What is called resistivity. Electrical resistivity of steel at different temperatures

Therefore, it is important to know the parameters of all elements and materials used. And not only electrical, but also mechanical. And have some convenient ones at your disposal reference materials, allowing you to compare characteristics different materials and choose for design and work exactly what will be optimal in a particular situation.
In energy transmission lines, where the task is to deliver energy to the consumer in the most productive way, that is, with high efficiency, both the economics of losses and the mechanics of the lines themselves are taken into account. The final result depends on the mechanics - that is, the device 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 the materials selected for each structural element. economic efficiency line, its operation and operating costs. In addition, in lines transmitting electricity, there are higher requirements for ensuring the safety of both the lines themselves and everything around where they pass. And this adds costs both for providing electricity wiring and for an additional margin of safety of all structures.

For comparison, data are usually reduced to a single, comparable form. Often, the epithet “specific” is added to such characteristics, and the meanings themselves are considered on some unified basis. physical parameters standards. For example, specific electrical resistance- this is the resistance (ohms) of a conductor made of some metal (copper, aluminum, steel, tungsten, gold), having a unit length and a unit cross-section in the system of units of measurement 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 environmental parameters (temperature, pressure), coefficients are introduced and additional tables and dependency graphs are compiled.

Types of resistivity

Since resistance happens:

• active - or ohmic, resistive - resulting from the expenditure of electricity on heating the conductor (metal) when passing through it electric current, And
• reactive - capacitive or inductive - which occurs from the inevitable losses due to the creation of any changes in the current passing through the conductor of electric fields, then the resistivity of the conductor comes in two varieties:

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

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

In alternating current circuits, the phenomena associated with reactance are much more diverse. They depend not only on the actual passage of current through a certain cross 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” the actual main movement of charges, from the depths 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 certain layer close to the surface, the remaining thickness of the conductor 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, resistance is measured in such sections of conductors where its entire 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, reducing the thickness of wires with a round cross-section is not limited to effective implementation AC. 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, and accordingly, the resistance will be lower. In addition, simply increasing the surface area will have the effect of increasing the effective cross-section. The same can be achieved by using stranded wire instead of single-core; moreover, stranded wire is more flexible than single-core wire, which is often valuable. On the other hand, taking into account the skin effect in wires, it is possible to make the wires composite by making the core from a metal that has good strength characteristics, for example, steel, but low electrical characteristics. 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 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 conductive complex - playing the role of wires of other phases, neutral, grounding.

All the listed phenomena found in all electrical designs, this further reinforces the importance of having at your disposal summary background information on a variety of materials.

Resistivity for conductors it is measured with very sensitive and precise instruments, since metals that have the lowest resistance are selected for wiring - on the order of ohms * 10 -6 per meter of length and sq. mm. sections. To measure insulation resistivity, you need instruments, on the contrary, that have ranges of very large resistance values ​​- usually megohms. It is clear that conductors must conduct well, and insulators must insulate well.

Table

Table of resistivity 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 the cheapest and has excellent strength characteristics, so it is used everywhere as the basis for 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 through the appropriate cross-section.

Having a table of resistivities 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, nickel and iron wire. Let's take aluminum wire with a cross-section of 2.5 mm as the initial one.

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

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

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

After this, let us 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 microohms per 1 mm 2 section, then we got it in microohms. To get it in ohms, you need to multiply the value by 10 -6. But we don’t necessarily need to get the number ohm with 6 zeros after the decimal point, since we still find the final result in mm2.

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

But there are materials for which it is even greater, for example, nickel or constantan.

Metals are a measure of their ability to resist the passage of electric current. This value is expressed in Ohm-meter (Ohm⋅m).

The symbol representing resistivity is greek letterρ (rho). High resistivity means the material is a poor conductor of electrical charge.

Electrical resistivity is defined as the ratio between the electric field strength inside a metal and the current density within it:

Where:
ρ—metal resistivity (Ohm⋅m),
E - electric field strength (V/m),
J is the value of electric current density in the metal (A/m2)

If the electric field strength (E) in a metal is very high and the current density (J) is very small, this means that the metal has high resistivity.

The reciprocal of resistivity is electrical conductivity, which indicates how well a material conducts electric current:

σ is the conductivity of the material, expressed in siemens per meter (S/m).

Electrical resistance, one of the components of Ohm's law, is expressed in ohms (Ohms). It should be noted that electrical resistance and resistivity are not the same thing. Resistivity is a property of a material, while electrical resistance is a property of an object.

The electrical resistance of a resistor is determined by a combination of its shape and the resistivity of the material from which it is made.

For example, a wire resistor made from a long and thin wire has a higher resistance than a resistor made from a short and thick wire of the same metal.

At the same time, a wirewound resistor made of a high resistivity material has greater electrical resistance than a resistor made of a low resistivity material. And all this despite the fact that both resistors are made of wire of the same length and diameter.

To illustrate this, we can draw an analogy with a hydraulic system, where water is pumped through pipes.

• The longer and thinner the pipe, the greater the resistance to water.
• A pipe filled with sand will resist water more than a pipe without sand.

The amount of wire resistance depends on three parameters: the resistivity of the metal, the length and diameter of the wire itself. Formula for calculating wire resistance:

Where:
R - wire resistance (Ohm)
ρ - metal resistivity (Ohm.m)
L - wire length (m)
A - cross-sectional area of ​​the wire (m2)

As an example, consider a nichrome wirewound resistor with a resistivity of 1.10×10-6 Ohm.m. The wire has a length of 1500 mm and a diameter of 0.5 mm. Based on these three parameters, we calculate the resistance of the nichrome wire:

R=1.1*10 -6 *(1.5/0.000000196) = 8.4 Ohm

Nichrome and constantan are often used as resistance materials. Below in the table you can see the resistivity of some of the most commonly used metals.

The surface resistance value is calculated in the same way as the wire resistance. In this case, the cross-sectional area can be represented as the product of w and t: For some materials, such as thin films, the relationship between resistivity and film thickness is called sheet sheet resistance RS:

where RS is measured in ohms. For this calculation, the film thickness must be constant.

Often, resistor manufacturers cut tracks into the film to increase resistance to increase the path for electrical current.

Properties of resistive materials

The resistivity of a metal depends on temperature. Their values ​​are usually given for room temperature (20°C). The change in resistivity as a result of a change in temperature is characterized by a temperature coefficient.

For example, thermistors (thermistors) use this property to measure temperature. On the other hand, in precision electronics, this is a rather undesirable effect.
Metal film resistors have excellent temperature stability properties. This is achieved not only due to the low resistivity of the material, but also due to the mechanical design of the resistor itself.

Many different materials and alloys are used in the manufacture of resistors. Nichrome (an alloy of nickel and chromium), due to its high resistivity and resistance to oxidation at high temperatures, is often used as a material for the manufacture of wirewound resistors. Its disadvantage is that it cannot be soldered. Constantan, another popular material, is easy to solder and has a lower temperature coefficient.

Electric current occurs as a result of closing a circuit with a potential difference across the terminals. Field forces act on free electrons and they move along the conductor. During this journey, electrons meet atoms and transfer some of their accumulated energy to them. As a result, their speed decreases. But, due to the influence of the electric field, it is gaining momentum again. Thus, electrons constantly experience resistance, which is why the electric current heats up.

The property of a substance to convert electricity into heat when exposed to current is electrical resistance and is denoted as R, its measuring unit is Ohm. The amount of resistance depends mainly on the ability of various materials to conduct current.
For the first time, the German researcher G. Ohm spoke about resistance.

In order to find out the dependence of current on resistance, the famous physicist conducted many experiments. For experiments he used various conductors and obtained various indicators.
The first thing that G. Ohm determined was that the resistivity depends on the length of the conductor. That is, if the length of the conductor increased, the resistance also increased. As a result, this relationship was determined to be directly proportional.

The second relationship is the cross-sectional area. It could be determined by cross-sectioning the conductor. The area of ​​the figure formed on the cut is the cross-sectional area. Here the relationship is inversely proportional. That is, the larger the cross-sectional area, the lower the conductor resistance became.

And the third, important quantity on which resistance depends is the material. As a result of what Om used in experiments various materials, he discovered various resistance properties. All these experiments and indicators were summarized in a table from which it can be seen different meaning specific resistance of various substances.

It is known that the best conductors are metals. Which metals are the best conductors? The table shows that copper and silver have the least resistance. Copper is used more often due to its lower cost, and silver is used in the most important and critical devices.

Substances with high resistivity in the table do not conduct electricity well, which means they can be excellent insulating materials. Substances that have this property to the greatest extent are porcelain and ebonite.

In general, electrical resistivity is very important factor, after all, by determining its indicator, we can find out what substance the conductor is made of. To do this, you need to measure the cross-sectional area, find out the current using a voltmeter and ammeter, and also measure the voltage. This way we will find out the value of the resistivity and, using the table, we can easily identify the substance. It turns out that resistivity is like a fingerprint of a substance. In addition, resistivity is important when planning long electrical circuits: we need to know this indicator in order to maintain a balance between length and area.

There is a formula that determines that resistance is 1 ohm if, at a voltage of 1V, its current is 1A. That is, the resistance of a unit area and a unit length made of a certain substance is the specific resistance.

It should also be noted that the resistivity indicator directly depends on the frequency of the substance. That is, whether it has impurities. However, adding just one percent of manganese increases the resistance of the most conductive substance, copper, by three times.

This table shows the electrical resistivity of some substances.

Highly conductive materials

Copper
As we have already said, copper is most often used as a conductor. This is explained not only by its low resistance. Copper has the advantages of high strength, corrosion resistance, ease of use and good machinability. Good brands copper is considered M0 and M1. The amount of impurities in them does not exceed 0.1%.

The high cost of the metal and its predominance in lately scarcity encourages manufacturers to use aluminum as a conductor. Also, alloys of copper with various metals are used.
Aluminum
This metal is much lighter than copper, but aluminum has large values heat capacity and melting point. In this regard, in order to bring it to a molten state, more energy is required than copper. However, the fact of copper deficiency must be taken into account.
In the production of electrical products, as a rule, A1 grade aluminum is used. It contains no more than 0.5% impurities. And metal highest frequency- this is aluminum grade AB0000.
Iron
The cheapness and availability of iron is overshadowed by its high resistivity. In addition, it corrodes quickly. For this reason, steel conductors are often coated with zinc. The so-called bimetal is widely used - this is steel coated with copper for protection.
Sodium
Sodium is also an accessible and promising material, but its resistance is almost three times that of copper. In addition, metallic sodium has high chemical activity, which requires covering such a conductor with hermetically sealed protection. It should also protect the conductor from mechanical damage, since sodium is a very soft and rather fragile material.

Superconductivity
The table below shows the resistivity of substances at a temperature of 20 degrees. The indication of temperature is not accidental, because resistivity directly depends on this indicator. This is explained by the fact that when heated, the speed of atoms also increases, which means the probability of them meeting electrons will also increase.

It is interesting what happens to resistance under cooling conditions. For the first time, the behavior of atoms at very low temperatures noted by G. Kamerlingh Onnes in 1911. He cooled the mercury wire to 4K and found that its resistance dropped to zero. The change in the resistivity index of some alloys and metals under low temperature conditions is called superconductivity by the physicist.

Superconductors go into a state of superconductivity when cooled, and their optical and structural characteristics do not change. The main discovery is that electrical and magnetic properties metals in a superconducting state are very different from their properties in the normal state, as well as from the properties of other metals that cannot transition to this state when the temperature decreases.
The use of superconductors is carried out mainly in obtaining super-strong magnetic field, the force of which reaches 107 A/m. Superconducting power line systems are also being developed.

Similar materials.

Or electrical circuit electric current.

Electrical resistance is defined as a proportionality coefficient R between voltage U and DC power I in Ohm's law for a section of a circuit.

The unit of resistance is called ohm(Ohm) in honor of the German scientist G. Ohm, who introduced this concept into physics. One ohm (1 Ohm) is the resistance of such a conductor in which, at voltage 1 IN the current is equal to 1 A.

Resistivity.

The resistance of a homogeneous conductor of constant cross-section depends on the material of the conductor, its length l and cross section S and can be determined by the formula:

Where ρ - specific resistance of the substance from which the conductor is made.

Specific resistance of a substance is a physical quantity that shows what resistance a conductor made from this substance of unit length and unit cross-sectional area has.

From the formula it follows that

Reciprocal value ρ , called conductivity σ :

Since the SI unit of resistance is 1 ohm. unit of area is 1 m2, and unit of length is 1 m, then the SI unit of resistivity is 1 Ohm · m 2 /m, or 1 Ohm m. The SI unit of conductivity is Ohm -1 m -1 .

In practice, the cross-sectional area of ​​thin wires is often expressed in square millimeters (mm2). In this case, a more convenient unit of resistivity is Ohm mm 2 /m. Since 1 mm 2 = 0.000001 m 2, then 1 Ohm mm 2 /m = 10 -6 Ohm m. Metals have a very low resistivity - about (1·10 -2) Ohm·mm 2 /m, dielectrics - 10 15 -10 20 greater.

Dependence of resistance on temperature.

As the temperature rises, the resistance of metals increases. However, there are alloys whose resistance almost does not change with increasing temperature (for example, constantan, manganin, etc.). The resistance of electrolytes decreases with increasing temperature.

Temperature coefficient of resistance of a conductor is the ratio of the change in resistance of the conductor when heated by 1 °C to the value of its resistance at 0 ºC:

.

The dependence of the resistivity of conductors on temperature is expressed by the formula:

.

In general α depends on temperature, but if the temperature range is small, then the temperature coefficient can be considered constant. For pure metals α = (1/273)K -1. For electrolyte solutions α < 0 . For example, for a 10% solution of table salt α = -0.02 K -1. For constantan (copper-nickel alloy) α = 10 -5 K -1.

The dependence of conductor resistance on temperature is used in resistance thermometers.

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

Electrons and current

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

• Conductivity is related to resistance in a mutually inverse relationship.

It is known that when there is a certain voltage applied to an electrical circuit, an electric current appears in it, the magnitude of which is related to the conductivity of this circuit. This fundamental discovery was made at one 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 there is one type of charge carrier particle in it, the current in the conductor is similar to the flow of liquid, which has a certain density. It is determined by the following formula:

Most metals correspond to the same type of charged particles, thanks to which electric current exists. For metals, the specific electrical conductivity is calculated using the following formula:

Since conductivity can be calculated, determining electrical resistivity is now easy. It was already mentioned above that the resistivity of a conductor is the reciprocal of conductivity. Hence,

In this formula the letter Greek alphabetρ (rho) is used to indicate electrical resistivity. This designation is most often used in technical literature. However, you can also find slightly different formulas that are used to calculate the resistivity of conductors. If the classical theory of metals and electronic conductivity in them is used for calculations, the resistivity is calculated using 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 electric field. With a single ionizing effect on a 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:

Deviations of conductivity and resistance

Next, let's look at what it depends on conductivity, which is inversely related to resistivity. Specific resistance of a substance 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 internal structure. They are taken into account as separate terms of the expression that determines the resistivity in accordance with Matthiessen's rule. This rule also takes into account the scattering of a moving electron flow at nodes that fluctuate depending on temperature crystal lattice sample.

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 samples, the resistivity of materials is measured for two temperatures of the sample material. One temperature value is room temperature, and the other corresponds to liquid helium. In relation to the measurement result at room temperature to the result at the temperature of liquid helium, 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 solid solution structure that is disordered is considered as a conductor of electric current, the value of the residual resistivity can be significantly greater than the resistivity. This feature of metal alloys of two components 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 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 will differ in its resistivity to a greater extent from a 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 left for electrons to move. Therefore, they begin to interfere with each other’s movement in an orderly manner, which leads to an increase in resistivity. For metal films, resistivity is calculated using a special formula obtained based on experiments. The formula is named after Fuchs, a scientist who studied the resistivity of films.

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

Resistors are formed from metal films on the substrate of microcircuits. For this reason, resistivity calculations are a highly sought-after task in microelectronics. The value of resistivity is obviously influenced by temperature and is related to it by direct proportionality. For most metals, this dependence has some linear portion in a certain temperature range. In this case, the resistivity is determined by the formula:

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

The tantalizing prospects of superconductivity

However, the most amazing processes occur at the minimum 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 many times greater than under normal conditions. If this became possible in practice, the economic effect would be invaluable.

Even more surprising was the discovery of high-temperature conductors. Under normal conditions, these types of ceramics were very far from metals in their resistivity. But at temperatures about three tens of degrees above liquid helium, they became superconductors. The discovery of this behavior of nonmetallic materials has provided a powerful stimulus for research. Because of the greatest economic consequences practical application Very significant financial resources were devoted to superconductivity in 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 achieved at a temperature of 165 degrees Kelvin, but this requires high blood pressure. The creation and maintenance of such special conditions again denies the commercial use of this technical solution.

Additional influencing factors

Currently, everything continues to go its 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 a little 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 used at high voltage frequencies and when great strength current

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. The correct conductors should be selected for specific tasks. The tables shown below will help with this.