contributes to the decarburization of steel, which leads to an increase in magnetic permeability, reduces hysteresis losses and increases its electrical resistivity. An increase in the electrical resistivity of steel makes it possible to reduce losses in it from eddy currents. In addition, silicon weakens the aging of steel (an increase in losses in steel over time), reduces its magnetostriction (changes in the shape and size of the body during magnetization) and, consequently, the noise of transformers. At the same time, the presence of silicon in steel leads to an increase in its brittleness and makes it difficult mechanical processing.  

Pages: 1 2

www.ngpedia.ru

Resistivity | Wikitronic Wiki

Resistivity is a characteristic of a material that determines its ability to conduct electric current. It is defined as the ratio of the electric field to the current density. In the general case, it is a tensor; however, for most materials that do not exhibit anisotropic properties, it is assumed to be a scalar value.

Designation - ρ

$ \ vec E = \ rho \ vec j, $

$ \ vec E $ is the electric field strength, $ \ vec j $ is the current density.

The SI unit of measurement is ohm-meter (ohm m, Ω m).

The resistance of a cylinder or prism (between the ends) made of material with a length l, and a section S in terms of resistivity is determined as follows:

$ R = \ frac (\ rho l) (S). $

In technology, the definition of resistivity is used, as the resistance of a conductor of a unit cross-section and unit length.

Resistivity of some materials used in electrical engineering Edit

Material ρ at 300 K, Ohm m TCR, K⁻¹

silver	1.59 10⁻⁸	4.10 · 10⁻³
copper	1.67 10⁻⁸	4.33 · 10⁻³
gold	2.35 10⁻⁸	3.98 · 10⁻³
aluminum	2.65 10⁻⁸	4.29 · 10⁻³
tungsten	5.65 10⁻⁸	4.83 · 10⁻³
brass	6.5 10⁻⁸	1.5 · 10⁻³
nickel	6.84 10⁻⁸	6.75 · 10⁻³
iron (α)	9.7 10⁻⁸	6.57 · 10⁻³
tin gray	1.01 10⁻⁷	4.63 · 10⁻³
platinum	1.06 10⁻⁷	6.75 · 10⁻³
tin white	1.1 10⁻⁷	4.63 · 10⁻³
steel	1.6 10⁻⁷	3.3 · 10⁻³
lead	2.06 10⁻⁷	4.22 · 10⁻³
duralumin	4.0 10⁻⁷	2.8 · 10⁻³
manganin	4.3 10⁻⁷	± 2 10⁻⁵
constantan	5.0 10⁻⁷	± 3 10⁻⁵
Mercury	9.84 10⁻⁷	9.9 10⁻⁴
nichrome 80/20	1.05 10⁻⁶	1.8 · 10⁻⁴
cantal A1	1.45 10⁻⁶	3 10⁻⁵
carbon (diamond, graphite)	1,3 · 10⁻⁵
germanium	4.6 10⁻¹
silicon	6.4 · 10²
ethanol	3 · 10³
distilled water	5 · 10³
ebonite	10⁸
hard paper	10¹⁰
transformer oil	10¹¹
ordinary glass	5 10¹¹
polyvinyl	10¹²
porcelain	10¹²
wood	10¹²
PTFE (Teflon)	> 10¹³
rubber	5 · 10¹³
quartz glass	10¹⁴
waxed paper	10¹⁴
polystyrene	> 10¹⁴
mica	5 10¹⁴
paraffin	10¹⁵
polyethylene	3 10¹⁵
acrylic resin	10¹⁹

ru.electronics.wikia.com

Specific electrical resistance | formula, volumetric, table

Resistivity is a physical quantity that indicates the degree to which a material can resist the passage of an electric current through it. Some people may confuse this characteristic with ordinary electrical resistance. Despite the similarity of the concepts, the difference between them lies in the fact that the specific refers to substances, and the second term refers exclusively to conductors and depends on the material of their manufacture.

The reciprocal of a given material is electrical conductivity. The higher this parameter, the better the current passes through the substance. Accordingly, the higher the resistance, the more losses are expected at the output.

Calculation formula and measurement value

Considering what the specific electrical resistance is measured in, it is also possible to trace the connection with the non-specific, since the units of Ohm · m are used to designate the parameter. The quantity itself is denoted as ρ. With this value, you can determine the resistance of a substance in a particular case, based on its size. This unit of measurement corresponds to the SI system, but other options can also be found. In technology, you can periodically see the outdated designation Ohm · mm2 / m. To transfer from this system to international, you do not need to use complex formulas, since 1 Ohm · mm2 / m is equal to 10-6 Ohm · m.

The formula for electrical resistivity is as follows:

R = (ρ l) / S, where:

• R is the resistance of the conductor;
• Ρ - material resistivity;
• l is the length of the conductor;
• S - conductor cross-section.

Temperature dependent

The electrical resistivity is temperature dependent. But all groups of substances manifest themselves in different ways when it changes. This must be taken into account when calculating wires that will work in certain conditions. For example, on the street, where the temperature values ​​depend on the season, necessary materials with less susceptibility to changes in the range from -30 to +30 degrees Celsius. If you plan to use it in a technique that will work in the same conditions, then here you also need to optimize the wiring for specific parameters. The material is always selected taking into account the operation.

In the nominal table, electrical resistivity is taken at a temperature of 0 degrees Celsius. Improving performance this parameter when the material is heated, it is due to the fact that the intensity of the movement of atoms in the substance begins to increase. Carriers of electric charges are chaotically scattered in all directions, which leads to the creation of obstacles in the movement of particles. The magnitude of the electrical flow decreases.

With a decrease in temperature, the conditions for the passage of current become better. Upon reaching a certain temperature, which will differ for each metal, superconductivity appears, at which the considered characteristic almost reaches zero.

Differences in parameters sometimes reach very large values. Those materials that have high rates, can be used as insulators. They help protect wiring from short circuits and unintentional human contact. Some substances are generally not applicable for electrical engineering if they have a high value of this parameter. Other properties can interfere with this. For example, the specific electrical conductivity of water will not matter much for a given area. Here are the values ​​of some substances with high values.

High resistivity materials	ρ (Ohm m)
Bakelite	1016
Benzene	1015...1016
Paper	1015
Distilled water	104
Sea water	0.3
Dry wood	1012
The earth is wet	102
Quartz glass	1016
Kerosene	1011
Marble	108
Paraffin	1015
Paraffin oil	1014
Plexiglass	1013
Polystyrene	1016
PVC	1013
Polyethylene	1012
Silicone oil	1013
Mica	1014
Glass	1011
Transformer oil	1010
Porcelain	1014
Slate	1014
Ebonite	1016
Amber	1018

Substances with low rates are more actively used in electrical engineering. Often these are metals that serve as conductors. There are also many differences between them. To find out the electrical resistivity of copper or other materials, it is worth looking at the lookup table.

Low resistivity materials	ρ (Ohm m)
Aluminum	2.7 · 10-8
Tungsten	5.5 · 10-8
Graphite	8.0 10-6
Iron	1.0 10-7
Gold	2.2 10-8
Iridium	4.74 10-8
Constantan	5.0 10-7
Cast steel	1.3 10-7
Magnesium	4.4 · 10-8
Manganin	4.3 10-7
Copper	1.72 10-8
Molybdenum	5.4 10-8
Nickel silver	3.3 10-7
Nickel	8.7 10-8
Nichrome	1.12 10-6
Tin	1.2 10-7
Platinum	1.07 10-7
Mercury	9.6 10-7
Lead	2.08 10-7
Silver	1.6 10-8
Gray cast iron	1.0 10-6
Carbon brushes	4.0 10-5
Zinc	5.9 10-8
Nickelin	0.4 10-6

Specific volumetric electrical resistance

This parameter characterizes the ability to pass current through the volume of the substance. For measurement, it is necessary to apply a voltage potential from different sides of the material, the product from which will be included in the electrical circuit. It is supplied with rated current. After passing, the output data is measured.

Use in electrical engineering

Parameter change at different temperatures widely used in electrical engineering. Most simple example is an incandescent lamp where a nichrome filament is used. When heated, it starts to glow. When a current passes through it, it begins to heat up. As the heating increases, so does the resistance. Accordingly, the initial current that was needed to obtain illumination is limited. The nichrome spiral, using the same principle, can become a regulator on various devices.

Widespread use has also touched upon precious metals, which have suitable characteristics for electrical engineering. For critical circuits that require performance, silver contacts are selected. They have a high cost, but given the relatively small amount of materials, their use is quite justified. Copper is inferior to silver in conductivity, but has a more affordable price, which makes it more often used to create wires.

In conditions where extremely low temperatures can be used, superconductors are used. For room temperature and outdoor use, they are not always appropriate, since as the temperature rises, their conductivity will begin to drop, therefore, for such conditions, aluminum, copper and silver remain the leaders.

In practice, many parameters are taken into account and this one is one of the most important. All calculations are carried out at the design stage, for which reference materials are used.

One of the physical quantities used in electrical engineering is electrical resistivity. Considering the resistivity of aluminum, it should be remembered that this value characterizes the ability of a substance to prevent the passage of an electric current through it.

Resistivity concepts

The opposite value to resistivity is called conductivity or electrical conductivity. Ordinary electrical resistance is characteristic only of a conductor, and specific electrical resistance is characteristic only of one or another substance.

As a rule, this value is calculated for a conductor with a homogeneous structure. To determine electrical homogeneous conductors, the formula is used:

The physical meaning of this quantity lies in a certain resistance of a homogeneous conductor with a certain unit length and cross-sectional area. The unit of measurement is the SI unit Ohm.m or the off-system unit Ohm.mm2 / m. The last unit means that a conductor of a homogeneous substance, 1 m long, having a cross-sectional area of ​​1 mm2, will have a resistance of 1 Ohm. Thus, the resistivity of any substance can be calculated using a 1 m section of an electrical circuit, the cross section of which will be 1 mm2.

Resistivity of different metals

Each metal has its own individual characteristics. If we compare the resistivity of aluminum, for example, with copper, it can be noted that for copper this value is 0.0175 Ohm.mm2 / m, and for aluminum - 0.0271 Ohm.mm2 / m. Thus, the resistivity of aluminum is significantly higher than that of copper. From this it follows that the electrical conductivity is much higher than that of aluminum.

Certain factors affect the value of the resistivity of metals. For example, during deformations, the structure of the crystal lattice is disturbed. Due to the resulting defects, the resistance to the passage of electrons inside the conductor increases. Therefore, there is an increase in the resistivity of the metal.

Temperature also has an effect. When heated, the nodes of the crystal lattice begin to vibrate more strongly, thereby increasing the resistivity. At present, due to the high resistivity, aluminum wires are being replaced by copper wires, which have a higher conductivity.

The term "specific copper" is often used in electrical engineering literature. And you involuntarily ask yourself a question, what is it?

The concept of "resistance" for any conductor is continuously associated with the understanding of the process of electric current flowing through it. Since the article will focus on the resistance of copper, then we should consider its properties and properties of metals.

When it comes to metals, you involuntarily remember that they all have a certain structure - a crystal lattice. The atoms are located in the nodes of such a lattice and make relative to them. Distances and the location of these nodes depend on the forces of interaction of atoms with each other (repulsion and attraction), and are different for different metals. And electrons revolve around atoms in their orbits. They are also kept in orbit by a balance of forces. Only this is atomic and centrifugal. Imagine a picture? You can call it, in some sense, static.

Now let's add the speakers. An electric field begins to act on a piece of copper. What happens inside the conductor? Electrons, ripped off by the force of the electric field from their orbits, rush to its positive pole. Here is the directional movement of electrons, or rather, an electric current. But on the way of their movement, they stumble upon atoms in the nodes of the crystal lattice and electrons, which still continue to revolve around their atoms. At the same time, they lose their energy and change the direction of movement. Now the meaning of the phrase "conductor resistance" becomes a little clearer? These are the atoms of the lattice and the electrons revolving around them resist the directional movement of the electrons torn from their orbits by the electric field. But the concept of conductor resistance can be called general characteristic... Resistivity characterizes each conductor more individually. Copper as well. This characteristic is individual for each metal, since it directly depends only on the shape and size of the crystal lattice and, to some extent, on temperature. As the temperature of the conductor rises, the atoms vibrate more intensely at the lattice sites. And electrons revolve around nodes at a higher speed and in orbits of a larger radius. And, naturally, free electrons encounter greater resistance when moving. This is the physics of the process.

For the needs of the electrical industry, a widespread production of metals such as aluminum and copper has been established, the resistivity of which is quite low. These metals are used to make cables and of various types wires, which are widely used in construction, for the production of household appliances, the manufacture of tires, transformer windings and other electrical products.

Specific electrical resistance, or simply resistivity substance - a physical quantity that characterizes the ability of a substance to prevent the passage of electric current.

Resistivity is indicated by the Greek letter ρ. The reciprocal of resistivity is called conductivity (electrical conductivity). Unlike electrical resistance, which is a property conductor and depending on its material, shape and size, electrical resistivity is a property only substances.

Electrical resistance of a homogeneous conductor with resistivity ρ, length l and cross-sectional area S can be calculated by the formula R = ρ ⋅ l S (\ displaystyle R = (\ frac (\ rho \ cdot l) (S)))(this assumes that neither the area nor the cross-sectional shape changes along the conductor). Accordingly, ρ satisfies ρ = R ⋅ S l. (\ displaystyle \ rho = (\ frac (R \ cdot S) (l)).)

From the last formula it follows: the physical meaning of the resistivity of a substance is that it is the resistance of a homogeneous conductor made of this substance of unit length and unit cross-sectional area.

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  The unit of measurement for resistivity in the International System of Units (SI) is Ohm ·. From the ratio ρ = R ⋅ S l (\ displaystyle \ rho = (\ frac (R \ cdot S) (l))) it follows that the unit of resistivity in the SI system is equal to the specific resistance of the substance at which a uniform conductor 1 m long with a cross-sectional area of ​​1 m2, made of this substance, has a resistance of 1 Ohm. Accordingly, the resistivity of an arbitrary substance, expressed in SI units, is numerically equal to the resistance of an electrical circuit section made of this substance, 1 m long and a cross-sectional area of ​​1 m2.

  The technology also uses the outdated off-system unit Ohm · mm² / m, equal to 10 −6 of 1 Ohm · m. This unit is equal to the specific resistance of a substance at which a homogeneous conductor 1 m long with a cross-sectional area of ​​1 mm², made of this substance, has a resistance of 1 Ohm. Accordingly, the specific resistance of a substance, expressed in these units, is numerically equal to the resistance of a section of an electrical circuit made of this substance, 1 m long and a cross-sectional area of ​​1 mm².

  Generalization of the concept of resistivity

  Resistivity can also be determined for an inhomogeneous material, the properties of which vary from point to point. In this case, it is not a constant, but a scalar function of coordinates - a coefficient connecting the electric field strength E → (r →) (\ displaystyle (\ vec (E)) ((\ vec (r)))) and current density J → (r →) (\ displaystyle (\ vec (J)) ((\ vec (r)))) at this point r → (\ displaystyle (\ vec (r)))... The specified relationship is expressed by Ohm's law in differential form:

  E → (r →) = ρ (r →) J → (r →). (\ displaystyle (\ vec (E)) ((\ vec (r))) = \ rho ((\ vec (r))) (\ vec (J)) ((\ vec (r))).)

  This formula is valid for an inhomogeneous but isotropic substance. A substance can also be anisotropic (most crystals, magnetized plasma, etc.), that is, its properties can depend on direction. In this case, the resistivity is a coordinate-dependent second-rank tensor containing nine components. In an anisotropic substance, the vectors of the current density and the electric field strength at each given point of the substance are not codirectional; the connection between them is expressed by the ratio

  E i (r →) = ∑ j = 1 3 ρ i j (r →) J j (r →). (\ displaystyle E_ (i) ((\ vec (r))) = \ sum _ (j = 1) ^ (3) \ rho _ (ij) ((\ vec (r))) J_ (j) (( \ vec (r))).)

  In an anisotropic but homogeneous substance, the tensor ρ i j (\ displaystyle \ rho _ (ij)) does not depend on coordinates.

  Tensor ρ i j (\ displaystyle \ rho _ (ij)) symmetrical, that is, for any i (\ displaystyle i) and j (\ displaystyle j) performed ρ i j = ρ j i (\ displaystyle \ rho _ (ij) = \ rho _ (ji)).

  As for any symmetric tensor, for ρ i j (\ displaystyle \ rho _ (ij)) you can choose an orthogonal Cartesian coordinate system in which the matrix ρ i j (\ displaystyle \ rho _ (ij)) becomes diagonal, that is, it takes the form in which of the nine components ρ i j (\ displaystyle \ rho _ (ij)) only three are nonzero: ρ 11 (\ displaystyle \ rho _ (11)), ρ 22 (\ displaystyle \ rho _ (22)) and ρ 33 (\ displaystyle \ rho _ (33))... In this case, denoting ρ i i (\ displaystyle \ rho _ (ii)) how, instead of the previous formula, we get a simpler

  E i = ρ i J i. (\ displaystyle E_ (i) = \ rho _ (i) J_ (i).)

  The quantities ρ i (\ displaystyle \ rho _ (i)) are called main values resistivity tensor.

  Relation to conductivity

  In isotropic materials, the relationship between resistivity ρ (\ displaystyle \ rho) and conductivity σ (\ displaystyle \ sigma) expressed by equality

  ρ = 1 σ. (\ displaystyle \ rho = (\ frac (1) (\ sigma)).)

  In the case of anisotropic materials, the relationship between the components of the resistivity tensor ρ i j (\ displaystyle \ rho _ (ij)) and the conductivity tensor is more complex. Indeed, Ohm's law in differential form for anisotropic materials is:

  J i (r →) = ∑ j = 1 3 σ i j (r →) E j (r →). (\ displaystyle J_ (i) ((\ vec (r))) = \ sum _ (j = 1) ^ (3) \ sigma _ (ij) ((\ vec (r))) E_ (j) (( \ vec (r))).)

  From this equality and the previously given relation for E i (r →) (\ displaystyle E_ (i) ((\ vec (r)))) it follows that the resistivity tensor is the inverse of the conductivity tensor. Taking this into account, for the components of the resistivity tensor, the following is performed:

  ρ 11 = 1 det (σ) [σ 22 σ 33 - σ 23 σ 32], (\ displaystyle \ rho _ (11) = (\ frac (1) (\ det (\ sigma))) [\ sigma _ ( 22) \ sigma _ (33) - \ sigma _ (23) \ sigma _ (32)],) ρ 12 = 1 det (σ) [σ 33 σ 12 - σ 13 σ 32], (\ displaystyle \ rho _ (12) = (\ frac (1) (\ det (\ sigma))) [\ sigma _ ( 33) \ sigma _ (12) - \ sigma _ (13) \ sigma _ (32)],)

  where det (σ) (\ displaystyle \ det (\ sigma))- determinant of a matrix composed of tensor components σ i j (\ displaystyle \ sigma _ (ij))... The remaining components of the resistivity tensor are obtained from the above equations as a result of the cyclic permutation of the indices 1 , 2 and 3 .

  Specific electrical resistance of some substances

  Metallic single crystals

  The table shows the main values ​​of the resistivity tensor of single crystals at a temperature of 20 ° C.

  Crystal	ρ 1 = ρ 2, 10 −8 Ohm m	ρ 3, 10 −8 Ohm · m
  Tin	9,9	14,3
  Bismuth	109	138
  Cadmium	6,8	8,3
  Zinc	5,91	6,13