The resistance of a copper cable with a cross section of 2.5 mm2. Resistivity and superconductivity

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 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. (Actual 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. Conductivity is measured in units of (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 within the limits of accuracy modern measurements to zero. This property is called superconductivity; it was first observed by the Dutch physicist Heike Kamerling-Onnes (1853-1926) in 1911 when mercury was cooled below 4.2 K. At this temperature electrical resistance The 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). Observed electricity in a superconducting ring that remained virtually unimpaired in the absence of voltage for several years.

IN last years superconductivity is being intensively studied in order to elucidate its mechanism and find materials that exhibit superconductivity at higher temperatures. high 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.

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Copper resistivity This is a physical concept found in electrical engineering. What is this, you ask.

So let's start with the concept of conductor resistance, which means the process of electricity passing through it. In this case, copper will serve as a conductor, which means we will consider its properties.

All metals have a specific structure in the form crystal lattice. At each corner of this lattice there are atoms that periodically vibrate around the nodes. When atoms repel or attract each other, this affects the location and arrangement of all nodes, in all metals differently. The environment of the atoms is occupied by electrons, which rotate in their orbit, remaining in it due to the balance of forces.

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How does copper react when an electric field is applied to it? Inside this conductor, all electrons torn off by electrical force, from their orbit, tend to the pole with a plus sign. This movement is called electric current. As they move, electrons collide with atoms and other electrons that have not been torn from their orbits. In this case, the colliding electrons change direction and their energy is lost. This is the basic definition of conductor resistance. In other words, these are lattices of atoms with electrons rotating in their orbits, which create resistance to the moving conductor electrodes torn from their orbits.

However, resistance also depends on several factors; it is individual for each metal. It is affected by the size of the crystal lattice and temperature. When the temperature of a conductor increases, its atoms vibrate more rapidly. And therefore, electrons move with highest speed and resistance, and the orbits will be large in radius.

The resistivity value of copper can be found in physics reference tables. It is 0.0175 Ohm*mm2/m, at a temperature of 20 degrees. The closest metal in value to copper will be aluminum = 0.0271 Ohm*mm2/m. Conductivity of copper second only to silver = 0.016 Ohm*mm2/m. as evidenced by its widespread use, for example in power cables or in a variety of conductors. However, without copper you cannot create power transformers and motors for small energy-saving appliances.

You need to know the designations of resistivity, since without this it is impossible to calculate the total resistance of different conductors during the development or design of new devices. There is a formula for this:

R=p*I/S

in which: R - will be the total resistance of the conductors, p - will be the specific resistance of the metals, I - will be the length of a specific conductor, S - the cross-sectional area of ​​the conductors.

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 it comes to 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. It begins to act on a piece of copper electric field. What happens inside the conductor? Electrons, torn from their orbits by the force of the electric field, 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 off electric field from their orbits. 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 household appliances, manufacturing of busbars, transformer windings and other electrical products.

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 mm2. 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, which has high purity, are especially appreciated. This material made it possible to produce wires with minimum thickness at 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 passes a charge through itself, the lower its resistance. For copper, the resistivity is 0.0171 Ohm x 1 mm2/1 m and is only slightly inferior to silver. However, the use of silver on an industrial scale is not economically profitable, therefore, copper is the best conductor used in energy.

The specific resistance of copper is also associated with 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 influenced 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.