Resistivity of manganese. What is copper resistivity: values, characteristics, values

The concept of “specific copper” is often found in electrical engineering literature. And you can’t help but wonder, what is this?

The concept of “resistance” for any conductor is continuously associated with an understanding of the process of electric current flowing through it. Since the article will focus on the resistance of copper, we should consider its properties and the properties of metals.

When we're talking about about metals, you involuntarily remember that they all have a certain structure - a crystal lattice. Atoms are located in the nodes of such a lattice and move relative to them. The distances and location of these nodes depend on the forces of interaction of atoms with each other (repulsion and attraction), and are different for different metals. And electrons revolve around atoms in their orbits. They are also kept in orbit by the balance of forces. Only this is atomic and centrifugal. Can you imagine the picture? You can call it, in some respects, static.

Now let's add dynamics. An electric field begins to act on a piece of copper. What happens inside the conductor? Electrons stripped by force electric field from their orbits, rush to its positive pole. Here you have the directed movement of electrons, or rather, electric current. But on the way of their movement they come across atoms at the nodes of the crystal lattice and electrons that still continue to rotate around their atoms. At the same time, they lose their energy and change the direction of movement. Now does the meaning of the phrase “conductor resistance” become a little clearer? It is the atoms of the lattice and the electrons rotating around them that resist the directional movement of electrons torn from their orbits by the electric field. But the concept of conductor resistance can be called general characteristic. Resistivity characterizes each conductor more individually. Including copper. This characteristic is individual for each metal, since it directly depends only on the shape and size of the crystal lattice and, to some extent, on temperature. As the temperature of the conductor increases, the atoms vibrate more intensely at the lattice sites. And electrons rotate around nodes at higher speeds and in orbits of larger radius. And, naturally, free electrons encounter greater resistance when moving. This is the physics of the process.

For the needs of the electrical engineering sector, widespread production of metals such as aluminum and copper, the resistivity of which is quite low, has been established. These metals are used to make cables and various types wires that are widely used in construction, for the production of household appliances, for the manufacture of tires, transformer windings and other electrical products.

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

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

Resistivity

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

Where p– metal resistivity, l – conductor length, s – cross-sectional area.

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

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

Dependence of resistivity on deformation

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

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

Effect of temperature on resistivity

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

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

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

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

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

Electrical resistance is the main characteristic of conductor materials. Depending on the area of ​​application of the conductor, the value of its resistance can play both a positive and negative role in the functioning of the electrical system. Also, the specific application of the conductor may necessitate taking into account additional characteristics, the influence of which in a particular case cannot be neglected.

Conductors are pure metals and their alloys. In a metal, atoms fixed in a single “strong” structure have free electrons (the so-called “electron gas”). It is these particles that in this case are charge carriers. Electrons are in constant, random motion from one atom to another. When an electric field appears (connecting a voltage source to the ends of the metal), the movement of electrons in the conductor becomes ordered. Moving electrons encounter obstacles on their path caused by the peculiarities of the molecular structure of the conductor. When they collide with a structure, charge carriers lose their energy, giving it to the conductor (heating it). The more obstacles a conductive structure creates to charge carriers, the higher the resistance.

As the cross section of the conducting structure increases for one number of electrons, the “transmission channel” will become wider and the resistance will decrease. Accordingly, as the length of the wire increases, there will be more such obstacles and the resistance will increase.

Thus, the basic formula for calculating resistance includes the length of the wire, the cross-sectional area and a certain coefficient that relates these dimensional characteristics to the electrical quantities of voltage and current (1). This coefficient is called resistivity.
R= r*L/S (1)

Resistivity

Resistivity is unchanged and is a property of the substance from which the conductor is made. Units of measurement r - ohm*m. Often the resistivity value is given in ohm*mm sq./m. This is due to the fact that the cross-sectional area of ​​the most commonly used cables is relatively small and is measured in mm2. Let's give a simple example.

Task No. 1. Copper wire length L = 20 m, cross-section S = 1.5 mm. sq. Calculate the wire resistance.
Solution: resistivity of copper wire r = 0.018 ohm*mm. sq./m. Substituting the values ​​into formula (1) we get R=0.24 ohms.
When calculating the resistance of the power system, the resistance of one wire must be multiplied by the number of wires.
If instead of copper you use aluminum with a higher resistivity (r = 0.028 ohm * mm sq. / m), then the resistance of the wires will increase accordingly. For the example above, the resistance will be R = 0.373 ohms (55% more). Copper and aluminum are the main materials for wires. There are metals with lower resistivity than copper, such as silver. However, its use is limited due to its obvious high cost. The table below shows the resistance and other basic characteristics of conductor materials.
Table - main characteristics of conductors

Heat losses of wires

If, using the cable from the above example, a load of 2.2 kW is connected to a single-phase 220 V network, then current I = P / U or I = 2200/220 = 10 A will flow through the wire. Formula for calculating power losses in the conductor:
Ppr=(I^2)*R (2)
Example No. 2. Calculate active losses when transmitting power of 2.2 kW in a network with a voltage of 220 V for the mentioned wire.
Solution: substituting the values ​​of current and wire resistance into formula (2), we obtain Ppr=(10^2)*(2*0.24)=48 W.
Thus, when transmitting energy from the network to the load, losses in the wires will be slightly more than 2%. This energy is converted into heat generated by the conductor in environment. According to the heating condition of the conductor (according to the current value), its cross-section is selected, guided by special tables.
For example, for the above conductor, the maximum current is 19 A or 4.1 kW in a 220 V network.

To reduce active losses in power lines, they use increased voltage. At the same time, the current in the wires decreases, losses fall.

Effect of temperature

An increase in temperature leads to an increase in vibrations of the metal crystal lattice. Accordingly, electrons meet large quantity obstacles, which leads to increased resistance. The magnitude of the “sensitivity” of the metal resistance to an increase in temperature is called the temperature coefficient α. The formula for calculating temperature is as follows
R=Rн*, (3)
where Rн – wire resistance under normal conditions (at temperature t°н); t° is the temperature of the conductor.
Usually t°n = 20° C. The value of α is also indicated for temperature t°n.
Task 4. Calculate the resistance of a copper wire at a temperature t° = 90° C. α copper = 0.0043, Rн = 0.24 Ohm (task 1).
Solution: substituting the values ​​into formula (3) we get R = 0.312 Ohm. The resistance of the heated wire being analyzed is 30% greater than its resistance at room temperature.

Effect of frequency

As the frequency of the current in the conductor increases, the process of displacing charges closer to its surface occurs. As a result of an increase in the concentration of charges in the surface layer, the resistance of the wire also increases. This process is called the “skin effect” or surface effect. Skin coefficient– the effect also depends on the size and shape of the wire. For the above example, at an AC frequency of 20 kHz, the wire resistance will increase by approximately 10%. Note that high-frequency components can have a current signal from many modern industrial and household consumers (energy-saving lamps, switching power supplies, frequency converters, and so on).

Influence of neighboring conductors

There is a magnetic field around any conductor through which current flows. The interaction of the fields of neighboring conductors also causes energy loss and is called the “proximity effect”. Also note that any metal conductor has inductance created by the conductive core and capacitance created by the insulation. These parameters are also characterized by the proximity effect.

Technologies

High voltage wires with zero resistance

This type of wire is widely used in car ignition systems. The resistance of high-voltage wires is quite low and amounts to several fractions of an ohm per meter of length. Let us remind you that resistance of this magnitude cannot be measured with an ohmmeter. general use. Often, measuring bridges are used for the task of measuring low resistances.
Structurally, such wires have a large number of copper conductors with insulation based on silicone, plastics or other dielectrics. The peculiarity of the use of such wires is not only the operation at high voltage, but also the transfer of energy in a short period of time (pulse mode).

Bimetallic cable

The main area of ​​application of the mentioned cables is the transmission of high-frequency signals. The core of the wire is made of one type of metal, the surface of which is coated with another type of metal. Since at high frequencies only the surface layer of the conductor is conductive, it is possible to replace the inside of the wire. This saves expensive material and improves the mechanical characteristics of the wire. Examples of such wires: silver-plated copper, copper-plated steel.

Conclusion

Wire resistance is a value that depends on a group of factors: conductor type, temperature, current frequency, geometric parameters. The significance of the influence of these parameters depends on the operating conditions of the wire. Optimization criteria, depending on the tasks for wires, can be: reducing active losses, improving mechanical characteristics, reducing prices.

It has been experimentally established that resistance R metal conductor is directly proportional to its length L and inversely proportional to its cross-sectional area A:

R = ρ L/ A (26.4)

where is the coefficient ρ is called resistivity and serves as a characteristic of the substance from which the conductor is made. This is common sense: a thick wire should have less resistance than a thin wire because electrons can move over a larger area in a thick wire. And we can expect an increase in resistance with increasing length of the conductor, as the number of obstacles to the flow of electrons increases.

Typical values ρ For different materials are given in the first column of the table. 26.2. ( Real values depend on the purity of the substance, heat treatment, temperature and other factors.)

Silver has the lowest resistivity, which thus turns out to be the best conductor; however it is expensive. Copper is slightly inferior to silver; It is clear why wires are most often made of copper.

Aluminum has a higher resistivity than copper, but it has a much lower density and is preferred in some applications (for example, in power lines) because the resistance of aluminum wires of the same mass is less than that of copper. The reciprocal of resistivity is often used:

σ = 1/ρ (26.5)

σ called specific conductivity. Specific conductivity is measured in units (Ohm m) -1.

The resistivity of a substance depends on temperature. As a rule, the resistance of metals increases with temperature. This should not be surprising: as temperature increases, atoms move faster, their arrangement becomes less ordered, and we can expect them to interfere more with the flow of electrons. In narrow temperature ranges, the resistivity of the metal increases almost linearly with temperature:

Where ρ T- resistivity at temperature T, ρ 0 - resistivity at standard temperature T 0 , a α - temperature coefficient of resistance (TCR). The values ​​of a are given in table. 26.2. Note that for semiconductors the TCR can be negative. This is obvious, since with increasing temperature the number of free electrons increases and they improve the conductive properties of the substance. Thus, the resistance of a semiconductor may decrease with increasing temperature (although not always).

The values ​​of a depend on temperature, so you should pay attention to the temperature range within which given value(for example, according to the directory physical quantities). If the range of temperature changes turns out to be wide, then linearity will be violated, and instead of (26.6) it is necessary to use an expression containing terms that depend on the second and third powers of temperature:

ρ T = ρ 0 (1+αT+ + βT 2 + γT 3),

where are the coefficients β And γ usually very small (we put T 0 = 0°С), but at large T the contributions of these members become significant.

At very low temperatures ah, the resistivity of some metals, as well as alloys and compounds, drops to zero within the accuracy of modern measurements. This property is called superconductivity; it was first observed by the Dutch physicist Geike Kamerling Onnes (1853-1926) in 1911 when mercury was cooled below 4.2 K. At this temperature, the electrical resistance of mercury suddenly dropped to zero.

Superconductors enter a superconducting state below the transition temperature, which is typically a few degrees Kelvin (just above absolute zero). An electric current was observed in a superconducting ring, which practically did not weaken in the absence of voltage for several years.

IN last years Superconductivity is being intensively researched to understand its mechanism and to find materials that superconduct at higher temperatures to reduce the cost and inconvenience of having to cool to very low temperatures. The first successful theory of superconductivity was created by Bardeen, Cooper and Schrieffer in 1957. Superconductors are already used in large magnets, where the magnetic field is created by an electric current (see Chapter 28), which significantly reduces energy consumption. Of course, maintaining a superconductor at a low temperature also requires energy.

Comments and suggestions are accepted and welcome!

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

What is electric current

At different poles of a battery or other current source there are opposite electric charge carriers. 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. Different metals have different atomic densities and numbers of free electrons;
• Impurities. In pure metals the crystal lattice is 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 vibrations, 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 the permissible temperature depends 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 the choice of cross-section based on permissible heating, voltage losses do not depend on 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 only travels along the surface of the wire. Therefore, it is sometimes coated with a thin layer of silver or Litz wire is used.