Resistivity of zinc ohm m. What is resistivity of copper: values, characteristics, values

One of the most common metals for making wires is copper. Its electrical resistance is the lowest among affordable metals. It is less only for precious metals (silver and gold) and depends on various factors.

What is electric current

There are different carriers at different poles of a battery or other current source electric charge. If they are connected to a conductor, charge carriers begin to move from one pole of the voltage source to the other. These carriers in liquids are ions, and in metals they are free electrons.

Definition. Electric current is the directed movement of charged particles.

Resistivity

Electrical resistivity is a value that determines the electrical resistance of a reference sample of a material. The Greek letter “p” is used to denote this quantity. Formula for calculation:

p=(R*S)/ l.

This value is measured in Ohm*m. You can find it in reference books, in resistivity tables or on the Internet.

Free electrons move through the metal within the crystal lattice. Three factors influence the resistance to this movement and the resistivity of the conductor:

• Material. U different metals different densities of atoms and the number of free electrons;
• Impurities. In pure metals crystal lattice more ordered, therefore the resistance is lower than in alloys;
• Temperature. Atoms are not stationary in their places, but vibrate. The higher the temperature, the greater the amplitude of oscillations, which interferes with the movement of electrons, and the higher the resistance.

In the following figure you can see a table of the resistivity of metals.

Interesting. There are alloys whose electrical resistance drops when heated or does not change.

Conductivity and electrical resistance

Since cable dimensions are measured in meters (length) and mm² (section), the electrical resistivity has the dimension Ohm mm²/m. Knowing the dimensions of the cable, its resistance is calculated using the formula:

R=(p* l)/S.

In addition to electrical resistance, some formulas use the concept of “conductivity”. This is the reciprocal of resistance. It is designated “g” and is calculated using the formula:

Conductivity of liquids

The conductivity of liquids is different from the conductivity of metals. The charge carriers in them are ions. Their number and electrical conductivity increase when heated, so the power of the electrode boiler increases several times when heated from 20 to 100 degrees.

Interesting. Distilled water is an insulator. Dissolved impurities give it conductivity.

Electrical resistance of wires

The most common metals for making wires are copper and aluminum. Aluminum has a higher resistance, but is cheaper than copper. The resistivity of copper is lower, so the wire cross-section can be chosen smaller. In addition, it is stronger, and flexible stranded wires are made from this metal.

The following table shows the electrical resistivity of metals at 20 degrees. In order to determine it at other temperatures, the value from the table must be multiplied by a correction factor, different for each metal. You can find out this coefficient from the relevant reference books or using an online calculator.

Selection of cable cross-section

Because a wire has resistance, when electric current passes through it, heat is generated and a voltage drop occurs. Both of these factors must be taken into account when choosing cable cross-sections.

Selection by permissible heating

When current flows in a wire, energy is released. Its quantity can be calculated using the electric power formula:

In a copper wire with a cross section of 2.5 mm² and a length of 10 meters, R = 10 * 0.0074 = 0.074 Ohm. At a current of 30A P=30²*0.074=66W.

This power heats the conductor and the cable itself. The temperature to which it heats up depends on the installation conditions, the number of cores in the cable and other factors, and permissible temperature– on the insulation material. Copper has greater conductivity, so the power output and the required cross-section are lower. It is determined using special tables or using an online calculator.

Permissible voltage loss

In addition to heating, when electric current passes through the wires, the voltage near the load decreases. This value can be calculated using Ohm's law:

Reference. According to PUE standards, it should be no more than 5% or in a 220V network - no more than 11V.

Therefore, the longer the cable, the larger its cross-section should be. You can determine it using tables or using an online calculator. In contrast to choosing a section according to permissible heating, voltage losses do not depend on the laying conditions and insulation material.

In a 220V network, voltage is supplied through two wires: phase and neutral, so the calculation is made using double the length of the cable. In the cable from the previous example it will be U=I*R=30A*2*0.074Ohm=4.44V. This is not much, but with a length of 25 meters it turns out to be 11.1V - the maximum permissible value, you will have to increase the cross-section.

Electrical resistance of other metals

In addition to copper and aluminum, other metals and alloys are used in electrical engineering:

• Iron. Steel has a higher resistivity, but is stronger than copper and aluminum. Steel strands are woven into cables designed to be laid through the air. The resistance of iron is too high to transmit electricity, so the core cross-sections are not taken into account when calculating the cross-section. In addition, it is more refractory, and leads are made from it for connecting heaters in high-power electric furnaces;
• Nichrome (an alloy of nickel and chromium) and fechral (iron, chromium and aluminum). They have low conductivity and refractoriness. Wirewound resistors and heaters are made from these alloys;
• Tungsten. Its electrical resistance is high, but it is a refractory metal (3422 °C). It is used to make filaments in electric lamps and electrodes for argon-arc welding;
• Constantan and manganin (copper, nickel and manganese). The resistivity of these conductors does not change with changes in temperature. Used in high-precision devices for the manufacture of resistors;
• Precious metals – gold and silver. They have the highest specific conductivity, but due to their high price, their use is limited.

Inductive reactance

Formulas for calculating the conductivity of wires are valid only in a direct current network or in straight conductors at low frequencies. Inductive reactance appears in coils and in high-frequency networks, many times higher than usual. In addition, high-frequency current travels only along the surface of the wire. Therefore, it is sometimes coated with a thin layer of silver or Litz wire is used.

In practice, it is often necessary to calculate the resistance of various wires. This can be done using formulas or using the data given in table. 1.

The influence of the conductor material is taken into account using resistivity, denoted Greek letter? and having a length of 1 m and a cross-sectional area of ​​1 mm2. Lowest resistivity? = 0.016 Ohm mm2/m has silver. Let us give the average value of the resistivity of some conductors:

At various quantities impurities and different ratios components included in rheostatic alloys, the resistivity may change slightly.

Resistance is calculated using the formula:

where R is resistance, Ohm; resistivity, (Ohm mm2)/m; l - wire length, m; s - cross-sectional area of ​​the wire, mm2.

If the wire diameter d is known, then its cross-sectional area is equal to:

It is best to measure the diameter of the wire using a micrometer, but if you don’t have one, you should wind 10 or 20 turns of wire tightly onto a pencil and measure the length of the winding with a ruler. Dividing the length of the winding by the number of turns, we find the diameter of the wire.

To determine the length of a wire of known diameter from of this material necessary to obtain the required resistance, use the formula

Table 1.

Note. 1. Data for wires not listed in the table should be taken as some average values. For example, for a nickel wire with a diameter of 0.18 mm, we can approximately assume that the cross-sectional area is 0.025 mm2, the resistance of one meter is 18 Ohms, and the permissible current is 0.075 A.

2. For a different value of current density, the data in the last column must be changed accordingly; for example, at a current density of 6 A/mm2, they should be doubled.

Example 1. Find the resistance of 30 m of copper wire with a diameter of 0.1 mm.

Solution. We determine according to the table. 1 resistance of 1 m of copper wire, it is equal to 2.2 Ohms. Therefore, the resistance of 30 m of wire will be R = 30 2.2 = 66 Ohms.

Calculation using the formulas gives the following results: cross-sectional area of ​​the wire: s = 0.78 0.12 = 0.0078 mm2. Since the resistivity of copper is 0.017 (Ohm mm2)/m, we get R = 0.017 30/0.0078 = 65.50 m.

Example 2. How much nickel wire with a diameter of 0.5 mm is needed to make a rheostat with a resistance of 40 Ohms?

Solution. According to the table 1, we determine the resistance of 1 m of this wire: R = 2.12 Ohm: Therefore, to make a rheostat with a resistance of 40 Ohms, you need a wire whose length is l = 40/2.12 = 18.9 m.

Let's do the same calculation using the formulas. We find the cross-sectional area of ​​the wire s = 0.78 0.52 = 0.195 mm2. And the length of the wire will be l = 0.195 40/0.42 = 18.6 m.

Electrical resistivity, or just resistivity substances - 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 of 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 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)) 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 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 tensor conductivity has more complex character. 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

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

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

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

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

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

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

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

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

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

  

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

  This table shows the specific electrical resistance some substances.

  
  
  Highly conductive materials

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

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

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

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

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

  Similar materials.

  For each conductor there is a concept of resistivity. This value consists of Ohms multiplied by a square millimeter, then divided by one meter. In other words, this is the resistance of a conductor whose length is 1 meter and cross-section is 1 mm 2. The same is true for the resistivity of copper, a unique metal that is widely used in electrical engineering and energy.

  Properties of copper

  Due to its properties, this metal was one of the first to be used in the field of electricity. First of all, copper is a malleable and ductile material with excellent electrical conductivity properties. There is still no equivalent replacement for this conductor in the energy sector.

  The properties of special electrolytic copper with high purity. This material made it possible to produce wires with a minimum thickness of 10 microns.

  

  In addition to high electrical conductivity, copper lends itself very well to tinning and other types of processing.

  Copper and its resistivity

  Any conductor exhibits resistance if an electric current is passed through it. The value depends on the length of the conductor and its cross-section, as well as on the effect of certain temperatures. Therefore, the resistivity of conductors depends not only on the material itself, but also on its specific length and cross-sectional area. The easier a material allows a charge to pass through itself, the lower its resistance. For copper, the resistivity is 0.0171 Ohm x 1 mm 2 /1 m and is only slightly inferior to silver. However, the use of silver in industrial scale economically unprofitable, therefore, copper is the best conductor used in energy.

  

  The resistivity of copper is also related to its high conductivity. These values ​​are directly opposite to each other. The properties of copper as a conductor also depend on the temperature coefficient of resistance. This is especially true for resistance, which is affected by the temperature of the conductor.

  Thus, due to its properties, copper has become widespread not only as a conductor. This metal is used in most instruments, devices and units whose operation is associated with electric current.