Electrical resistivity of copper ohm x km. Advantages of Electrolytic Copper

When closed electrical circuit, at the terminals of which there is a potential difference, a electric current. Free electrons, under the influence of electric field forces, move along the conductor. In their movement, electrons collide with the atoms of the conductor and give them a supply of their kinetic energy. The speed of electrons continuously changes: when electrons collide with atoms, molecules and other electrons, it decreases, then under the influence electric field increases and decreases again with a new collision. As a result, the conductor is installed uniform motion flow of electrons at a speed of several fractions of a centimeter per second. Consequently, electrons passing through a conductor always encounter resistance to their movement from its side. When electric current passes through a conductor, the latter heats up.

Electrical resistance

The electrical resistance of a conductor, which is designated Latin letter r, is the property of a body or medium to transform electrical energy into heat when an electric current passes through it.

On the diagrams electrical resistance designated as shown in Figure 1, A.

Variable electrical resistance, which serves to change the current in a circuit, is called rheostat. In the diagrams, rheostats are designated as shown in Figure 1, b. IN general view A rheostat is made from a wire of one resistance or another, wound on an insulating base. The slider or rheostat lever is placed in a certain position, as a result of which the required resistance is introduced into the circuit.

A long conductor with a small cross-section creates a large resistance to the current. Short conductors with a large cross-section provide little resistance to current.

If we take two conductors from different materials, but the same length and cross-section, then the conductors will conduct current differently. This shows that the resistance of a conductor depends on the material of the conductor itself.

The temperature of the conductor also affects its resistance. As temperature increases, the resistance of metals increases, and the resistance of liquids and coal decreases. Only some special metal alloys (manganin, constantan, nickel and others) hardly change their resistance with increasing temperature.

So, we see that the electrical resistance of a conductor depends on: 1) the length of the conductor, 2) the cross-section of the conductor, 3) the material of the conductor, 4) the temperature of the conductor.

The unit of resistance is one ohm. Om is often represented by the Greek capital letter Ω (omega). Therefore, instead of writing “The conductor resistance is 15 ohms,” you can simply write: r= 15 Ω.
1,000 ohms is called 1 kiloohm(1kOhm, or 1kΩ),
1,000,000 ohms is called 1 megaohm(1mOhm, or 1MΩ).

When comparing the resistance of conductors from various materials It is necessary to take a certain length and cross-section for each sample. Then we will be able to judge which material conducts electric current better or worse.

Video 1. Conductor resistance

Electrical resistivity

The resistance in ohms of a conductor 1 m long, with a cross section of 1 mm² is called resistivity and is designated Greek letter ρ (ro).

Table 1 shows the resistivities of some conductors.

Table 1

Resistivities of various conductors

The table shows that an iron wire with a length of 1 m and a cross-section of 1 mm² has a resistance of 0.13 Ohm. To get 1 Ohm of resistance you need to take 7.7 m of such wire. Silver has the lowest resistivity. 1 Ohm of resistance can be obtained by taking 62.5 m of silver wire with a cross section of 1 mm². Silver is the best conductor, but the cost of silver excludes the possibility of its mass use. After silver in the table comes copper: 1 m of copper wire with a cross section of 1 mm² has a resistance of 0.0175 Ohm. To get a resistance of 1 ohm, you need to take 57 m of such wire.

Chemically pure copper, obtained by refining, has found widespread use in electrical engineering for the manufacture of wires, cables, windings of electrical machines and devices. Aluminum and iron are also widely used as conductors.

The conductor resistance can be determined by the formula:

Where r– conductor resistance in ohms; ρ – resistivity conductor; l– conductor length in m; S– conductor cross-section in mm².

Example 1. Determine the resistance of 200 m of iron wire with a cross section of 5 mm².

Example 2. Calculate the resistance of 2 km of aluminum wire with a cross section of 2.5 mm².

From the resistance formula you can easily determine the length, resistivity and cross-section of the conductor.

Example 3. For a radio receiver, it is necessary to wind a 30 Ohm resistor from nickel wire with a cross section of 0.21 mm². Determine the required wire length.

Example 4. Determine the cross-section of 20 m of nichrome wire if its resistance is 25 Ohms.

Example 5. A wire with a cross section of 0.5 mm² and a length of 40 m has a resistance of 16 Ohms. Determine the wire material.

The material of the conductor characterizes its resistivity.

Using the resistivity table, we find that lead has this resistance.

It was stated above that the resistance of conductors depends on temperature. Let's do the following experiment. Let's wind several meters of thin metal wire in the form of a spiral and connect this spiral to the battery circuit. To measure current, we connect an ammeter to the circuit. When the coil is heated in the burner flame, you will notice that the ammeter readings will decrease. This shows that the resistance of a metal wire increases with heating.

For some metals, when heated by 100°, the resistance increases by 40–50%. There are alloys that change their resistance slightly with heating. Some special alloys show virtually no change in resistance when temperature changes. The resistance of metal conductors increases with increasing temperature, while the resistance of electrolytes (liquid conductors), coal and some solids, on the contrary, decreases.

The ability of metals to change their resistance with changes in temperature is used to construct resistance thermometers. This thermometer is a platinum wire wound on a mica frame. By placing a thermometer, for example, in a furnace and measuring the resistance of the platinum wire before and after heating, the temperature in the furnace can be determined.

The change in resistance of a conductor when it is heated per 1 ohm of initial resistance and per 1° temperature is called temperature coefficient of resistance and is denoted by the letter α.

If at temperature t 0 conductor resistance is r 0 , and at temperature t equals r t, then the temperature coefficient of resistance

Note. Calculation using this formula can only be done in a certain temperature range (up to approximately 200°C).

We present the values ​​of the temperature coefficient of resistance α for some metals (Table 2).

Table 2

Temperature coefficient values ​​for some metals

From the formula for the temperature coefficient of resistance we determine r t:

r t = r 0 .

Example 6. Determine the resistance of an iron wire heated to 200°C if its resistance at 0°C was 100 Ohms.

r t = r 0 = 100 (1 + 0.0066 × 200) = 232 ohms.

Example 7. A resistance thermometer made of platinum wire had a resistance of 20 ohms in a room at 15°C. The thermometer was placed in the oven and after some time its resistance was measured. It turned out to be equal to 29.6 Ohms. Determine the temperature in the oven.

Electrical conductivity

So far, we have considered the resistance of a conductor as the obstacle that the conductor provides to the electric current. But still, current passes through the conductor. Therefore, in addition to resistance (obstacle), the conductor also has the ability to conduct electric current, that is, conductivity.

The more resistance a conductor has, the less conductivity it has, the worse it conducts electric current, and, conversely, the lower the resistance of a conductor, the more conductivity it has, the easier it is for current to pass through the conductor. Therefore, the resistance and conductivity of a conductor are reciprocal quantities.

From mathematics it is known that the inverse of 5 is 1/5 and, conversely, the inverse of 1/7 is 7. Therefore, if the resistance of a conductor is denoted by the letter r, then the conductivity is defined as 1/ r. Conductivity is usually symbolized by the letter g.

Electrical conductivity is measured in (1/Ohm) or in siemens.

Example 8. The conductor resistance is 20 ohms. Determine its conductivity.

If r= 20 Ohm, then

Example 9. The conductivity of the conductor is 0.1 (1/Ohm). Determine its resistance

If g = 0.1 (1/Ohm), then r= 1 / 0.1 = 10 (Ohm)

As we know from Ohm’s law, the current in a section of the circuit is in the following relationship: I=U/R. The law was derived through a series of experiments by the German physicist Georg Ohm in the 19th century. He noticed a pattern: the current strength in any section of the circuit directly depends on the voltage that is applied to this section, and inversely on its resistance.

It was later found that the resistance of a section depends on its geometric characteristics as follows: R=ρl/S,

where l is the length of the conductor, S is its cross-sectional area, and ρ is a certain proportionality coefficient.

Thus, the resistance is determined by the geometry of the conductor, as well as by such a parameter as resistivity (hereinafter referred to as resistivity) - this is the name of this coefficient. If you take two conductors with the same cross-section and length and place them in a circuit one by one, then by measuring the current and resistance, you can see that in the two cases these indicators will be different. Thus, the specific electrical resistance- this is a characteristic of the material from which the conductor is made, or, to be even more precise, the substance.

Conductivity and resistance

U.S. shows the ability of a substance to prevent the passage of current. But in physics there is also reciprocal- conductivity. It shows the ability to conduct electric current. It looks like this:

σ=1/ρ, where ρ is the resistivity of the substance.

If we talk about conductivity, it is determined by the characteristics of charge carriers in this substance. So, metals have free electrons. There are no more than three of them on the outer shell, and it is more profitable for the atom to “give them away,” which is what happens when chemical reactions with substances from the right side of the periodic table. In a situation where we have a pure metal, it has a crystalline structure in which these outer electrons are shared. They are the ones that transfer charge if an electric field is applied to the metal.

In solutions, charge carriers are ions.

If we talk about substances such as silicon, then in its properties it is semiconductor and it works on a slightly different principle, but more on that later. In the meantime, let’s figure out how these classes of substances differ:

1. Conductors;
2. Semiconductors;
3. Dielectrics.

Conductors and dielectrics

There are substances that almost do not conduct current. They are called dielectrics. Such substances are capable of polarization in an electric field, that is, their molecules can rotate in this field depending on how they are distributed in them electrons. But since these electrons are not free, but serve for communication between atoms, they do not conduct current.

The conductivity of dielectrics is almost zero, although there are no ideal ones among them (this is the same abstraction as an absolutely black body or an ideal gas).

The conventional boundary of the concept of “conductor” is ρ<10^-5 Ом, а нижний порог такового у диэлектрика - 10^8 Ом.

In between these two classes there are substances called semiconductors. But their separation into a separate group of substances is associated not so much with their intermediate state in the “conductivity - resistance” line, but with the features of this conductivity under different conditions.

Dependence on environmental factors

Conductivity is not a completely constant value. The data in the tables from which ρ is taken for calculations exists for normal environmental conditions, that is, for a temperature of 20 degrees. In reality, it is difficult to find such ideal conditions for the operation of a circuit; actually US (and therefore conductivity) depend on the following factors:

1. temperature;
2. pressure;
3. presence of magnetic fields;
4. light;
5. state of aggregation.

Different substances have their own schedule for changing this parameter under different conditions. Thus, ferromagnets (iron and nickel) increase it when the direction of the current coincides with the direction of the magnetic field lines. As for temperature, the dependence here is almost linear (there is even a concept of temperature coefficient of resistance, and this is also a tabular value). But the direction of this dependence is different: for metals it increases with increasing temperature, and for rare earth elements and electrolyte solutions it increases - and this is within the same state of aggregation.

For semiconductors, the dependence on temperature is not linear, but hyperbolic and inverse: with increasing temperature, their conductivity increases. This qualitatively distinguishes conductors from semiconductors. This is what the dependence of ρ on temperature for conductors looks like:

The resistivities of copper, platinum and iron are shown here. Some metals, for example, mercury, have a slightly different graph - when the temperature drops to 4 K, it loses it almost completely (this phenomenon is called superconductivity).

And for semiconductors this dependence will be something like this:

When transitioning to the liquid state, the ρ of the metal increases, but then they all behave differently. For example, for molten bismuth it is lower than at room temperature, and for copper it is 10 times higher than normal. Nickel leaves the linear graph at another 400 degrees, after which ρ falls.

But tungsten has such a high temperature dependence that it causes incandescent lamps to burn out. When turned on, the current heats the coil, and its resistance increases several times.

Also y. With. alloys depends on the technology of their production. So, if we are dealing with a simple mechanical mixture, then the resistance of such a substance can be calculated using the average, but for a substitution alloy (this is when two or more elements are combined into one crystal lattice) it will be different, as a rule, much greater. For example, nichrome, from which spirals for electric stoves are made, has such a value for this parameter that when connected to the circuit, this conductor heats up to the point of redness (which is why, in fact, it is used).

Here is the characteristic ρ of carbon steels:

As can be seen, as it approaches the melting temperature, it stabilizes.

Resistivity of various conductors

Be that as it may, in the calculations ρ is used precisely under normal conditions. Here is a table by which you can compare this characteristic of different metals:

As can be seen from the table, the best conductor is silver. And only its cost prevents its widespread use in cable production. U.S. aluminum is also small, but less than gold. From the table it becomes clear why the wiring in houses is either copper or aluminum.

The table does not include nickel, which, as we have already said, has a slightly unusual graph of y. With. on temperature. The resistivity of nickel after increasing the temperature to 400 degrees begins not to increase, but to fall. It also behaves interestingly in other substitution alloys. This is how an alloy of copper and nickel behaves, depending on the percentage of both:

And this interesting graph shows the resistance of Zinc - magnesium alloys:

High-resistivity alloys are used as materials for the manufacture of rheostats, here are their characteristics:

These are complex alloys consisting of iron, aluminum, chromium, manganese, and nickel.

As for carbon steels, it is approximately 1.7*10^-7 Ohm m.

The difference between y. With. The different conductors are determined by their application. Thus, copper and aluminum are widely used in the production of cables, and gold and silver are used as contacts in a number of radio engineering products. High-resistance conductors have found their place among manufacturers of electrical appliances (more precisely, they were created for this purpose).

The variability of this parameter depending on environmental conditions formed the basis for such devices as magnetic field sensors, thermistors, strain gauges, and photoresistors.

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 magnitude is very small.

But conductors also conduct current differently. According to Georg 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 electric current, being a dielectric. But distilled water does not exist in nature; it always contains salts, bacteria and other impurities. This cocktail is a conductor of electric current with resistivity.

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.

Dependence of resistivity on temperature

The resistivities 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 is conducted inside the material free electrons. Under the influence of an electric field, they are separated from their atoms and move between them in the direction specified by this field. The atoms of a substance form a crystal lattice, between the nodes of which a flow of electrons, also called “electron gas,” moves. Under the influence of temperature, lattice nodes (atoms) vibrate. 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 their trajectory. At some points in time, electrons can move in the direction opposite to the direction of the electric current.

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

An example of the use of the dependence of resistivity on temperature is the operation of an incandescent lamp. The tungsten spiral from which the filament is made has a low resistivity at the moment of switching on. An inrush 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 nichrome wire of a known cross-section to create the required resistance. For calculations, you need the resistivity of the heated wire, and reference books give values ​​for room temperature. Therefore, the final length of the nichrome spiral is adjusted experimentally. Calculations determine the approximate length, and when adjusting, the thread is gradually shortened section by section.

Temperature coefficient of resistance

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

To quantify the dependence of material resistance on temperature, the concept 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 measuring equipment circuits, materials with low TCR are used. They are more expensive, but the device parameters do not change over a wide range of ambient temperatures.

But the properties of materials with high TCS are also used. The operation of some temperature sensors is based on changes 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 current against a standard thermometer, an electronic temperature meter is obtained. This principle is used not only for measurements, but also for overheating sensors. Disabling the device when abnormal operating conditions occur, leading to overheating of the windings of transformers or power semiconductor elements.

Elements are also used in electrical engineering that change their resistance not from the ambient temperature, but from the current through them - thermistors. An example of their use is demagnetization systems for cathode ray tubes of televisions and monitors. When voltage is applied, the resistance of the resistor is minimal, and current passes through it into the demagnetization coil. But the same current heats the thermistor material. Its resistance increases, reducing the current and voltage across the coil. And so on until it completely disappears. 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 tube filament heats up, it is already demagnetized. And the control circuit remains locked 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°C. There are no temperatures below this limit. 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 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 in domestic conditions 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 become familiar with the principles of calculating the length of nichrome wire for making a heating element. But there are other situations where knowledge of the resistivity of materials is necessary.

For calculation contours of grounding devices 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 first measured. This way, the calculation results are more accurate, which eliminates the need to adjust the circuit parameters during manufacturing: adding the number of electrodes, leading to an increase in the geometric dimensions of the grounding device.

The resistivity 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, use 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.

Electrical resistivity, or just resistivity substance - a physical quantity characterizing the ability of a substance to prevent the passage of electric current.

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

Electrical resistance of a homogeneous conductor with resistivity ρ, length l and cross-sectional area S can be calculated using the formula R = ρ ⋅ l S (\displaystyle R=(\frac (\rho \cdot l)(S)))(it is assumed that neither the area nor the cross-sectional shape changes along the conductor). Accordingly, for ρ we have ρ = R ⋅ S l . (\displaystyle \rho =(\frac (R\cdot S)(l)).)

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

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

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

  Generalization of the concept of resistivity

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

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

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

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

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

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

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

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

  Quantities ρ i (\displaystyle \rho _(i)) called main values resistivity tensor.

  Relation to conductivity

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

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

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

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

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

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

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

  Electrical resistivity of some substances

  Metal single crystals

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

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

  Resistivity is an applied concept in electrical engineering. It denotes how much resistance per unit length a material of a unit cross-section has to the current flowing through it - in other words, what resistance a wire of a millimeter cross-section one meter long has. This concept is used in various electrical calculations.

  It is important to understand the differences between DC electrical resistivity and AC electrical resistivity. In the first case, the resistance is caused solely by the action of direct current on the conductor. In the second case, alternating current (it can be of any shape: sinusoidal, rectangular, triangular or arbitrary) causes an additional vortex field in the conductor, which also creates resistance.

  Physical representation

  In technical calculations involving the laying of cables of various diameters, parameters are used to calculate the required cable length and its electrical characteristics. One of the main parameters is resistivity. Electrical resistivity formula:

  ρ = R * S / l, where:

  • ρ is the resistivity of the material;
  • R is the ohmic electrical resistance of a particular conductor;
  • S - cross section;
  • l - length.

  The dimension ρ is measured in Ohm mm 2 /m, or, to abbreviate the formula - Ohm m.

  The value of ρ for the same substance is always the same. Therefore, this is a constant characterizing the material of the conductor. It is usually indicated in directories. Based on this, it is already possible to calculate technical quantities.

  It is important to say about specific electrical conductivity. This value is the inverse of the resistivity of the material, and is used equally with it. It is also called electrical conductivity. The higher this value, the better the metal conducts current. For example, the conductivity of copper is 58.14 m/(Ohm mm2). Or, in SI units: 58,140,000 S/m. (Siemens per meter is the SI unit of electrical conductivity).

  We can talk about resistivity only in the presence of elements that conduct current, since dielectrics have infinite or close to infinite electrical resistance. In contrast, metals are very good conductors of current. You can measure the electrical resistance of a metal conductor using a milliohmmeter, or an even more accurate microohmmeter. The value is measured between their probes applied to the conductor section. They allow you to check circuits, wiring, windings of motors and generators.

  Metals vary in their ability to conduct current. The resistivity of various metals is a parameter that characterizes this difference. The data is given at a material temperature of 20 degrees Celsius:

  

  The parameter ρ shows what resistance a meter conductor with a cross section of 1 mm 2 will have. The higher this value, the greater the electrical resistance of the desired wire of a certain length. The smallest ρ, as can be seen from the list, is silver; the resistance of one meter of this material will be equal to only 0.015 Ohms, but this is too expensive a metal to use on an industrial scale. Next comes copper, which is much more common in nature (not a precious metal, but a non-ferrous metal). Therefore, copper wiring is very common.

  Copper is not only a good conductor of electric current, but also a very ductile material. Thanks to this property, copper wiring fits better and is resistant to bending and stretching.

  Copper is in great demand on the market. Many different products are made from this material:

  • A huge variety of conductors;
  • Auto parts (eg radiators);
  • Clock mechanisms;
  • Computer components;
  • Parts of electrical and electronic devices.

  The electrical resistivity of copper is one of the best among current-conducting materials, so many electrical industry products are created based on it. In addition, copper is easy to solder, so it is very common in amateur radio.

  The high thermal conductivity of copper allows it to be used in cooling and heating devices, and its plasticity makes it possible to create the smallest parts and the thinnest conductors.

  Conductors of electric current are of the first and second kind. Conductors of the first kind are metals. Conductors of the second type are conductive solutions of liquids. The current in the first type is carried by electrons, and the current carriers in conductors of the second type are ions, charged particles of the electrolytic liquid.

  We can only talk about the conductivity of materials in the context of ambient temperature. At a higher temperature, conductors of the first type increase their electrical resistance, and the second, on the contrary, decrease. Accordingly, there is a temperature coefficient of resistance of materials. The resistivity of copper Ohm m increases with increasing heating. The temperature coefficient α also depends only on the material; this value has no dimension and for different metals and alloys is equal to the following indicators:

  • Silver - 0.0035;
  • Iron - 0.0066;
  • Platinum - 0.0032;
  • Copper - 0.0040;
  • Tungsten - 0.0045;
  • Mercury - 0.0090;
  • Constantan - 0.000005;
  • Nickelin - 0.0003;
  • Nichrome - 0.00016.

  Determination of the electrical resistance value of a conductor section at elevated temperature R (t) is calculated using the formula:

  R (t) = R (0) · , where:

  • R (0) - resistance at initial temperature;
  • α - temperature coefficient;
  • t - t (0) - temperature difference.

  For example, knowing the electrical resistance of copper at 20 degrees Celsius, you can calculate what it will be equal to at 170 degrees, that is, when heated by 150 degrees. The initial resistance will increase by a factor of 1.6.

  As the temperature increases, the conductivity of materials, on the contrary, decreases. Since this is the reciprocal of electrical resistance, it decreases exactly the same amount. For example, the electrical conductivity of copper when the material is heated by 150 degrees will decrease by 1.6 times.

  There are alloys that practically do not change their electrical resistance when temperature changes. This is, for example, constantan. When the temperature changes by one hundred degrees, its resistance increases by only 0.5%.

  While the conductivity of materials deteriorates with heat, it improves with decreasing temperature. This is related to the phenomenon of superconductivity. If you lower the temperature of the conductor below -253 degrees Celsius, its electrical resistance will sharply decrease: almost to zero. In this regard, the costs of transmitting electrical energy are falling. The only problem was cooling the conductors to such temperatures. However, due to the recent discoveries of high-temperature superconductors based on copper oxides, materials have to be cooled to acceptable values.