Therefore, it is important to know the parameters of all the elements and materials used. And not only electrical, but also mechanical. And have at your disposal some convenient reference materials that allow you to compare the characteristics different materials and choose for design and work exactly what will be optimal in a particular situation.
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. From mechanics - that is, the device and location 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 chosen for each structural element, the final economic efficiency line, 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 passing through it electric current, 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 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 reduction in the thickness of wires round in cross section is not limited to effective implementation alternating current. 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 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 it is measured with very sensitive and accurate instruments, since metals are selected for wiring and have the lowest resistance - of the order of ohms * 10 -6 per meter of length and sq. 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 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 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 the number of ohms with 6 zeros after the decimal point is not necessary for us to get, 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.

Though this topic may seem quite banal, in it I will answer one very important question on the calculation of voltage loss and the calculation of short circuit currents. I think for many of you this will be as much of a revelation as it was for me.

Recently I studied one very interesting GOST:

GOST R 50571.5.52-2011 Low-voltage electrical installations. Part 5-52. Selection and installation of electrical equipment. Wiring.

This document provides a formula for calculating voltage loss and states:

p is the resistivity of conductors under normal conditions, taken equal to the resistivity at temperature under normal conditions, that is, 1.25 resistivity at 20 ° C, or 0.0225 Ohm mm 2 / m for copper and 0.036 Ohm mm 2 / m for aluminum;

I did not understand anything =) Apparently, when calculating voltage losses and when calculating short-circuit currents, we must take into account the resistance of the conductors, as under normal conditions.

It is worth noting that all tabular values ​​\u200b\u200bare given at a temperature of 20 degrees.

What are the normal conditions? I thought 30 degrees Celsius.

Let's remember physics and calculate at what temperature the resistance of copper (aluminum) will increase by 1.25 times.

R1=R0

R0 - resistance at 20 degrees Celsius;

R1 - resistance at T1 degrees Celsius;

T0 - 20 degrees Celsius;

α \u003d 0.004 per degree Celsius (copper and aluminum are almost the same);

1.25=1+α (T1-T0)

Т1=(1.25-1)/α+Т0=(1.25-1)/0.004+20=82.5 degrees Celsius.

As you can see, it's not 30 degrees at all. Apparently, all calculations must be performed at the maximum allowable temperatures cables. The maximum operating temperature of the cable is 70-90 degrees, depending on the type of insulation.

To be honest, I do not agree with this, because. given temperature corresponds to almost emergency mode of the electrical installation.

In my programs, I laid down the specific resistance of copper - 0.0175 Ohm mm 2 / m, and for aluminum - 0.028 Ohm mm 2 / m.

If you remember, I wrote that in my program for calculating short-circuit currents, the result is about 30% less than the tabular values. There, the resistance of the phase-zero loop is calculated automatically. I tried to find the error but couldn't. Apparently, the inaccuracy of the calculation lies in the resistivity, which is used in the program. And everyone can ask the resistivity, so there should be no questions for the program if you specify the resistivity from the above document.

But I most likely will have to make changes to the programs for calculating voltage losses. This will increase the calculation results by 25%. Although in the ELECTRIC program, the voltage losses are almost the same as mine.

If this is your first time on this blog, then you can get acquainted with all my programs on the page

What do you think, at what temperature should voltage losses be considered: at 30 or 70-90 degrees? Whether there is a regulations who will answer this question?

Substances and materials capable of conducting electric current are called conductors. The rest are classified as dielectrics. But there are no pure dielectrics, they all also conduct current, but its value is very small.

But conductors conduct current differently. According to George Ohm's formula, the current flowing through a conductor is linearly proportional to the magnitude of the voltage applied to it, and inversely proportional to a quantity called resistance.

The unit of measurement of resistance was named Ohm in honor of the scientist who discovered this relationship. But it turned out that conductors made of different materials and having the same geometric dimensions have different electrical resistance. To determine the resistance of a conductor of known length and cross section, the concept of resistivity was introduced - a coefficient that depends on the material.


As a result, the resistance of a conductor of known length and cross section will be equal to


Resistivity applies not only to solid materials, but also to liquids. But its value also depends on impurities or other components in the source material. Pure water does not conduct electricity, being a dielectric. But in nature there is no distilled water, it always contains salts, bacteria and other impurities. This cocktail is a conductor of electric current with specific resistance.


By introducing various additives into metals, new materials are obtained - alloys, the resistivity of which differs from that of the original material, even if the percentage addition to it is insignificant.

Resistivity versus temperature

Specific resistances of materials are given in reference books for temperatures close to room temperature (20 °C). As the temperature increases, the resistance of the material increases. Why is this happening?

Electric current inside the material is conducted free electrons. They are under the influence electric field break away from their atoms and move between them in the direction given by this field. Atoms of a substance form a crystal lattice, between the nodes of which a stream of electrons moves, also called "electron gas". Under the action of temperature, the lattice nodes (atoms) oscillate. The electrons themselves also do not move in a straight line, but along an intricate path. At the same time, they often collide with atoms, changing the trajectory of movement. At some moments in time, the electrons can move in the direction opposite to the direction of the electric current.

As the temperature increases, the amplitude of atomic vibrations increases. The collision of electrons with them occurs more often, the movement of the electron flow slows down. Physically, this is expressed in an increase in resistivity.

An example of using the dependence of resistivity on temperature is the operation of an incandescent lamp. The tungsten filament, from which the filament is made, has a low resistivity at the moment of switching on. The surge of current at the moment of switching on quickly heats it up, the resistivity increases, and the current decreases, becoming nominal.

The same process occurs with nichrome heating elements. Therefore, it is impossible to calculate their operating mode by determining the length of a nichrome wire of a known cross section to create the required resistance. For calculations, you need the specific resistance of the heated wire, and the reference books give values ​​​​for room temperature. Therefore, the final length of the nichrome helix is ​​adjusted experimentally. Calculations determine the approximate length, and when fitting, the thread is gradually shortened section by section.

Temperature coefficient of resistance

But not in all devices, the dependence of the resistivity of conductors on temperature is beneficial. In measuring technology, a change in the resistance of circuit elements leads to an error.

To quantitatively determine the dependence of the resistance of a material on temperature, the concept is introduced temperature coefficient of resistance (TCR). It shows how much the resistance of a material changes when the temperature changes by 1°C.

For the manufacture of electronic components - resistors used in the circuits of measuring equipment, materials with a low TCR are used. They are more expensive, but the parameters of the device do not change over a wide temperature range. environment.

But the properties of materials with high TCR are also used. The operation of some temperature sensors is based on a change in the resistance of the material from which the measuring element is made. To do this, you need to maintain a stable supply voltage and measure the current passing through the element. By calibrating the scale of the device that measures the current, according to a reference thermometer, an electronic temperature meter is obtained. This principle is used not only for measurements, but also for overheating sensors. Disconnecting the device in the event of abnormal operating modes, leading to overheating of the windings of transformers or power semiconductor elements.

Used in electrical engineering and elements that change their resistance not from the ambient temperature, but from the current through them - thermistors. An example of their use - degaussing systems cathode ray tubes TVs and monitors. When voltage is applied, the resistance of the resistor is minimal, the current through it passes into the demagnetization coil. But the same current heats the thermistor material. Its resistance increases, decreasing the current and voltage across the coil. And so - until its complete disappearance. As a result, a sinusoidal voltage with a smoothly decreasing amplitude is applied to the coil, creating the same magnetic field in its space. The result is that by the time the filament of the tube is heated, it is already demagnetized. And the control circuit remains in the locked state until the device is turned off. Then the thermistors will cool down and be ready to work again.

The phenomenon of superconductivity

What happens if the temperature of the material is reduced? The resistivity will decrease. There is a limit to which the temperature decreases, called absolute zero . This - 273°С. Below this temperature limit does not happen. At this value, the resistivity of any conductor is zero.

At absolute zero the atoms of the crystal lattice stop vibrating. As a result, the electron cloud moves between lattice nodes without colliding with them. The resistance of the material becomes equal to zero, which opens up the possibility of obtaining infinitely large currents in conductors of small cross sections.

The phenomenon of superconductivity opens up new horizons for the development of electrical engineering. But there are still difficulties associated with obtaining at home the ultra-low temperatures necessary to create this effect. When the problems are solved, electrical engineering will switch to new level development.

Examples of Using Resistivity Values ​​in Calculations

We have already got acquainted with the principles of calculating the length of nichrome wire for the manufacture of a heating element. But there are other situations when knowledge of the resistivity of materials is needed.

For calculation grounding device circuits coefficients corresponding to typical soils are used. If the type of soil at the location of the ground loop is unknown, then for correct calculations, its resistivity is preliminarily measured. So the calculation results are more accurate, which eliminates the adjustment of the circuit parameters during manufacture: adding the number of electrodes, leading to an increase in the geometric dimensions of the grounding device.


The specific resistance of the materials from which cable lines and busbars are made is used to calculate their active resistance. In the future, at the rated load current with it the voltage value at the end of the line is calculated. If its value turns out to be insufficient, then the cross-sections of the conductors are increased in advance.

14.04.2018

As conductive parts in electrical installations, conductors made of copper, aluminum, their alloys and iron (steel) are used.

Copper is one of the best conductive materials. The density of copper at 20 ° C is 8.95 g / cm 3, the melting point is 1083 ° C. Copper is chemically slightly active, but easily dissolves in nitric acid, and dissolves in dilute hydrochloric and sulfuric acids only in the presence of oxidizing agents (oxygen). In air, copper is quickly covered with a thin layer of dark-colored oxide, but this oxidation does not penetrate deep into the metal and serves as protection against further corrosion. Copper lends itself well to forging and rolling without heating.

Used for manufacturing electrolytic copper in ingots containing 99.93% pure copper.

The electrical conductivity of copper strongly depends on the amount and type of impurities and, to a lesser extent, on mechanical and thermal processing. at 20 ° C is 0.0172-0.018 ohm x mm2 / m.

For the manufacture of conductors, soft, semi-hard or hard copper is used with a specific gravity of 8.9, 8.95 and 8.96 g / cm 3, respectively.

For the manufacture of parts of current-carrying parts is widely used copper in alloys with other metals. The most commonly used alloys are:

Brass is an alloy of copper and zinc, containing at least 50% copper in the alloy, with the addition of other metals. brass 0.031 - 0.079 ohm x mm2/m. There are brass - tompak with a copper content of more than 72% (it has high ductility, anti-corrosion and anti-friction properties) and special brasses with addition of aluminium, tin, lead or manganese.

Brass contact

Bronzes are an alloy of copper and tin with an additive of various metals. Depending on the content of the main component in the alloy, bronzes are called tin, aluminum, silicon, phosphorous, and cadmium. Resistivity of bronze 0.021 - 0.052 ohm x mm 2 /m.

Brass and bronze are distinguished by good mechanical and physical and chemical properties. They are easy to process by casting and pressure, resistant to atmospheric corrosion.

Aluminum - by its qualities the second conductive material after copper. Melting point 659.8 ° C. The density of aluminum at a temperature of 20 ° - 2.7 g / cm 3. Aluminum is easy to cast and well machined. At a temperature of 100 - 150 ° C, aluminum is forged and ductile (it can be rolled into sheets up to 0.01 mm thick).

The electrical conductivity of aluminum is highly dependent on impurities and little on mechanical and heat treatment. The purer the composition of aluminum, the higher its electrical conductivity and better resistance to chemical attack. Machining, rolling and annealing significantly affect the mechanical strength of aluminum. Cold working aluminum increases its hardness, elasticity and tensile strength. Resistivity of aluminum at 20 ° С 0.026 - 0.029 ohm x mm 2 / m.

When replacing copper with aluminum, the cross section of the conductor must be increased in terms of conductivities, i.e., 1.63 times.

With equal conductivity, an aluminum conductor will be 2 times lighter than a copper conductor.

For the manufacture of conductors, aluminum is used, containing at least 98% pure aluminum, silicon not more than 0.3%, iron not more than 0.2%

For the manufacture of parts of current-carrying parts, use aluminum alloys with other metals, for example: Duralumin - an alloy of aluminum with copper and manganese.

Silumin is a light cast aluminum alloy with an admixture of silicon, magnesium, manganese.

Aluminum alloys have good casting properties and high mechanical strength.

The most widely used in electrical engineering are the following aluminum alloys:

Wrought aluminum alloy grade AD, having aluminum not less than 98.8 and other impurities up to 1.2.

Wrought aluminum alloy brand AD1, having aluminum not less than 99.3 n other impurities up to 0.7.

Wrought aluminum alloy brand AD31, having aluminum 97.35 - 98.15 and other impurities 1.85 -2.65.

Alloys of grades AD and AD1 are used for the manufacture of cases and dies of hardware clamps. Profiles and tires used for electrical conductors are made from the AD31 grade alloy.

Products made of aluminum alloys as a result of heat treatment acquire high tensile strength and yield (creep).

Iron - melting point 1539°C. The density of iron is 7.87. Iron dissolves in acids, oxidizes with halogens and oxygen.

In electrical engineering, steels of various grades are used, for example:

Carbon steels are malleable alloys of iron with carbon and other metallurgical impurities.

The specific resistance of carbon steels is 0.103 - 0.204 ohm x mm 2 /m.

Alloy steels are alloys with additions of chromium, nickel and other elements added to carbon steel.

Steels are good.

As additives in alloys, as well as for the manufacture of solders and the implementation of conductive metals, the following are widely used:

Cadmium is a malleable metal. The melting point of cadmium is 321°C. Resistivity 0.1 ohm x mm 2 /m. In electrical engineering, cadmium is used for the preparation of low-melting solders and for protective coatings (cadmium) on metal surfaces. In terms of its anticorrosion properties, cadmium is close to zinc, but cadmium coatings are less porous and are applied in a thinner layer than zinc.

Nickel - melting point 1455°C. The specific resistance of nickel is 0.068 - 0.072 ohm x mm 2 /m. At normal temperatures, it is not oxidized by atmospheric oxygen. Nickel is used in alloys and for protective coating (nickel plating) of metal surfaces.

Tin - melting point 231.9 ° C. The specific resistance of tin is 0.124 - 0.116 ohm x mm 2 /m. Tin is used for soldering a protective coating (tinning) of metals in its pure form and in the form of alloys with other metals.

Lead - melting point 327.4°C. Resistivity 0.217 - 0.227 ohm x mm 2 /m. Lead is used in alloys with other metals as an acid-resistant material. It is added to soldering alloys (solders).

Silver is a very malleable, malleable metal. The melting point of silver is 960.5°C. Silver is the best conductor of heat and electric current. The specific resistance of silver is 0.015 - 0.016 ohm x mm 2 / m. Silver is used for protective coating (silvering) of metal surfaces.

Antimony is a shiny brittle metal, melting point 631°C. Antimony is used in the form of additives in soldering alloys (solders).

Chrome is a hard, shiny metal. Melting point 1830°C. It does not change in air at normal temperature. The specific resistance of chromium is 0.026 ohm x mm 2 /m. Chromium is used in alloys and for protective coating (chrome plating) of metal surfaces.

Zinc - melting point 419.4°C. Resistivity of zinc 0.053 - 0.062 ohm x mm 2 /m. In humid air, zinc oxidizes, becoming covered with an oxide layer, which is protective against subsequent chemical attack. In electrical engineering, zinc is used as an additive in alloys and solders, as well as for a protective coating (galvanizing) of the surfaces of metal parts.

As soon as electricity left the laboratories of scientists and began to be widely introduced into practice Everyday life, the question arose of searching for materials that have certain, sometimes completely opposite, characteristics with respect to the flow of electric current through them.

For example, when transferring electrical energy over a long distance, the wire material was required to minimize losses due to Joule heating in combination with low weight characteristics. An example of this is the familiar high-voltage power lines made of aluminum wires with a steel core.

Or, conversely, to create compact tubular electric heaters, materials with a relatively high electrical resistance and high thermal stability were required. The simplest example of a device that uses materials with similar properties is the burner of an ordinary kitchen electric stove.

From conductors used in biology and medicine as electrodes, probes and probes, high chemical resistance and compatibility with biomaterials, combined with low contact resistance, are required.

A whole galaxy of inventors from different countries: England, Russia, Germany, Hungary and USA. Thomas Edison, having conducted more than a thousand experiments to test the properties of materials suitable for the role of filaments, created a lamp with a platinum spiral. Edison lamps, although they had a long service life, were not practical due to the high cost of the source material.

The subsequent work of the Russian inventor Lodygin, who proposed using relatively cheap refractory tungsten and molybdenum with a higher resistivity as thread materials, found practical use. In addition, Lodygin proposed pumping air out of incandescent bulbs, replacing it with inert or noble gases, which led to the creation of modern incandescent lamps. The pioneer of mass production of affordable and durable electric lamps was General Electric, to which Lodygin assigned the rights to his patents and then successfully worked in the company's laboratories for a long time.

This list can be continued, because the inquisitive human mind is so inventive that sometimes, in order to solve a certain technical task he needs materials with properties never seen before, or with incredible combinations of these properties. Nature no longer keeps up with our appetites, and scientists from all over the world have joined the race to create materials that have no natural analogues.

It is the intentional connection of an electrical enclosure or housing to a protective earthing device. Usually, grounding is carried out in the form of steel or copper strips, pipes, rods or angles buried in the ground to a depth of more than 2.5 meters, which, in the event of an accident, ensure the flow of current along the circuit device - case or casing - earth - neutral wire of the AC source. The resistance of this circuit should be no more than 4 ohms. In this case, the voltage on the case of the emergency device is reduced to values ​​that are safe for humans, and automatic protection devices electrical circuit in one way or another, the emergency device is turned off.

When calculating the elements of protective grounding, knowledge of the resistivity of soils plays a significant role, which can vary over a wide range.

In accordance with the data of the reference tables, the area of ​​the grounding device is selected, the number of grounding elements and the actual design of the entire device are calculated from it. The connection of structural elements of the protective earthing device is carried out by welding.

Electrotomography

Electrical exploration studies the near-surface geological environment, is used to search for ore and non-metallic minerals and other objects based on the study of various artificial electric and electromagnetic fields. A special case of electrical exploration is electrical resistivity tomography - a method for determining the properties rocks according to their resistivity.

The essence of the method is that at a certain position of the electric field source, voltage measurements are taken on various probes, then the field source is moved to another place or switched to another source and the measurements are repeated. Field sources and field receiver probes are placed on the surface and in wells.

Then the received data is processed and interpreted using modern computer processing methods that allow visualizing information in the form of two-dimensional and three-dimensional images.

Being a very accurate search method, electrotomography provides invaluable assistance to geologists, archaeologists and paleozoologists.

Determining the form of occurrence of mineral deposits and the boundaries of their distribution (outlining) makes it possible to identify the occurrence of vein deposits of minerals, which significantly reduces the cost of their subsequent development.

For archaeologists, this search method provides valuable information about the location of ancient burials and the presence of artifacts in them, thereby reducing excavation costs.

Paleozoologists use electrotomography to look for fossilized remains of ancient animals; the results of their work can be seen in museums natural sciences in the form of amazing reconstructions of the skeletons of prehistoric megafauna.

In addition, electrical tomography is used in the construction and subsequent operation of engineering structures: high-rise buildings, dams, dams, embankments, and others.

Resistivity definitions in practice

Sometimes, to solve practical problems, we may face the task of determining the composition of a substance, for example, a wire for a polystyrene foam cutter. We have two coils of wire of a suitable diameter from various materials unknown to us. To solve the problem, it is necessary to find their electrical resistivity and then determine the material of the wire using the difference between the values ​​found or using a reference table.

We measure with a tape measure and cut off 2 meters of wire from each sample. Let's determine the wire diameters d₁ and d₂ with a micrometer. Turning on the multimeter to the lower limit of resistance measurement, we measure the resistance of the sample R₁. We repeat the procedure for another sample and also measure its resistance R₂.

We take into account that the cross-sectional area of ​​the wires is calculated by the formula

S \u003d π ∙ d 2 / 4

Now the formula for calculating electrical resistivity will look like this:

ρ = R ∙ π ∙ d 2 /4 ∙ L

Substituting the obtained values ​​of L, d₁ and R₁ into the formula for calculating the resistivity given in the article above, we calculate the value of ρ₁ for the first sample.

ρ 1 \u003d 0.12 ohm mm 2 / m

Substituting the obtained values ​​of L, d₂ and R₂ into the formula, we calculate the value of ρ₂ for the second sample.

ρ 2 \u003d 1.2 ohm mm 2 / m

From comparing the values ​​of ρ₁ and ρ₂ with the reference data of the above Table 2, we conclude that the material of the first sample is steel, and the second sample is nichrome, from which we will make the cutter string.

The ability of a metal to pass a charged current through itself is called. In turn, resistance is one of the characteristics of the material. The greater the electrical resistance at a given voltage, the smaller it will be. It characterizes the resistance force of the conductor to the movement of charged electrons directed along it. Since the transmission property of electricity is the reciprocal of resistance, it means that it will be expressed in the form of formulas as a ratio of 1 / R.

Resistivity always depends on the quality of the material used in the manufacture of devices. It is measured based on the parameters of a conductor with a length of 1 meter and a cross-sectional area of ​​​​1 square millimeter. For example, the property of specific resistance for copper is always 0.0175 Ohm, for aluminum - 0.029, iron - 0.135, constantan - 0.48, nichrome - 1-1.1. The specific resistance of steel is equal to the number 2 * 10-7 Ohm.m

The resistance to current is directly proportional to the length of the conductor along which it moves. The longer the device, the higher the resistance. It will be easier to learn this dependence if you imagine two imaginary pairs of vessels communicating with each other. Let the connecting tube remain thinner for one pair of devices, and thicker for the other. When both pairs are filled with water, the transition of the liquid into the thick tube will be much faster, because it will have less resistance to the flow of water. By this analogy, it is easier for him to pass along a thick conductor than a thin one.

Resistivity, as an SI unit, is measured in ohm.m. Conductivity depends on the mean free path of charged particles, which is characterized by the structure of the material. Metals without impurities, which have the most correct smallest values counteraction. Conversely, impurities distort the lattice, thereby increasing its performance. The resistivity of metals is located in a narrow range of values ​​at normal temperature: from silver from 0.016 to 10 µOhm.m (alloys of iron and chromium with aluminum).

On the features of the movement of charged

electrons in a conductor is affected by temperature, since as it increases, the amplitude of wave oscillations of existing ions and atoms increases. As a result, the electrons have less free space for normal movement in the crystal lattice. And this means that the obstacle to orderly movement is increasing. The resistivity of any conductor, as usual, increases linearly with increasing temperature. And for semiconductors, on the contrary, a decrease with increasing degrees is characteristic, since because of this, many charges are released that create a direct electric current.

The process of cooling some metal conductors to the desired temperature, brings their resistivity to a jump-like state and drops to zero. This phenomenon was discovered in 1911 and called superconductivity.

Electrical resistance -a physical quantity that shows what kind of obstacle is created by the current when it passes through the conductor. The units of measurement are ohms, after Georg Ohm. In his law, he derived a formula for finding resistance, which is given below.

Consider the resistance of conductors using the example of metals. Metals have internal structure in the form of a crystal lattice. This lattice has a strict order, and its nodes are positively charged ions. The charge carriers in the metal are “free” electrons, which do not belong to a particular atom, but randomly move between lattice sites. It is known from quantum physics that the movement of electrons in a metal is the propagation of an electromagnetic wave in a solid. That is, an electron in a conductor moves at the speed of light (practically), and it has been proven that it exhibits properties not only as a particle, but also as a wave. And the resistance of the metal arises as a result of scattering electromagnetic waves(that is, electrons) on thermal vibrations of the lattice and its defects. When electrons collide with the nodes of the crystal lattice, part of the energy is transferred to the nodes, as a result of which energy is released. This energy can be calculated at direct current, thanks to the Joule-Lenz law - Q \u003d I 2 Rt. As you can see, the greater the resistance, the more energy is released.

Resistivity

There is such an important concept as resistivity, this is the same resistance, only in a unit of length. Each metal has its own, for example, for copper it is 0.0175 Ohm*mm2/m, for aluminum it is 0.0271 Ohm*mm2/m. This means that a copper bar with a length of 1 m and a cross-sectional area of ​​1 mm2 will have a resistance of 0.0175 Ohm, and the same bar, but made of aluminum, will have a resistance of 0.0271 Ohm. It turns out that the electrical conductivity of copper is higher than that of aluminum. Each metal has its own resistivity, and the resistance of the entire conductor can be calculated using the formula

where p is the resistivity of the metal, l is the length of the conductor, s is the cross-sectional area.

Resistivity values ​​are given in metal resistivity table(20°C)

Substance

p, Ohm * mm 2 / 2

α,10 -3 1/K

Aluminum

0.0271

Tungsten

0.055

Iron

0.098

Gold

0.023

Brass

0.025-0.06

Manganin

0.42-0.48

0,002-0,05

Copper

0.0175

Nickel

Constantan

0.44-0.52

0.02

Nichrome

0.15

Silver

0.016

Zinc

0.059

In addition to resistivity, the table contains TCR values, more on this coefficient a little later.

Dependence of resistivity on deformations

During cold working of metals by pressure, the metal undergoes plastic deformation. During plastic deformation, the crystal lattice is distorted, the number of defects becomes larger. With an increase in the defects of the crystal lattice, the resistance to the flow of electrons through the conductor increases, therefore, the resistivity of the metal increases. For example, a wire is made by drawing, which means that the metal undergoes plastic deformation, as a result of which, the resistivity increases. In practice, recrystallization annealing is used to reduce resistance, this is a complex process. technological process, after which the crystal lattice, as it were, “straightens out” and the number of defects decreases, therefore, the resistance of the metal too.

When stretched or compressed, the metal undergoes elastic deformation. With elastic deformation caused by stretching, the amplitudes of thermal vibrations of the crystal lattice nodes increase, therefore, the electrons experience great difficulties, and in connection with this, the resistivity increases. With elastic deformation caused by compression, the amplitudes of thermal oscillations of nodes decrease, therefore, it is easier for electrons to move, and the resistivity decreases.

Effect of Temperature on Resistivity

As we have already found out above, the cause of resistance in a metal is the nodes of the crystal lattice and their vibrations. So, with an increase in temperature, the thermal fluctuations of the nodes increase, which means that the resistivity also increases. There is such a value as temperature coefficient of resistance(TCS), which shows how much the resistivity of the metal increases or decreases when heated or cooled. For example, the temperature coefficient of copper at 20 degrees Celsius is 4.1 10 − 3 1/degree. This means that when, for example, a copper wire is heated by 1 degree Celsius, its resistivity will increase by 4.1 · 10 − 3 Ohm. Resistivity with temperature change can be calculated by the formula

where r is the resistivity after heating, r 0 is the resistivity before heating, a is the temperature coefficient of resistance, t 2 is the temperature before heating, t 1 is the temperature after heating.

Substituting our values, we get: r=0.0175*(1+0.0041*(154-20))=0.0271 Ohm*mm2/m. As you can see, our bar of copper, 1 m long and with a cross-sectional area of ​​​​1 mm 2, after heating to 154 degrees, would have resistance, like the same bar, only made of aluminum and at a temperature of 20 degrees Celsius.

The property of changing resistance with temperature, used in resistance thermometers. These instruments can measure temperature based on resistance readings. Resistance thermometers have high measurement accuracy, but small temperature ranges.

In practice, the properties of conductors prevent the passage current are used very widely. An example is an incandescent lamp, where a tungsten filament is heated due to the high resistance of the metal, large length and narrow cross section. Or any heating device where the coil is heated due to high resistance. In electrical engineering, an element whose main property is resistance is called - resistor. The resistor is used in almost any electrical circuit.