• 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 circuit options. 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 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 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 a conductor of electric current, 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 arises due to the large number of 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 enormous economic consequences of the practical application of 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. The 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 the ambient temperature affect the losses in it during the passage of an 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. It is necessary to choose the right conductors for specific tasks. The tables below will help you with this.

Resistivity metals is a measure of their properties to resist the passage of electric current. This value is expressed in Ohm-meter (Ohm⋅m). The symbol for resistivity is the Greek letter ρ (rho). High resistivity means that the material does not conduct electrical charge well.

Resistivity

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

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

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

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

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

Electrical resistance

Electrical resistance, one of the components, is expressed in ohms (Ohm). 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 the combination of shape and resistivity of the material it is made from.

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

At the same time, a wire-wound resistor made of a high resistivity material has a higher 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.

As an illustration, we can draw an analogy with a hydraulic system, where water is pumped through pipes.

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

Wire resistance

The resistance value of the wire 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 - specific resistance of the metal (Ohm.m)
L - wire length (m)
A - cross-sectional area of ​​\u200b\u200bthe wire (m2)

As an example, consider a nichrome wire 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 \u003d 1.1 * 10 -6 * (1.5 / 0.000000196) \u003d 8.4 ohms

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

Surface resistance

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 referred to as layer sheet resistance RS:

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

Often, resistor manufacturers cut out tracks in the film to increase the resistance to increase the path for electric current.

Properties of resistive materials

The resistivity of a metal depends on temperature. Their values ​​are given, as a rule, 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, in thermistors (thermistors), this property is used 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 making wirewound resistors. Its disadvantage is that it cannot be soldered. Constantan, another popular material, is easy to solder and has a lower temperature coefficient.

Many have heard about Ohm's law, but not everyone knows what it is. The study begins with a school course in physics. In more detail pass on physical faculty and electrodynamics. This knowledge is unlikely to be useful to an ordinary layman, but it is necessary for general development, and for someone for a future profession. On the other hand, basic knowledge about electricity, its structure, features at home will help to warn yourself against trouble. No wonder Ohm's law is called the fundamental law of electricity. The home master needs to have knowledge in the field of electricity in order to prevent overvoltage, which can lead to an increase in load and a fire.

The concept of electrical resistance

The relationship between the basic physical quantities of an electrical circuit - resistance, voltage, current strength was discovered by the German physicist Georg Simon Ohm.

The electrical resistance of a conductor is a value that characterizes its resistance to electric current. In other words, part of the electrons under the action of an electric current on the conductor leaves its place in the crystal lattice and goes to the positive pole of the conductor. Some of the electrons remain in the lattice, continuing to rotate around the atom of the nucleus. These electrons and atoms form an electrical resistance that prevents the movement of released particles.

The above process is applicable to all metals, but the resistance in them occurs in different ways. This is due to the difference in size, shape, material of which the conductor consists. Accordingly, the dimensions of the crystal lattice have an unequal shape for different materials, therefore, the electrical resistance to the movement of current through them is not the same.

From this concept follows the definition of the resistivity of a substance, which is an individual indicator for each metal separately. Electrical resistivity (ER) is a physical quantity denoted by the Greek letter ρ and characterized by the ability of a metal to prevent the passage of electricity through it.

Copper is the main material for conductors

The resistivity of a substance is calculated by the formula, where one of the important indicators is the temperature coefficient of electrical resistance. The table contains the resistivity values ​​of three known metals in the temperature range from 0 to 100°C.

If we take the resistivity index of iron, as one of the available materials, equal to 0.1 Ohm, then 10 meters will be needed for 1 Ohm. Silver has the lowest electrical resistance; for its indicator of 1 Ohm, 66.7 meters will come out. A significant difference, but silver is an expensive metal that is not widely used. The next in terms of performance is copper, where 1 ohm requires 57.14 meters. Due to its availability, cost compared to silver, copper is one of the most popular materials for use in electrical networks. The low resistivity of copper wire or the resistance of copper wire makes it possible to use a copper conductor in many branches of science, technology, as well as in industrial and domestic purposes.

Resistivity value

The resistivity value is not constant, it changes depending on the following factors:

• The size. The larger the diameter of the conductor, the more electrons it passes through itself. Therefore, the smaller its size, the greater the resistivity.
• Length. Electrons pass through atoms, so the longer the wire, the more electrons have to travel through them. When calculating, it is necessary to take into account the length, size of the wire, because the longer, thinner the wire, the greater its resistivity and vice versa. Failure to calculate the load of the equipment used can lead to overheating of the wire and fire.
• Temperature. It is known that the temperature regime is of great importance on the behavior of substances in different ways. Metal, like nothing else, changes its properties at different temperatures. The resistivity of copper directly depends on the temperature coefficient of resistance of copper and increases when heated.
• Corrosion. The formation of corrosion significantly increases the load. This happens due to environmental influences, ingress of moisture, salt, dirt, etc. manifestations. It is recommended to isolate and protect all connections, terminals, twists, install protection for outdoor equipment, timely replace damaged wires, assemblies, assemblies.

Resistance calculation

Calculations are made when designing objects for various purposes and uses, because the life support of each comes from electricity. Everything is taken into account, from lighting fixtures to technically complex equipment. At home, it will also be useful to make a calculation, especially if it is planned to replace the wiring. For private housing construction, it is necessary to calculate the load, otherwise the “handicraft” assembly of electrical wiring can lead to a fire.

The purpose of the calculation is to determine the total resistance of the conductors of all devices used, taking into account their technical parameters. It is calculated by the formula R=p*l/S , where:

R is the calculated result;

p is the resistivity index from the table;

l is the length of the wire (conductor);

S is the diameter of the section.

Units

In the international system of units of physical quantities (SI), electrical resistance is measured in Ohms (Ohm). The unit of measurement of resistivity according to the SI system is equal to such a resistivity of a substance at which a conductor made of one material 1 m long with a cross section of 1 sq. m. has a resistance of 1 ohm. The use of 1 ohm / m with respect to different metals is clearly shown in the table.

Significance of Resistivity

The relationship between resistivity and conductivity can be viewed as reciprocals. The higher the index of one conductor, the lower the index of the other and vice versa. Therefore, when calculating the electrical conductivity, the calculation 1 / r is used, because the number reciprocal to X is 1 / X and vice versa. The specific indicator is denoted by the letter g.

Benefits of electrolytic copper

Low resistivity (after silver) as an advantage, copper is not limited. It has properties unique in its characteristics, namely plasticity, high malleability. Thanks to these qualities, high-purity electrolytic copper is produced for the production of cables that are used in electrical appliances, computer technology, the electrical industry and the automotive industry.

The dependence of the resistance index on temperature

The temperature coefficient is a value that equals the change in the voltage of a part of the circuit and the resistivity of the metal as a result of changes in temperature. Most metals tend to increase resistivity with increasing temperature due to thermal vibrations of the crystal lattice. The temperature coefficient of resistance of copper affects the specific resistance of the copper wire and at temperatures from 0 to 100°C is 4.1 10−3(1/Kelvin). For silver, this indicator under the same conditions has a value of 3.8, and for iron, 6.0. This once again proves the effectiveness of using copper as a conductor.

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. Under the action of an electric field, they 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 range of ambient temperatures.

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 is the systems for degaussing cathode ray tubes of 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 is - 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 move to a new level of 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.

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1 ohm centimeter [ohm cm] = 0.01 ohm meter [ohm m]

Initial value

Converted value

ohm meter ohm centimeter ohm inch microohm centimeter microohm inch abohm centimeter stat per centimeter circular mil ohm per foot ohm sq. millimeter per meter

More about Electrical Resistivity

General information

As soon as electricity left the laboratories of scientists and began to be widely introduced into the practice of everyday life, the question arose of finding materials that have certain, sometimes completely opposite, characteristics in relation to the flow of electric current through them.

For example, when transmitting electrical energy over a long distance, requirements were imposed on the material of the wires 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 the USA put their efforts into the development of such a device now familiar to everyone as an incandescent lamp. 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 application. 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 problem, it needs materials with hitherto unknown properties 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.

One of the most important characteristics of both natural and synthesized materials is electrical resistivity. An example of an electrical device in which this property is used in its purest form is a fuse that protects our electrical and electronic equipment from the effects of current exceeding permissible values.

At the same time, it should be noted that it is home-made substitutes for standard fuses, made without knowledge of the resistivity of the material, that sometimes cause not only burnout of various elements of electrical circuits, but also fires in houses and ignition of wiring in cars.

The same applies to the replacement of fuses in power networks, when a fuse with a higher operating current rating is installed instead of a fuse of a smaller rating. This leads to overheating of the electrical wiring and even, as a result, to the occurrence of fires with sad consequences. This is especially true for frame houses.

History reference

The concept of electrical resistivity appeared thanks to the works of the famous German physicist Georg Ohm, who theoretically substantiated and in the course of numerous experiments proved the relationship between the current strength, the electromotive force of the battery and the resistance of all parts of the circuit, thus discovering the law of the elementary electrical circuit, then named after him. Ohm investigated the dependence of the magnitude of the flowing current on the magnitude of the applied voltage, on the length and shape of the conductor material, and also on the type of material used as a conducting medium.

At the same time, we must pay tribute to the work of Sir Humphrey Davy, an English chemist, physicist and geologist, who was the first to establish the dependence of the electrical resistance of a conductor on its length and cross-sectional area, and also noted the dependence of electrical conductivity on temperature.

Investigating the dependence of the flow of electric current on the type of materials, Ohm found that each conductive material available to him had some inherent characteristic of resistance to the flow of current.

It should be noted that in the time of Ohm, one of the most common conductors today - aluminum - had the status of a particularly precious metal, so Ohm limited himself to experiments with copper, silver, gold, platinum, zinc, tin, lead and iron.

Ultimately, Ohm introduced the concept of electrical resistivity of a material as a fundamental characteristic, knowing absolutely nothing about the nature of current flow in metals, or about the dependence of their resistance on temperature.

Specific electrical resistance. Definition

Electrical resistivity or simply resistivity is a fundamental physical characteristic of a conductive material that characterizes the ability of a substance to prevent the passage of an electric current. It is denoted by the Greek letter ρ (pronounced rho) and is calculated from the empirical formula for calculating resistance obtained by Georg Ohm.

or from here

where R is the resistance in ohms, S is the area in m²/, L is the length in m

The unit of electrical resistivity in the International System of Units SI is expressed in Ohm m.

This is the resistance of a conductor with a length of 1 m and a cross-sectional area of ​​1 m² / a value of 1 ohm.

In electrical engineering, for the convenience of calculations, it is customary to use the derivative of electrical resistivity, expressed in Ohm mm² / m. Resistivity values ​​for the most common metals and their alloys can be found in the relevant reference books.

Tables 1 and 2 show the resistivity values ​​of the various most common materials.

Table 1. Resistivity of some metals

Table 2. Resistivity of common alloys

Specific electrical resistance of various media. Physics of phenomena

Specific electrical resistances of metals and their alloys, semiconductors and dielectrics

Today, armed with knowledge, we are able to pre-calculate the electrical resistivity of any material, both natural and synthesized, based on its chemical composition and assumed physical state.

This knowledge helps us to better use the possibilities of materials, sometimes quite exotic and unique.

In view of the prevailing ideas, from the point of view of physics, solids are divided into crystalline, polycrystalline and amorphous substances.

The easiest way, in terms of technical calculation of resistivity or its measurement, is the case with amorphous substances. They do not have a pronounced crystalline structure (although they may have microscopic inclusions of such substances), are relatively homogeneous in chemical composition and exhibit properties characteristic of a given material.

For polycrystalline substances formed by a collection of relatively small crystals of the same chemical composition, the behavior of properties is not very different from the behavior of amorphous substances, since electrical resistivity is usually defined as an integral aggregate property of a given material sample.

The situation is more complicated with crystalline substances, especially with single crystals, which have different electrical resistivity and other electrical characteristics with respect to the symmetry axes of their crystals. This property is called crystal anisotropy and is widely used in technology, in particular, in radio engineering circuits of quartz oscillators, where frequency stability is determined precisely by the generation of frequencies inherent in a given quartz crystal.

Each of us, being the owner of a computer, tablet, mobile phone or smartphone, including owners of electronic watches up to iWatch, is also the owner of a quartz crystal. Based on this, one can judge the scale of the use of quartz resonators in electronics, estimated in tens of billions.

Among other things, the resistivity of many materials, especially semiconductors, depends on temperature, so reference data is usually given with the measurement temperature, usually 20 °C.

The unique properties of platinum, which has a constant and well-studied dependence of electrical resistivity on temperature, as well as the possibility of obtaining high-purity metal, served as a prerequisite for the creation of sensors on its basis in a wide temperature range.

For metals, the spread of reference values ​​of resistivity is due to the methods of manufacturing samples and the chemical purity of the metal of this sample.

For alloys, a wider range of reference values ​​of resistivity is due to the methods of sample preparation and the variability of the composition of the alloy.

Electrical resistivity of liquids (electrolytes)

Understanding the resistivity of liquids is based on theories of thermal dissociation and mobility of cations and anions. For example, in the most common liquid on Earth, ordinary water, some of its molecules decompose into ions under the influence of temperature: H+ cations and OH– anions. When an external voltage is applied to electrodes immersed in water under normal conditions, a current arises due to the movement of the aforementioned ions. As it turned out, whole associations of molecules are formed in water - clusters, sometimes combined with H+ cations or OH– anions. Therefore, the transfer of ions by clusters under the influence of an electric voltage occurs as follows: accepting an ion in the direction of the applied electric field on one side, the cluster "drops" a similar ion on the other side. The presence of clusters in water perfectly explains the scientific fact that at a temperature of about 4 ° C, water has the highest density. Most of the water molecules in this case are in clusters due to the action of hydrogen and covalent bonds, practically in a quasi-crystalline state; in this case, thermal dissociation is minimal, and the formation of ice crystals, which has a lower density (ice floats in water), has not yet begun.

In general, the resistivity of liquids shows a stronger dependence on temperature, so this characteristic is always measured at a temperature of 293 K, which corresponds to a temperature of 20 °C.

In addition to water, there are a large number of other solvents capable of creating cations and anions of solutes. Knowledge and measurement of the resistivity of such solutions is also of great practical importance.

For aqueous solutions of salts, acids and alkalis, the concentration of the dissolved substance plays a significant role in determining the resistivity of the solution. An example is the following table, which shows the resistivity values ​​of various substances dissolved in water at a temperature of 18 ° C:

Table 3. Resistivity values ​​of various substances dissolved in water at a temperature of 18 °C

The data of the tables are taken from the Brief Physical and Technical Reference, Volume 1, - M .: 1960

Resistivity of insulators

Of great importance in the branches of electrical engineering, electronics, radio engineering and robotics is a whole class of various substances that have a relatively high resistivity. Regardless of their state of aggregation, be it solid, liquid or gaseous, such substances are called insulators. Such materials are used to isolate individual parts of electrical circuits from each other.

An example of solid insulators is the familiar flexible electrical tape, thanks to which we restore insulation when connecting various wires. Many are familiar with porcelain insulators for the suspension of overhead power lines, textolite boards with electronic components that are part of most electronic products, ceramics, glass and many other materials. Modern solid insulating materials based on plastics and elastomers make it safe to use electric current of various voltages in a wide variety of devices and devices.

In addition to solid insulators, liquid insulators with high resistivity are widely used in electrical engineering. In power transformers of electrical networks, liquid transformer oil prevents inter-turn breakdowns due to self-induction EMF, reliably isolating the turns of the windings. In oil circuit breakers, oil is used to extinguish the electric arc that occurs when switching current sources. Capacitor oil is used to create compact capacitors with high electrical performance; in addition to these oils, natural castor oil and synthetic oils are used as liquid insulators.

At normal atmospheric pressure, all gases and their mixtures are excellent insulators from the point of view of electrical engineering, but noble gases (xenon, argon, neon, krypton), due to their inertness, have a higher resistivity, which is widely used in some areas of technology.

But the most common insulator is air, mainly composed of molecular nitrogen (75% by mass), molecular oxygen (23.15% by mass), argon (1.3% by mass), carbon dioxide, hydrogen, water and some impurities. various noble gases. It isolates the flow of current in conventional household light switches, relay-based current switches, magnetic starters and mechanical circuit breakers. It should be noted that a decrease in the pressure of gases or their mixtures below atmospheric pressure leads to an increase in their electrical resistivity. The ideal insulator in this sense is vacuum.

Specific electrical resistance of various soils

One of the most important ways to protect a person from the damaging effects of electric current in case of accidents in electrical installations is a protective grounding device.

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 devices for protecting the electrical circuit in one way or another turn off the emergency device.

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 of rocks by 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 natural science museums 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 = 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.

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