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How to find out resistivity. What is copper resistivity: values, characteristics, values

Electrical resistivity, or simply 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 area cross section 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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  Encyclopedic YouTube The unit of resistivity in the International System of Units (SI) is Ohm · . From the relationρ = R ⋅ S l (\displaystyle \rho =(\frac (R\cdot S)(l)))

  In technology, the outdated non-systemic unit Ohm mm²/m is also used, equal to 10 −6 of 1 Ohm m. This unit is equal to the resistivity of a substance at which a homogeneous conductor 1 m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 non-uniform 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 current density and voltage vectors electric field

  at any given point the substances 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)) (\displaystyle E_(i)((\vec (r)))=\sum _(j=1)^(3)\rho _(ij)((\vec (r)))J_(j)(( \vec (r))).) does not depend on coordinates. Tensor symmetrical, that is, for any i (\displaystyle i) And j (\displaystyle j).

  performed (\displaystyle E_(i)((\vec (r)))=\sum _(j=1)^(3)\rho _(ij)((\vec (r)))J_(j)(( \vec (r))).)ρ i j = ρ j i (\displaystyle \rho _(ij)=\rho _(ji)) As for any symmetric tensor, for you can choose an orthogonal system (\displaystyle E_(i)((\vec (r)))=\sum _(j=1)^(3)\rho _(ij)((\vec (r)))J_(j)(( \vec (r))).) Cartesian coordinates , in which the matrix becomes (\displaystyle E_(i)((\vec (r)))=\sum _(j=1)^(3)\rho _(ij)((\vec (r)))J_(j)(( \vec (r))).) diagonal , that is, it takes on the form in which out of nine components, Only three are non-zero:, that is, for any ρ 11 (\displaystyle \rho _(11))ρ 22 (\displaystyle \rho _(22)) 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).) Quantitiesρ i (\displaystyle \rho _(i)) called main values

  resistivity tensor.

  Relation to conductivity In isotropic materials, the relationship between resistivityρ (\displaystyle \rho ) and specific conductivityσ (\displaystyle \sigma )

  expressed by equality

  ρ = 1 σ. (\displaystyle E_(i)((\vec (r)))=\sum _(j=1)^(3)\rho _(ij)((\vec (r)))J_(j)(( \vec (r))).)(\displaystyle \rho =(\frac (1)(\sigma )).)

  In the case of anisotropic materials, the relationship between the components of the resistivity tensor

  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)) 1 , 2 , that is, for any 3 .

  - 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

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

  Bismuth

  Cadmium

  During experiments on the interaction of electricity with various substances, including metals, he established a fundamental relationship between density, electric field strength and the property of a substance, which was called “specific conductivity”. The formula corresponding to this pattern, called “Ohm’s Law,” is as follows:

  j= λE , wherein

  • j— density electric current;
  • λ — specific conductivity, also called “electrical conductivity”;
  • E – electric field strength.

  In some cases, a different letter of the Greek alphabet is used to indicate conductivity - σ . Specific conductivity depends on certain parameters of the substance. Its value is influenced by temperature, substances, pressure, if it is a gas, and most importantly, the structure of this substance. Ohm's law is observed only for homogeneous substances.

  For more convenient calculations the reciprocal of specific conductivity is used. It is called “resistivity”, which is also associated with the properties of the substance in which the electric current flows, denoted by the Greek letter ρ and has the dimension Ohm*m. But since different theoretical justifications apply to different physical phenomena, alternative formulas can be used for resistivity. They are a reflection of the classical electronic theory of metals, as well as quantum theory.

  Formulas

  In these formulas, which are tedious for ordinary readers, factors such as Boltzmann's constant, Avogadro's constant and Planck's constant appear. These constants are used for calculations that take into account the free path of electrons in a conductor, their speed during thermal movement, the degree of ionization, concentration and density of the substance. In short, everything is quite complicated for a non-specialist. In order not to be unfounded, below you can familiarize yourself with how everything actually looks:

  Features of metals

  Since the movement of electrons depends on the homogeneity of the substance, the current in a metal conductor flows according to its structure, which affects the distribution of electrons in the conductor, taking into account its heterogeneity. It is determined not only by the presence of impurity inclusions, but also by physical defects - cracks, voids, etc. The heterogeneity of the conductor increases its resistivity, which is determined by Matthiesen's rule.

  This easy-to-understand rule essentially says that several separate resistivities can be distinguished in a current-carrying conductor. And the resulting value will be their sum. The components will be the resistivity of the metal crystal lattice, impurities and conductor defects. Since this parameter depends on the nature of the substance, corresponding laws have been defined to calculate it, including for mixed substances.

  Despite the fact that alloys are also metals, they are considered as solutions with a chaotic structure, and for calculating the resistivity, it matters which metals are included in the alloy. Basically, most alloys of two components that do not belong to transition metals, as well as rare earth metals, fall under the description of Nodheim's law.

  The resistivity of metal thin films is considered as a separate topic. It is quite logical to assume that its value should be greater than that of a bulk conductor made of the same metal. But at the same time, a special empirical Fuchs formula is introduced for the film, which describes the interdependence of resistivity and film thickness. It turns out that metals in films exhibit semiconductor properties.

  And the process of charge transfer is influenced by electrons, which move in the direction of the film thickness and interfere with the movement of “longitudinal” charges. At the same time, they are reflected from the surface of the film conductor, and thus one electron oscillates between its two surfaces for quite a long time. Another significant factor in increasing resistivity is the temperature of the conductor. The higher the temperature, the greater the resistance. Conversely, the lower the temperature, the lower the resistance.

  Metals are the substances with the lowest resistivity at so-called “room” temperature. The only non-metal that justifies its use as a conductor is carbon. Graphite, which is one of its varieties, is widely used for making sliding contacts. He has a very good combination properties such as resistivity and sliding friction coefficient. Therefore, graphite is an indispensable material for electric motor brushes and other sliding contacts. The resistivity values ​​of the main substances used for industrial purposes are given in the table below.

  

  Superconductivity

  At temperatures corresponding to the liquefaction of gases, that is, up to the temperature of liquid helium, which is equal to -273 degrees Celsius, the resistivity decreases almost to complete disappearance. And not just good metal conductors such as silver, copper and aluminum. Almost all metals. Under such conditions, which are called superconductivity, the structure of the metal has no inhibitory effect on the movement of charges under the influence of an electric field. Therefore, mercury and most metals become superconductors.

  But, as it turned out, relatively recently in the 80s of the 20th century, some types of ceramics are also capable of superconductivity. Moreover, you do not need to use liquid helium for this. Such materials were called high-temperature superconductors. However, several decades have already passed, and the range of high-temperature conductors has expanded significantly. But mass use of such high-temperature superconducting elements has not been observed. In some countries, single installations have been made with the replacement of conventional copper conductors with high-temperature superconductors. To maintain the normal regime of high-temperature superconductivity, liquid nitrogen is required. And this turns out to be a too expensive technical solution.

  Therefore, the low resistivity value given by Nature to copper and aluminum still makes them irreplaceable materials for the manufacture of various electrical conductors.

  We know what's the reason electrical resistance conductor is the interaction of electrons with ions of the metal crystal lattice (§ 43). Therefore, it can be assumed that the resistance of a conductor depends on its length and cross-sectional area, as well as on the substance from which it is made.

  Figure 74 shows the setup for conducting such an experiment. Various conductors are included in the current source circuit in turn, for example:

  1. nickel wires of the same thickness, but different lengths;
  2. nickel wires of the same length, but different thicknesses (different cross-sectional areas);
  3. nickel and nichrome wires of the same length and thickness.

  The current in the circuit is measured with an ammeter, and the voltage with a voltmeter.

  Knowing the voltage at the ends of the conductor and the current in it, using Ohm's law, you can determine the resistance of each of the conductors.

  Rice. 74. Dependence of conductor resistance on its size and type of substance

  After performing these experiments, we will establish that:

  1. of two nickel wires of the same thickness, the longer wire has greater resistance;
  2. of two nickelin wires of the same length, the wire with a smaller cross-section has the greater resistance;
  3. nickel and nichrome wire Same sizes have different resistances.

  Ohm was the first to study experimentally the dependence of the resistance of a conductor on its size and the substance from which the conductor is made. He found that resistance is directly proportional to the length of the conductor, inversely proportional to its cross-sectional area and depends on the substance of the conductor.

  How to take into account the dependence of resistance on the material from which the conductor is made? To do this, calculate the so-called resistivity of a substance.

  Specific resistance is a physical quantity that determines the resistance of a conductor made of a given substance with a length of 1 m and a cross-sectional area of ​​1 m 2.

  Let's introduce letter designations: ρ is the resistivity of the conductor, I is the length of the conductor, S is its cross-sectional area. Then the conductor resistance R will be expressed by the formula

  From it we get that:

  

  From the last formula you can determine the unit of resistivity. Since the unit of resistance is 1 ohm, the unit of cross-sectional area is 1 m2, and the unit of length is 1 m, then the unit of resistivity is:

  

  It is more convenient to express the cross-sectional area of ​​the conductor in square millimeters, since it is most often small. Then the unit of resistivity will be:

  Table 8 shows the resistivity values ​​of some substances at 20 °C. Specific resistance changes with temperature. It has been experimentally established that for metals, for example, the resistivity increases with increasing temperature.

  Table 8. Electrical resistivity of some substances (at t = 20 °C)

  

  Of all the metals, silver and copper have the lowest resistivity. Therefore, silver and copper are the best conductors of electricity.

  When wiring electrical circuits, aluminum, copper and iron wires are used.

  In many cases, devices with high resistance are needed. They are made from specially created alloys - substances with high resistivity. For example, as can be seen from Table 8, the nichrome alloy has a resistivity almost 40 times greater than aluminum.

  Porcelain and ebonite have such a high resistivity that they almost do not conduct electric current at all; they are used as insulators.

  Questions

  1. How does the resistance of a conductor depend on its length and cross-sectional area?
  2. How to experimentally show the dependence of the resistance of a conductor on its length, cross-sectional area and the substance from which it is made?
  3. What is the resistivity of a conductor?
  4. What formula can be used to calculate the resistance of conductors?
  5. What units is the resistivity of a conductor expressed in?
  6. What substances are conductors used in practice made from?

  What is the resistivity of a substance? To reply in simple words To answer this question, you need to remember the physics course and imagine the physical embodiment of this definition. An electric current is passed through a substance, and it, in turn, prevents the passage of current with some force.

  The concept of resistivity of a substance

  It is this value, which shows how strongly a substance impedes the flow of current, that is the specific resistance (the Latin letter “rho”). In the international system of units, resistance expressed in Ohms, multiplied by meter. The formula for the calculation is: “Resistance is multiplied by the cross-sectional area and divided by the length of the conductor.”

  The question arises: “Why is another resistance used when finding resistivity?” The answer is simple, there are two different quantities - resistivity and resistance. The second shows how capable a substance is of preventing current from passing through it, and the first shows practically the same thing, only we are no longer talking about a substance in in a general sense, but about a conductor with a specific length and cross-sectional area, which are made of this substance.

  The reciprocal quantity that characterizes the ability of a substance to transmit electricity is called specific electrical conductivity, and the formula by which specific resistivity is calculated is directly related to specific conductivity.

  Copper Applications

  The concept of resistivity is widely used in calculating the conductivity of electric current. various metals. Based on these calculations, decisions are made on the advisability of using a particular metal for the manufacture of electrical conductors, which are used in construction, instrument making and other fields.

  Metal resistance table

  Are there specific tables? which bring together the available information on the transmission and resistance of metals, as a rule, these tables are calculated for certain conditions.

  In particular, it is widely known metal monocrystal resistance table at a temperature of twenty degrees Celsius, as well as a table of resistance of metals and alloys.

  These tables are used to calculate various data under so-called ideal conditions; in order to calculate values ​​for specific purposes, you need to use formulas.

  Copper. Its characteristics and properties

  Description of substance and properties

  Copper is a metal that was discovered by mankind a long time ago and has also long been used for various technical purposes. Copper is a very malleable and ductile metal with high electrical conductivity, making it very popular for making various wires and conductors.

  Physical properties of copper:

  • melting point - 1084 degrees Celsius;
  • boiling point - 2560 degrees Celsius;
  • density at 20 degrees - 8890 kilograms divided by cubic meter;
  • specific heat capacity at constant pressure and temperature 20 degrees - 385 kJ/J*kg
  • electrical resistivity - 0.01724;

  Copper grades

  This metal can be divided into several groups or grades, each of which has its own properties and its own application in industry:

  1. Grades M00, M0, M1 are excellent for the production of cables and conductors; when remelting, oversaturation with oxygen is eliminated.
  2. Grades M2 and M3 are low-cost options that are designed for small-scale rolling and satisfy most small-scale technical and industrial tasks.
  3. Brands M1, M1f, M1r, M2r, M3r are expensive copper grades that are manufactured for a specific consumer with specific requirements and requests.

  Stamps between each other differ in several ways:

  

  The influence of impurities on the properties of copper

  Impurities can affect the mechanical, technical and operational properties of products.

  One of the most popular metals in industries is copper. It is most widely used in electrical and electronics. Most often it is used in the manufacture of windings for electric motors and transformers. The main reason for using this particular material is that copper has the lowest electrical resistivity of any material currently available. Until it appears new material with a lower value of this indicator, we can say with confidence that there will be no replacement for copper.

  General characteristics of copper

  Speaking about copper, it must be said that at the dawn of the electrical era it began to be used in the production of electrical equipment. They began to use it largely due to unique properties, which this alloy possesses. In itself it represents a material that differs high properties in terms of ductility and good malleability.

  Along with the thermal conductivity of copper, one of its most important advantages is its high electrical conductivity. It is due to this property that copper and has become widespread in power plants, in which it acts as a universal conductor. Most valuable material is electrolytic copper with a high degree of purity -99.95%. Thanks to this material, it becomes possible to produce cables.

  Pros of using electrolytic copper

  The use of electrolytic copper allows you to achieve the following:

  • Ensure high electrical conductivity;
  • Achieve excellent styling ability;
  • Provide a high degree of plasticity.

  Areas of application

  Cable products made from electrolytic copper are widely used in various industries. Most often it is used in the following areas:

  • electrical industry;
  • electrical appliances;
  • automotive industry;
  • production of computer equipment.

  What is the resistivity?

  To understand what copper is and its characteristics, it is necessary to understand the main parameter of this metal - resistivity. It should be known and used when performing calculations.

  Specific resistance is usually understood as physical quantity, which is characterized as the ability of a metal to conduct electric current.

  It is also necessary to know this value in order to correctly calculate electrical resistance conductor. When making calculations, they are also guided by its geometric dimensions. When carrying out calculations, use the following formula:

  This formula is familiar to many. Using it, you can easily calculate the resistance copper cable, focusing only on the characteristics electrical network. It allows you to calculate the power that is inefficiently spent on heating the cable core. Besides, a similar formula allows you to calculate resistance any cable. It does not matter what material was used to make the cable - copper, aluminum or some other alloy.

  A parameter such as electrical resistivity is measured in Ohm*mm2/m. This indicator for copper wiring laid in an apartment is 0.0175 Ohm*mm2/m. If you try to look for an alternative to copper - a material that could be used instead, then only silver can be considered the only suitable one, whose resistivity is 0.016 Ohm*mm2/m. However, when choosing a material, it is necessary to pay attention not only to resistivity, but also to reverse conductivity. This value is measured in Siemens (Cm).

  Siemens = 1/ Ohm.

  For copper of any weight, this composition parameter is 58,100,000 S/m. As for silver, its reverse conductivity is 62,500,000 S/m.

  In our world of high technology, when every home has a large number of electrical devices and installations, the importance of a material such as copper is simply invaluable. This material used to make wiring, without which no room can do. If copper did not exist, then man would have to use wires from other available materials, for example, from aluminum. However, in this case one would have to face one problem. The thing is that this material has a much lower conductivity than copper conductors.

  Resistivity

  The use of materials with low electrical and thermal conductivity of any weight leads to large losses of electricity. A this affects power loss on the equipment used. Most experts call copper as the main material for making insulated wires. It is the main material from which individual elements of equipment powered by electric current are made.

  • Boards installed in computers are equipped with etched copper traces.
  • Copper is also used to make a wide variety of components used in electronic devices.
  • In transformers and electric motors it is represented by a winding, which is made of this material.

  There is no doubt that the expansion of the scope of application of this material will occur with further development technical progress. Although, besides copper, there are other materials, but still the designer when creating equipment and various installations use copper. main reason the demand for this material lies in good electrical and thermal conductivity of this metal, which it provides in conditions room temperature.

  Temperature coefficient of resistance

  All metals with any thermal conductivity have the property of decreasing conductivity with increasing temperature. As the temperature decreases, conductivity increases. Experts call the property of decreasing resistance with decreasing temperature particularly interesting. Indeed, in this case, when the temperature in the room drops to a certain value, the conductor may lose electrical resistance and it will move into the class of superconductors.

  In order to determine the resistance value of a particular conductor of a certain weight at room temperature, there is a critical resistance coefficient. It is a value that shows the change in resistance of a section of a circuit when the temperature changes by one Kelvin. To calculate the electrical resistance of a copper conductor in a certain time period, use the following formula:

  ΔR = α*R*ΔT, where α is the temperature coefficient of electrical resistance.

  Conclusion

  Copper is a material that is widely used in electronics. It is used not only in windings and circuits, but also as a metal for the manufacture of cable products. For machinery and equipment to work effectively, it is necessary correctly calculate the resistivity of the wiring, laid in the apartment. There is a certain formula for this. Knowing it, you can make a calculation that allows you to find out the optimal size of the cable cross-section. In this case, it is possible to avoid loss of equipment power and ensure its efficient use.