Specific electrical resistance of the material on the example of metal. Resistivity

Electric current I in any substance is created by the movement of charged particles in a certain direction due to the application of external energy (potential difference U). Each substance has individual properties that affect the passage of current in it in different ways. These properties are evaluated by the electrical resistance R.

Georg Ohm empirically determined the factors influencing the magnitude of the electrical resistance of a substance, deduced from voltage and current, which is named after him. The unit of measurement of resistance in the international SI system is named after him. 1 Ohm is the value of resistance measured at a temperature of 0 ° C at a homogeneous mercury column 106.3 cm long with a cross-sectional area of ​​\u200b\u200b1 mm 2.

Definition

In order to evaluate and put into practice materials for the manufacture of electrical devices, the term "conductor resistivity". The added adjective "specific" refers to the factor of using the reference volume value adopted for the substance in question. This makes it possible to evaluate the electrical parameters of different materials.

At the same time, it is taken into account that the resistance of the conductor increases with an increase in its length and a decrease in its cross section. The SI system uses the volume of a homogeneous conductor with a length of 1 meter and a cross section of 1m 2. In technical calculations, an outdated but convenient off-system unit of volume is used, consisting of a length of 1 meter and an area of ​​1 mm 2. The formula for resistivity ρ is shown in the figure.

To determine the electrical properties of substances, another characteristic is introduced - specific conductivity b. It is inversely proportional to the value of resistivity, determines the ability of the material to conduct electric current: b = 1/ρ.

How does resistivity depend on temperature?

The conductivity of a material is affected by its temperature. Miscellaneous groups substances behave differently when heated or cooled. This property is taken into account in electrical wires operating outdoors in heat and cold.

The material and resistivity of the wire are selected taking into account the conditions of its operation.

The increase in the resistance of conductors to the passage of current during heating is explained by the fact that with an increase in the temperature of the metal in it, the intensity of the movement of atoms and carriers of electric charges in all directions increases, which creates unnecessary obstacles for the movement of charged particles in one direction, reduces the magnitude of their flow.

If the temperature of the metal is reduced, then the conditions for the passage of current improve. When cooled to a critical temperature, the phenomenon of superconductivity appears in many metals, when their electrical resistance is practically zero. This property is widely used in powerful electromagnets.

The influence of temperature on the conductivity of a metal is used by the electrical industry in the manufacture of ordinary incandescent lamps. During the passage of current, they heat up to such a state that it emits a luminous flux. Under normal conditions, the specific resistance of nichrome is about 1.05 ÷ 1.4 (ohm ∙ mm 2) / m.

When the light bulb is turned on, a large current passes through the filament, which heats up the metal very quickly. At the same time, the resistance of the electrical circuit increases, limiting the initial current to the nominal value necessary to obtain lighting. In this way, a simple regulation of the current strength through a nichrome spiral is carried out, there is no need to use complex ballasts used in LED and luminescent sources.

How the resistivity of materials is used in engineering

Non-ferrous noble metals have better electrical conductivity properties. Therefore, critical contacts in electrical devices are made of silver. But this increases the final cost of the entire product. The most acceptable option is to use cheaper metals. For example, the resistivity of copper, equal to 0.0175 (ohm ∙ mm 2) / m, is quite suitable for such purposes.

noble metals- gold, silver, platinum, palladium, iridium, rhodium, ruthenium and osmium, named mainly due to their high chemical resistance and beautiful appearance in jewelry. In addition, gold, silver and platinum have high ductility, while platinum group metals have high melting point and, like gold, chemical inertness. These advantages of noble metals are combined.

Copper alloys with good conductivity are used to make shunts that limit the flow of high currents through the measuring head of high-power ammeters.

The specific resistance of aluminum 0.026 ÷ 0.029 (ohm ∙ mm 2) / m is slightly higher than that of copper, but the production and cost of this metal is lower. Plus, it's easier. This explains it wide application in the power industry for the manufacture of wires operating in the open air, and cable cores.

The specific resistance of iron 0.13 (ohm ∙ mm 2) / m also allows its use for transmission electric current, but this results in higher power losses. Steel alloys have increased strength. Therefore, steel threads are woven into the aluminum overhead wires of high-voltage power lines, which are designed to withstand the loads acting on the break.

This is especially true when ice forms on wires or strong gusts of wind.

Some alloys, for example, constantine and nickeline, have thermally stable resistive characteristics in a certain range. In nickeline, the electrical resistivity practically does not change from 0 to 100 degrees Celsius. Therefore, spirals for rheostats are made of nickeline.

In measuring instruments, the property of a strict change in the values ​​of the resistivity of platinum from its temperature is widely used. If an electric current is passed through a platinum conductor from a stabilized voltage source and the resistance value is calculated, then it will indicate the temperature of the platinum. This allows you to calibrate the scale in degrees, corresponding to Ohm values. This method allows you to measure the temperature with an accuracy of fractions of a degree.

Sometimes for a solution practical tasks want to know cable impedance or resistivity. To do this, in the reference books for cable products, the values ​​\u200b\u200bof the inductive and active resistance of one core for each value of the cross section are given. With their help, the permissible loads, the generated heat are calculated, the permissible operating conditions are determined and effective protections are selected.

The specific conductivity of metals is influenced by the way they are processed. Using pressure to plastically deform structure breaks crystal lattice, increases the number of defects and increases resistance. To reduce it, recrystallization annealing is used.

Stretching or compression of metals causes elastic deformation in them, from which the amplitudes of thermal oscillations of electrons decrease, and the resistance decreases somewhat.

When designing grounding systems, it is necessary to take into account. It has differences in definition from the above method and is measured in units of the SI system - Ohm∙meter. With its help, the quality of the spreading of electric current inside the earth is evaluated.

Soil conductivity is affected by many factors, including soil moisture, soil density, particle size, temperature, salt, acid, and alkali concentrations.

• Constantan (58.8 Cu, 40 Ni, 1.2 Mn)
• Manganin (85 Cu, 12 Mn, 3 Ni)
• Nickel silver (65 Cu, 20 Zn, 15 Ni)
• Nickelin (54 Cu, 20 Zn, 26 Ni)
• Nichrome (67.5 Ni, 15 Cr, 16 Fe, 1.5 Mn)
• Rheonate (84Cu, 12Mn, 4 Zn)
• Fechral (80 Fe, 14 Cr, 6 Al)

Resistivity of nichrome

Each body through which an electric current is passed automatically provides a certain resistance to it. The property of a conductor to resist electric current is called electrical resistance.

Consider the electron theory this phenomenon. When moving along a conductor, free electrons constantly meet other electrons and atoms on their way. Interacting with them, a free electron loses part of its charge. Thus, the electrons encounter resistance from the conductor material. Each body has its own atomic structure, which provides different resistance to electric current. The unit of resistance is the ohm. The resistance of materials is indicated - R or r.

The lower the resistance of the conductor, the easier it is for the electric current to pass through this body. And vice versa: the higher the resistance, the worse the body conducts electric current.

The resistance of each individual conductor depends on the properties of the material from which it is made. To accurately characterize the electrical resistance of a particular material, the concept was introduced - specific resistance (nichrome, aluminum, etc.). The specific resistance is considered to be the resistance of a conductor up to 1 m long, the cross section of which is 1 sq. mm. This indicator is denoted by the letter p. Each material used in the manufacture of a conductor has its own resistivity. For example, consider the resistivity of nichrome and fechral (more than 3 mm):

• Х15Н60 — 1.13 Ohm*mm/m
• Kh23Yu5T - 1.39 Ohm * mm / m
• Х20Н80 — 1.12 Ohm*mm/m
• XN70YU - 1.30 Ohm*mm/m
• XN20YUS - 1.02 Ohm*mm/m

The resistivity of nichrome, fechral indicates the main scope of their application: the manufacture of devices thermal action, household appliances and electric heating elements of industrial furnaces.

Since nichrome and fechral are mainly used in the production of heating elements, the most common products are nichrome thread, tape, Kh15N60 and Kh20N80 strip, as well as Kh23Yu5T fechral wire.

• conductors;
• dielectrics (with insulating properties);
• semiconductors.

Electrons and current

At the heart of the modern concept of electric current is the assumption that it consists of material particles - charges. But various physical and chemical experiments give grounds to assert that these charge carriers can be of different types in the same conductor. And this inhomogeneity of the particles affects the current density. For calculations that are related to the parameters of the electric current, certain physical quantities are used. Among them, an important place is occupied by conductivity along with resistance.

• Conductivity is related to resistance by a mutual inverse relationship.

It is known that when there is a certain voltage applied to an electric circuit, an electric current appears in it, the value of which is related to the conductivity of this circuit. This fundamental discovery was made at the time by the German physicist Georg Ohm. Since then, a law called Ohm's law has been in use. It exists for different options chains. Therefore, the formulas for them may be different from each other, since they correspond to completely different conditions.

Every electrical circuit has a conductor. If it contains one type of charge carrier particles, the current in the conductor is like a fluid flow that has a certain density. It is determined by the following formula:

Most metals correspond to the same type of charged particles, due to which there is an electric current. For metals, the calculation of electrical conductivity is carried out according to the following formula:

Since the conductivity can be calculated, it is now easy to determine the electrical resistivity. It has already been mentioned above that the resistivity of a conductor is the reciprocal of conductivity. Hence,

In this formula, the Greek letter ρ (rho) is used to denote electrical resistivity. This designation is most often used in technical literature. However, you can also find slightly different formulas with the help of which the resistivity of conductors is calculated. If the classical theory of metals and electronic conductivity in them are used for calculations, the resistivity is calculated by the following formula:

However, there is one "but". The state of atoms in a metal conductor is affected by the duration of the ionization process, which is carried out by an electric field. With a single ionizing effect on the conductor, the atoms in it will receive a single ionization, which will create a balance between the concentration of atoms and free electrons. And the values ​​of these concentrations will be equal. In this case, the following dependencies and formulas take place:

Conductivity and resistance deviations

Next, we consider what determines the specific conductivity, which is inversely related to resistivity. The resistivity of matter is a rather abstract physical quantity. Each conductor exists in the form of a specific sample. It is characterized by the presence of various impurities and defects in the internal structure. They are taken into account as separate terms in the expression that determines the resistivity in accordance with the Matthiessen rule. This rule also takes into account the scattering of a moving electron stream on the nodes of the crystal lattice of the sample that fluctuate depending on the temperature.

The presence of internal defects, such as inclusions of various impurities and microscopic voids, also increases the resistivity. To determine the amount of impurities in the samples, the resistivity of the materials is measured for two temperature values ​​of the sample material. One temperature value is room temperature, and the other corresponds to liquid helium. From the ratio of the measurement result at room temperature to the result at liquid helium temperature, a coefficient is obtained that illustrates the structural perfection of the material and its chemical purity. The coefficient is denoted by the letter β.

If a metal alloy with a disordered solid solution structure is considered as an electric current conductor, the value of the residual resistivity can be significantly greater than the resistivity. Such a feature of two-component metal alloys that are not related to rare earth elements, as well as to transition elements, is covered by a special law. It is called Nordheim's law.

Modern technologies in electronics are increasingly moving towards miniaturization. And so much so that the word "nanocircuit" will soon appear instead of a microcircuit. The conductors in such devices are so thin that it would be correct to call them metal films. It is quite clear that the film sample with its resistivity will differ upwards from the larger conductor. The small thickness of the metal in the film leads to the appearance of semiconductor properties in it.

The proportionality between the thickness of the metal and the free path of electrons in this material begins to appear. There is little room for electrons to move. Therefore, they begin to prevent each other from moving in an orderly manner, which leads to an increase in resistivity. For metal films, the resistivity is calculated using a special formula obtained from experiments. The formula is named after Fuchs, a scientist who studied the resistivity of films.

Films are very specific formations that are difficult to repeat so that the properties of several samples are the same. For acceptable accuracy in the evaluation of films, a special parameter is used - the specific surface resistance.

Resistors are formed from metal films on the microcircuit substrate. For this reason, resistivity calculations are a highly demanded task in microelectronics. The value of resistivity, obviously, has an influence on the part of temperature and is related to it by a direct proportionality dependence. For most metals, this dependence has a certain linear section in a certain temperature range. In this case, the resistivity is determined by the formula:

In metals, electric current occurs due to a large number free electrons, the concentration of which is relatively high. Moreover, electrons also determine the high thermal conductivity of metals. For this reason, a connection has been established between the electrical conductivity and thermal conductivity by a special law, which was substantiated experimentally. This Wiedemann-Franz law is characterized by the following formulas:

Tempting prospects for superconductivity

However, the most amazing processes occur at the lowest technically achievable temperature of liquid helium. Under such cooling conditions, all metals practically lose their resistivity. Copper wires cooled to the temperature of liquid helium are capable of conducting currents that are many times greater than under normal conditions. If in practice this became possible, the economic effect would be invaluable.

Even more surprising was the discovery of high-temperature conductors. These varieties of ceramics under normal conditions were very far in their resistivity from metals. But at a temperature of about three dozen degrees above liquid helium, they became superconductors. The discovery of this behavior of non-metallic materials has become a powerful stimulus for research. Due to the greatest economic consequences practical application superconductivity, very significant financial resources were thrown into this direction, and large-scale research began.

But for now, as they say, “things are still there” ... Ceramic materials turned out to be unsuitable for practical use. The conditions for maintaining the state of superconductivity required such large expenses that all the benefits from its use were destroyed. But experiments with superconductivity continue. There is progress. Superconductivity has already been obtained at a temperature of 165 degrees Kelvin, but this requires high pressure. Creation and maintenance of such special conditions again denies the commercial use of this technical solution.

Additional Influencing Factors

At present, everything continues to go its own way, and for copper, aluminum and some other metals, the resistivity continues to ensure their industrial use for the manufacture of wires and cables. In conclusion, it is worth adding some more information that not only the resistivity of the conductor material and temperature environment affect the losses in it during the passage of electric current. The geometry of the conductor is very significant when using it at an increased voltage frequency and at high current strength.

Under these conditions, electrons tend to concentrate near the surface of the wire, and its thickness as a conductor loses its meaning. Therefore, it is possible to justifiably reduce the amount of copper in the wire by making only the outer part of the conductor from it. Another factor in increasing the resistivity of a conductor is deformation. Therefore, despite the high performance of some electrically conductive materials, under certain conditions they may not appear. Selecting the right conductors for specific tasks. The tables below will help you with this.

Content:

The resistivity of metals is their ability to resist the electric current passing through them. The unit of measurement of this value is Ohm * m (Ohm-meter). The Greek letter ρ (rho) is used as a symbol. High performance resistivity means poor conductivity of an electric charge by one or another material.

Steel Specifications

Before considering in detail the resistivity of steel, you should familiarize yourself with its basic physical and mechanical properties. Due to its qualities, this material is widely used in the manufacturing sector and other areas of people's lives and activities.

Steel is an alloy of iron and carbon, contained in an amount not exceeding 1.7%. In addition to carbon, steel contains a certain amount of impurities - silicon, manganese, sulfur and phosphorus. In terms of its qualities, it is much better than cast iron, it is easily hardened, forged, rolled and other types of processing. All types of steels are characterized by high strength and ductility.

According to its purpose, steel is divided into structural, tool, and also with special physical properties. Each of them contains a different amount of carbon, due to which the material acquires certain specific qualities, for example, heat resistance, heat resistance, resistance to rust and corrosion.

A special place is occupied by electrical steels produced in sheet format and used in the manufacture of electrical products. To obtain this material, doping with silicon is performed, which can improve its magnetic and electrical properties.

In order for electrical steel to acquire the necessary characteristics, certain requirements and conditions must be met. The material should be easily magnetized and remagnetized, that is, have a high magnetic permeability. Such steels have good, and their magnetization reversal is carried out with minimal losses.

The dimensions and mass of magnetic cores and windings, as well as the coefficient useful action transformers and their operating temperature. The fulfillment of the conditions is influenced by many factors, including the resistivity of steel.

Resistivity and other indicators

The electrical resistivity value is the ratio of the electric field strength in the metal and the current density flowing in it. For practical calculations, the formula is used: in which ρ is the resistivity of the metal (Ohm * m), E- electric field strength (V/m), and J- the density of the electric current in the metal (A / m 2). With a very high electric field strength and low current density, the resistivity of the metal will be high.

There is another quantity called electrical conductivity, the inverse of resistivity, indicating the degree of conductivity of electric current by a particular material. It is determined by the formula and is expressed in units of Sm / m - Siemens per meter.

Resistivity is closely related to electrical resistance. However, they have differences among themselves. In the first case, this is a property of the material, including steel, and in the second case, the property of the entire object is determined. The quality of a resistor is influenced by a combination of several factors, primarily the shape and resistivity of the material from which it is made. For example, if a thin and long wire was used to make a wire resistor, then its resistance will be greater than that of a resistor made from a thick and short wire of the same metal.

Another example is wire resistors of the same diameter and length. However, if in one of them the material has a high resistivity, and in the other it is low, then, accordingly, the electrical resistance in the first resistor will be higher than in the second.

Knowing the basic properties of the material, you can use the resistivity of steel to determine the resistance value of the steel conductor. For calculations, in addition to electrical resistivity, the diameter and length of the wire itself will be required. Calculations are performed according to the following formula: , in which R is (Ohm), ρ - resistivity of steel (Ohm * m), L- corresponds to the length of the wire, BUT- area of ​​its cross section.

There is a dependence of the resistivity of steel and other metals on temperature. In most calculations, room temperature is used - 20 0 C. All changes under the influence of this factor are taken into account using the temperature coefficient.

Therefore, it is important to know the parameters of all the elements and materials used. And not only electrical, but also mechanical. And to have at your disposal some convenient reference materials that allow you to compare the characteristics of different materials and choose exactly what will be optimal in a particular situation for design and work.
In power transmission lines, where the task is most productive, that is, with high efficiency, to bring energy to the consumer, both the economics 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 arrangement and arrangement of conductors, insulators, supports, step-up / step-down transformers, the weight and strength of all structures, including wires stretched over long distances, as well as on the materials chosen for each structural element. , its work and operating costs. In addition, in the lines that transmit electricity, the requirements for ensuring the safety of both the lines themselves and the environment where they pass are higher. And this adds to the cost of both providing electricity wiring and an additional margin of safety for all structures.

For comparison, the data is usually reduced to 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 metal (copper, aluminum, steel, tungsten, gold) having a unit length and unit section in the system of units used (usually in SI). In addition, the temperature is specified, since when heated, the resistance of the conductors can behave differently. Normal average operating conditions are taken as a basis - 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 compiled.

Types of resistivity

Because resistance is:

• active - or ohmic, resistive - resulting from the cost of electricity for heating the conductor (metal) when an electric current passes through it, and
• reactive - capacitive or inductive - which comes from the inevitable losses to create any changes in the current passing through the conductor of electric fields, then the resistivity of the conductor can be of two varieties:

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 components of the TP - active and reactive, since resistive resistance always exists when current passes, regardless of its nature, and reactive occurs only with any change in current in circuits. In DC circuits, reactance occurs only during transients that are associated with current on (change in current from 0 to nominal) or off (difference from nominal to 0). And they are usually taken into account only when designing overload protection.

In AC circuits, the phenomena associated with reactances are much more diverse. They depend not only on the actual passage of 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 an 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 out” the actual main movement of charges, from the depth of the entire section of the conductor to its surface, the so-called “skin effect” (from skin - skin). It turns out that eddy currents, as it were, “steal” its cross section from the conductor. The current flows in a certain 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 thickness of the conductors. Especially at high frequencies. Therefore, for alternating current, resistances are measured in such cross sections of conductors, 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 reducing the thickness of wires that are round 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. Also, simply increasing the surface area will have the effect of increasing effective cross section. The same can be achieved by using a stranded wire instead of a single strand, in addition, a stranded wire is superior in flexibility to a single strand, 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 that has good strength characteristics, such as steel, but low electrical characteristics. At the same time, 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 pickup currents, and they are induced both in metals that do not play the role of wiring (bearing structural elements), and in the wires of the entire conductive complex - playing the role of wires of other phases, zero, grounding.

All of these phenomena occur in all designs related to electricity, this further reinforces the importance of having at your disposal summary reference information for a wide variety of materials.

Resistivity for conductors is measured with very sensitive and accurate instruments, since metals are selected for wiring and have the lowest resistance - of the order of ohm * 10 -6 per meter of length and square. mm. sections. To measure the resistivity of the insulation, instruments 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

Table of specific resistances of conductors (metals and alloys)
Conductor material	Composition (for alloys)	Resistivity ρ mΩ × mm 2 / m
	copper, zinc, tin, nickel, lead, manganese, iron, etc.
Aluminum
Tungsten
Molybdenum
	copper, tin, aluminum, silicon, beryllium, lead, etc. (except zinc)
	iron, carbon
	copper, nickel, zinc
Manganin	copper, nickel, manganese
Constantan	copper, nickel, aluminum
	nickel, chromium, iron, manganese
	iron, chromium, aluminum, silicon, manganese

Iron as a conductor in electrical engineering

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

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

Having a table of specific resistances of various metals and alloys, it is possible to 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, nickel and iron wires. For the initial take aluminum wire with a cross section of 2.5 mm.

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

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

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

After that, we solve the formula for S

We will substitute the values ​​from the table and get the cross-sectional areas for different metals.

Since the resistivity in the table is measured on a wire 1 m long, in microohms per 1 mm 2 section, we got it in microohms. To get it in ohms, you need to multiply the value by 10 -6. But we don’t have to get the number of ohms with 6 zeros after the decimal point, since we still find the final result in mm 2.

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

But there are materials that have even more, such as nickeline or constantan.