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

Electrical resistance

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

In the diagrams, electrical resistance is indicated as shown in Figure 1, a.

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

A long conductor of small cross-section creates a high resistance to current. Short conductors of large cross-section have little resistance to current.

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

The temperature of a conductor also affects its resistance. As the temperature rises, the resistance of metals increases, and the resistance of liquids and coal decreases. Only some special metal alloys (manganin, constantan, nickeline and others) almost do not change their resistance with increasing temperature.

So, we see that the electrical resistance of the 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 denoted by the Greek capital letter Ω (omega). So instead of writing "The resistance of the conductor is 15 ohms", you can simply write: r= 15Ω.
1000 ohm is called 1 kiloohm(1kΩ, or 1kΩ),
1,000,000 ohms is called 1 megaohm(1mgOhm, or 1MΩ).

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

Video 1. Conductor resistance

Specific electrical resistance

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

Table 1 gives the specific resistances of some conductors.

Table 1

Resistivity 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 ohms. 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 precludes its widespread 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 ohms. To get a resistance of 1 ohm, you need to take 57 m of such wire.

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

The resistance of a conductor can be determined by the formula:

where r- conductor resistance in ohms; ρ - specific resistance of the conductor; l is the length of the conductor 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 resistance of 30 ohms 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 material of the wire.

The material of a conductor characterizes its resistivity.

According to the table of resistivity, we find that lead has such resistance.

It was stated above that the resistance of conductors depends on temperature. Let's do the following experiment. We wind several meters of thin metal wire in the form of a spiral and turn this spiral into a battery circuit. To measure the current in the circuit, turn on the ammeter. When heating the spiral in the flame of the burner, you can see that the ammeter readings will decrease. This shows that the resistance of the metal wire increases with heating.

For some metals, when heated by 100 °, the resistance increases by 40 - 50%. There are alloys that slightly change their resistance with heat. Some special alloys hardly change resistance with temperature. The resistance of metal conductors increases with increasing temperature, the resistance of electrolytes (liquid conductors), coal and some solids, on the contrary, decreases.

The ability of metals to change their resistance with temperature changes is used to construct resistance thermometers. Such a 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 the resistance of the conductor when it is heated, per 1 ohm of the initial resistance and 1 ° temperature, is called temperature coefficient of resistance and is denoted by the letter α.

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

Note. This formula can only be calculated within a certain temperature range (up to about 200°C).

We give 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 in a room with a temperature of 15°C had a resistance of 20 ohms. The thermometer was placed in the furnace and after a while its resistance was measured. It turned out to be equal to 29.6 ohms. Determine the temperature in the oven.

electrical conductivity

Until now, we have considered the resistance of the conductor as an obstacle that the conductor provides to the electric current. However, current flows through the conductor. Therefore, in addition to resistance (obstacles), 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 the conductor are reciprocal quantities.

It is known from mathematics that the reciprocal of 5 is 1/5 and, conversely, the reciprocal 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 denoted by the letter g.

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

Example 8 Conductor resistance is 20 ohms. Determine its conductivity.

If a r= 20 Ohm, then

Example 9 Conductor conductivity is 0.1 (1/ohm). Determine its resistance

If g \u003d 0.1 (1 / Ohm), then r= 1 / 0.1 = 10 (ohm)

One of the physical quantities used in electrical engineering is electrical resistivity. Considering the specific resistance of aluminum, it should be remembered that this value characterizes the ability of a substance to prevent the passage of electric current through it.

Concepts Related to Resistivity

The value opposite to resistivity is called conductivity or electrical conductivity. The usual electrical resistance is characteristic only of a conductor, and the specific electrical resistance is characteristic only of a particular substance.

As a rule, this value is calculated for a conductor having a uniform structure. To determine electrical homogeneous conductors, the formula is used:

The physical meaning of this quantity lies in a certain resistance of a homogeneous conductor with a certain unit length and cross-sectional area. The unit of measurement is the SI unit Ohm.m or the off-system unit Ohm.mm2/m. The last unit means that a conductor of a homogeneous substance, 1 m long, having a cross-sectional area of ​​1 mm2, will have a resistance of 1 ohm. Thus, the resistivity of any substance can be calculated using a section of an electrical circuit 1 m long, the cross section of which will be 1 mm2.

Resistivity of different metals

Each metal has its own individual characteristics. If we compare the resistivity of aluminum, for example, with copper, it can be noted that for copper this value is 0.0175 Ohm.mm2 / m, and for aluminum - 0.0271 Ohm.mm2 / m. Thus, the resistivity of aluminum is much higher than that of copper. It follows from this that the electrical conductivity is much higher than that of aluminum.

Certain factors influence the value of the resistivity of metals. For example, during deformations, the structure of the crystal lattice is disturbed. Due to the resulting defects, the resistance to the passage of electrons inside the conductor increases. Therefore, there is an increase in the resistivity of the metal.

Temperature also has an effect. When heated, the nodes of the crystal lattice begin to oscillate more strongly, thereby increasing the resistivity. Currently, due to the high resistivity, aluminum wires are being replaced everywhere with copper wires, which have a higher conductivity.

Or electric circuit electric current.

Electrical resistance is defined as a proportionality factor R between voltage U and direct current I in Ohm's law for a chain section.

The unit of resistance is called ohm(Ohm) in honor of the German scientist G. Ohm, who introduced this concept into physics. One ohm (1 ohm) is the resistance of such a conductor in which, at a voltage 1 AT current strength is 1 BUT.

Resistivity.

The resistance of a homogeneous conductor of constant cross section depends on the material of the conductor, its length l and cross section S and can be determined by the formula:

where ρ is the resistivity of the material from which the conductor is made.

Resistivity of matter- this is a physical quantity showing the resistance of a conductor made of this substance of unit length and unit cross-sectional area.

It follows from the formula that

Value, reciprocal ρ , is called conductivity σ :

Since in SI the unit of resistance is 1 ohm. unit of area is 1 m 2, and the unit of length is 1 m, then the unit of resistivity in SI will be 1 Ohm · m 2 /m, or 1 ohm m. The unit of conductivity in SI is Ohm -1 m -1.

In practice, the cross-sectional area of ​​thin wires is often expressed in square millimeters (mm2). In this case, a more convenient unit of resistivity is Ohm mm 2 /m. Since 1 mm 2 \u003d 0.000001 m 2, then 1 Ohm mm 2 / m \u003d 10 -6 Ohm m. Metals have very low resistivity - of the order of (1 10 -2) Ohm mm 2 /m, dielectrics - 10 15 -10 20 large.

Dependence of resistance on temperature.

As the temperature rises, the resistance of metals increases. However, there are alloys whose resistance almost does not change with increasing temperature (for example, constantan, manganin, etc.). The resistance of electrolytes decreases with increasing temperature.

temperature coefficient of resistance conductor is the ratio of the change in the resistance of the conductor when heated by 1 ° C to the value of its resistance at 0 º C:

.

The dependence of the resistivity of conductors on temperature is expressed by the formula:

.

In general α depends on temperature, but if the temperature interval is small, then the temperature coefficient can be considered constant. For pure metals α \u003d (1/273) K -1. For electrolyte solutions α < 0 . For example, for 10% saline solution α \u003d -0.02 K -1. For constantan (copper-nickel alloy) α \u003d 10 -5 K -1.

The dependence of conductor resistance on temperature is used in resistance thermometers.

Many have heard about Ohm's law, but not everyone knows what it is. The study begins with a school course in physics. In more detail pass on physical faculty and electrodynamics. This knowledge is unlikely to be useful to an ordinary layman, but it is necessary for general development, and for someone for a future profession. On the other hand, basic knowledge about electricity, its structure, features at home will help to warn yourself against trouble. No wonder Ohm's law is called the fundamental law of electricity. The home master needs to have knowledge in the field of electricity in order to prevent overvoltage, which can lead to an increase in load and a fire.

The concept of electrical resistance

The relationship between the basic physical quantities of an electrical circuit - resistance, voltage, current strength was discovered by the German physicist Georg Simon Ohm.

The electrical resistance of a conductor is a value that characterizes its resistance to electric current. In other words, part of the electrons under the action of an electric current on the conductor leaves its place in the crystal lattice and goes to the positive pole of the conductor. Some of the electrons remain in the lattice, continuing to rotate around the atom of the nucleus. These electrons and atoms form an electrical resistance that prevents the movement of released particles.

The above process is applicable to all metals, but the resistance in them occurs in different ways. This is due to the difference in size, shape, material of which the conductor consists. Accordingly, the dimensions of the crystal lattice have an unequal shape for different materials, therefore, the electrical resistance to the movement of current through them is not the same.

From this concept follows the definition of the resistivity of a substance, which is an individual indicator for each metal separately. Electrical resistivity (ER) is a physical quantity denoted by the Greek letter ρ and characterized by the ability of a metal to prevent the passage of electricity through it.

Copper is the main material for conductors

The resistivity of a substance is calculated by the formula, where one of the important indicators is the temperature coefficient of electrical resistance. The table contains the resistivity values ​​of three known metals in the temperature range from 0 to 100°C.

If we take the resistivity index of iron, as one of the available materials, equal to 0.1 Ohm, then 10 meters will be needed for 1 Ohm. Silver has the lowest electrical resistance; for its indicator of 1 Ohm, 66.7 meters will come out. A significant difference, but silver is an expensive metal that is not widely used. The next in terms of performance is copper, where 1 ohm requires 57.14 meters. Due to its availability, cost compared to silver, copper is one of the most popular materials for use in electrical networks. The low resistivity of copper wire or the resistance of copper wire makes it possible to use a copper conductor in many branches of science, technology, as well as in industrial and domestic purposes.

Resistivity value

The resistivity value is not constant, it changes depending on the following factors:

• The size. The larger the diameter of the conductor, the more electrons it passes through itself. Therefore, the smaller its size, the greater the resistivity.
• Length. Electrons pass through atoms, so the longer the wire, the more electrons have to travel through them. When calculating, it is necessary to take into account the length, size of the wire, because the longer, thinner the wire, the greater its resistivity and vice versa. Failure to calculate the load of the equipment used can lead to overheating of the wire and fire.
• Temperature. It is known that the temperature regime is of great importance on the behavior of substances in different ways. Metal, like nothing else, changes its properties at different temperatures. The resistivity of copper directly depends on the temperature coefficient of resistance of copper and increases when heated.
• Corrosion. The formation of corrosion significantly increases the load. This happens due to environmental influences, ingress of moisture, salt, dirt, etc. manifestations. It is recommended to isolate and protect all connections, terminals, twists, install protection for outdoor equipment, timely replace damaged wires, assemblies, assemblies.

Resistance calculation

Calculations are made when designing objects for various purposes and uses, because the life support of each comes from electricity. Everything is taken into account, from lighting fixtures to technically complex equipment. At home, it will also be useful to make a calculation, especially if it is planned to replace the wiring. For private housing construction, it is necessary to calculate the load, otherwise the “handicraft” assembly of electrical wiring can lead to a fire.

The purpose of the calculation is to determine the total resistance of the conductors of all devices used, taking into account their technical parameters. It is calculated by the formula R=p*l/S , where:

R is the calculated result;

p is the resistivity index from the table;

l is the length of the wire (conductor);

S is the diameter of the section.

Units

In the international system of units of physical quantities (SI), electrical resistance is measured in Ohms (Ohm). The unit of measurement of resistivity according to the SI system is equal to such a resistivity of a substance at which a conductor made of one material 1 m long with a cross section of 1 sq. m. has a resistance of 1 ohm. The use of 1 ohm / m with respect to different metals is clearly shown in the table.

Significance of Resistivity

The relationship between resistivity and conductivity can be viewed as reciprocals. The higher the index of one conductor, the lower the index of the other and vice versa. Therefore, when calculating the electrical conductivity, the calculation 1 / r is used, because the number reciprocal to X is 1 / X and vice versa. The specific indicator is denoted by the letter g.

Benefits of electrolytic copper

Low resistivity (after silver) as an advantage, copper is not limited. It has properties unique in its characteristics, namely plasticity, high malleability. Thanks to these qualities, high-purity electrolytic copper is produced for the production of cables that are used in electrical appliances, computer technology, the electrical industry and the automotive industry.

The dependence of the resistance index on temperature

The temperature coefficient is a value that equals the change in the voltage of a part of the circuit and the resistivity of the metal as a result of changes in temperature. Most metals tend to increase resistivity with increasing temperature due to thermal vibrations of the crystal lattice. The temperature coefficient of resistance of copper affects the specific resistance of the copper wire and at temperatures from 0 to 100°C is 4.1 10−3(1/Kelvin). For silver, this indicator under the same conditions has a value of 3.8, and for iron, 6.0. This once again proves the effectiveness of using copper as a conductor.

Copper is one of the most common wire materials. Its electrical resistance is the lowest of the affordable metals. It is less only in precious metals (silver and gold) and depends on various factors.

What is electric current

On different poles of a battery or other current source, there are oppositely named 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 quantity that determines the electrical resistance of a reference material sample. The Greek letter "r" is used to denote this value. Formula for calculation:

p=(R*S)/ l.

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

Free electrons move through the metal inside 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 the number of free electrons;
• impurities. In pure metals, the crystal lattice is more ordered, so the resistance is lower than in alloys;
• Temperature. Atoms do not sit still in their places, but oscillate. 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 the dimensions of the cables are measured in meters (length) and mm² (section), the electrical resistivity has the dimension of Ohm mm² / m. Knowing the dimensions of the cable, its resistance is calculated by 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 by 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. Conductivity is imparted to it by dissolved impurities.

Electrical resistance of wires

The most common wire materials are copper and aluminum. The resistance of aluminum is higher, but it is cheaper than copper. The specific resistance of copper is lower, so the wire size 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 that is different for each metal. You can find out this coefficient from the relevant reference books or using an online calculator.

Cable section selection

Since the wire has resistance, when an 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 sizes.

Selection according to allowable heating

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

In a copper wire with a cross section of 2.5mm² and a length of 10 meters R=10*0.0074=0.074Ohm. At a current of 30A, P \u003d 30² * 0.074 \u003d 66W.

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

Permissible voltage losses

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

Reference. According to the norms of the PUE, 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 from tables or using an online calculator. In contrast to the selection of the section according to the allowable heating, voltage losses do not depend on the conditions of the gasket and the insulation material.

In a 220V network, voltage is supplied through two wires: phase and zero, so the calculation is made for double the length of the cable. In the cable from the previous example, it will be U=I*R=30A*2*0.074Ω=4.44V. This is not much, but with a length of 25 meters it turns out 11.1V - the maximum allowable 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. The specific resistance of steel is higher, but it is stronger than copper and aluminum. Steel conductors are woven into cables intended for laying through the air. The resistance of iron is too high for the transmission of electricity, therefore, when calculating the cross section, the cores are not taken into account. In addition, it is more refractory, and leads are made from it for connecting heaters in electric furnaces of high power;
• 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. They are used in claim devices for the manufacture of resistors;
• Precious metals - gold and silver. They have the highest conductivity, but due to the high price, their use is limited.

Inductive reactance

The formulas for calculating the conductivity of wires are valid only in a DC network or in straight conductors at low frequency. In coils and in high-frequency networks, an inductive resistance appears many times higher than usual. In addition, the high frequency current only propagates over the surface of the wire. Therefore, it is sometimes coated with a thin layer of silver or litz wire is used.