What is conductivity? Copper resistivity

When an electrical circuit is closed, at the terminals of which there is a potential difference, an electric current occurs. Free electrons, under the influence of electric field forces, move along the conductor. In their movement, free electrons collide with the atoms of the conductor and give them a supply of their kinetic energy.

Thus, electrons passing through a conductor encounter resistance to their movement. When electric current passes through a conductor, the latter heats up.

The electrical resistance of the conductor (it is designated Latin letter r) due to the phenomenon of conversion of electrical energy into thermal energy when an electric current passes through a conductor. On the diagrams electrical resistance designated as shown in Fig. 18.

The unit of resistance is taken to be 1 ohm. Om is often represented by the Greek capital letter Ω (omega). Therefore, instead of writing: “The resistance of the conductor is 15 ohms,” you can simply write: r = 15 Ω.

1000 ohms is called 1 kiloohm (1 kohm, or 1 kΩ).

1,000,000 ohms is called 1 megohm (1 mg ohm, or 1 MΩ).

device, having variable electrical resistance and serving to change the current in the circuit is called a rheostat. In the diagrams, rheostats are designated as shown in Fig. 18. As a rule, a rheostat is made of a wire of one or another resistance, wound on an insulating base. The slider or rheostat lever is placed in a certain position, as a result of which the required resistance is introduced into the circuit.

A long conductor with a small cross-section creates a large resistance to the current. Short conductors with a large cross-section provide little resistance to current.

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

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

So, we see that the electrical resistance of a conductor depends on the length of the conductor, the cross-section of the conductor, the material of the conductor, and the temperature of the conductor.

When comparing the resistance of conductors from various materials It is necessary to take a certain length and cross-section for each sample. Then we can judge which material conducts better or worse electric current.

The resistance (in ohms) of a conductor 1 m long, with a cross section of 1 mm 2 is called resistivity and is designated Greek letterρ (rho).

The conductor resistance can be determined by the formula

where r is the conductor resistance, ohm;

ρ - conductor resistivity;

l- conductor length, m;

S - conductor cross-section, mm2.

From this formula we obtain the dimension for resistivity

In table 1 shows the resistivity of some 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 if you take 62.5 m of silver wire with a cross section of 1 mm 2. Silver is the best conductor, but the high cost of silver excludes the possibility of its mass use. After silver in the table comes copper: 1 m of copper wire with a cross section of 1 mm 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 copper, obtained by refining, has found widespread use in electrical engineering for the manufacture of wires, cables, windings of electrical machines and devices. Aluminum and iron are also widely used as conductors.

Detailed characteristics of metals and alloys are given in table. 2.

Example 1. Determine the resistance of 200 m of iron wire with a cross section of 5 mm 2:

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 30 ohm resistor from nickel wire with a cross section of 0.21 mm2. Determine the required wire length:

Example 4. Determine the cross-section of a nichrome wire with a length of 20 F, 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 wire material.

The conductor material characterizes its resistivity

Using the resistivity table, we find that lead has this resistance.

It was previously stated that the resistance of conductors depends on temperature. Let's do the following experiment. Let's wind several meters of thin metal wire in the form of a spiral and connect this spiral to the battery circuit. To measure current, an ammeter is included in the circuit. When the coil is heated in the burner flame, you will notice that the ammeter readings will decrease. This shows that the resistance of a metal wire increases with heating.

For some metals, when heated by 100°, the resistance increases by 40-50%. There are alloys that change their resistance slightly with heating. Some special alloys show virtually no change in resistance when temperature changes. The resistance of metal conductors increases with increasing temperature, while the resistance of electrolytes (liquid conductors), coal and some solids, on the contrary, decreases.

The ability of metals to change their resistance with changes in temperature is used to construct resistance thermometers. This 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 a conductor when it is heated, per 1 ohm of initial resistance and per 1 0 temperature, is called temperature coefficient of resistance and is denoted by the letter α (alpha).

If at temperature t 0 the resistance of the conductor is equal to r 0, and at temperature t is equal to r t, then the temperature coefficient of resistance

Electrical conductivity characterizes the body's ability to conduct electric current. Conductivity - resistance value. In the formula, it is inversely proportional to electrical resistance, and they are actually used to denote the same properties of the material. Conductivity is measured in Siemens: [Sm]=.

Types of electrical conductivity:

— Electronic conductivity, where the charge carriers are electrons. This conductivity is primarily characteristic of metals, but is present to one degree or another in almost any material. As temperature increases, electronic conductivity decreases.

— Ionic conductivity. Exists in gaseous and liquid media where there are free ions that also carry charges, moving throughout the volume of the medium under the influence of an electromagnetic field or other external influence. Used in electrolytes. With increasing temperature, ionic conductivity increases, since more ions with high energy, and the viscosity of the medium is reduced.

— Hole conductivity. This conductivity is caused by a lack of electrons in the crystal lattice of the material. In fact, electrons again carry the charge here, but they seem to move along the lattice, occupying sequentially free seats in it, in contrast to the physical movement of electrons in metals. This principle is used in semiconductors, along with electronic conductivity.

The very first materials that began to be used in electrical engineering were historically metals and dielectrics (insulators that have low electrical conductivity). Now received wide application in electronics semiconductors. They occupy an intermediate position between conductors and dielectrics and are characterized by the fact that the amount of electrical conductivity in semiconductors can be regulated by various influences. Most modern conductors are made from silicon, germanium and carbon. In addition, other substances can be used to make PP, but they are used much less frequently.

Current transmission with minimal losses is important. In this regard, metals with high electrical conductivity and, accordingly, low electrical resistance play an important role. The best in this regard is silver (62,500,000 S/m), followed by copper (58,100,000 S/m), gold (45,500,000 S/m), aluminum (37,000,000 S/m). In accordance with economic feasibility, aluminum and copper are most often used, while copper is slightly inferior in conductivity to silver. All other metals are of no industrial importance for the production of conductors.

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

Electrical resistance

The electrical resistance of a conductor, which is denoted by a Latin letter r, is the property of a body or medium to transform electrical energy into heat 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 a circuit, is called rheostat. In the diagrams, rheostats are designated as shown in Figure 1, b. IN general view A rheostat is made from a wire of one resistance or another, wound on an insulating base. The slider or rheostat lever is placed in a certain position, as a result of which the required resistance is introduced into the circuit.

A long conductor with a small cross-section creates a large resistance to the current. Short conductors with a large cross-section provide little resistance to current.

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

The temperature of the conductor also affects its resistance. As temperature increases, the resistance of metals increases, and the resistance of liquids and coal decreases. Only some special metal alloys (manganin, constantan, nickel and others) hardly change their resistance with increasing temperature.

So, we see that the electrical resistance of a 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 represented by the Greek capital letter Ω (omega). Therefore, instead of writing “The conductor resistance is 15 ohms,” you can simply write: r= 15 Ω.
1,000 ohms is called 1 kiloohm(1kOhm, or 1kΩ),
1,000,000 ohms is called 1 megaohm(1mOhm, or 1MΩ).

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

Video 1. Conductor resistance

Electrical resistivity

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 shows the resistivities of some conductors.

Table 1

Resistivities 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 Ohm. 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 excludes the possibility of its mass 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 Ohm. To get a resistance of 1 ohm, you need to take 57 m of such wire.

The conductor resistance can be determined by the formula:

Where r– conductor resistance in ohms; ρ – specific resistance of the conductor; l– conductor length 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 30 Ohm resistor 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 wire material.

The material of the conductor characterizes its resistivity.

According to the table of resistivities, we find that it has such resistance.

It was stated above that the resistance of conductors depends on temperature. Let's do the following experiment. Let's wind several meters of thin metal wire in the form of a spiral and connect this spiral to the battery circuit. To measure current, we connect an ammeter to the circuit. When the coil is heated in the burner flame, you will notice that the ammeter readings will decrease. This shows that the resistance of a metal wire increases with heating.

For some metals, when heated by 100°, the resistance increases by 40–50%. There are alloys that change their resistance slightly with heating. Some special alloys show virtually no change in resistance when temperature changes. Resistance increases with increasing temperature; the resistance of electrolytes (liquid conductors), coal and some solids, on the contrary, decreases.

The change in resistance of a conductor when it is heated per 1 ohm of initial resistance and per 1° temperature is called temperature coefficient of resistance and is denoted by the letter α.

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

Note. Calculation using this formula can only be done in a certain temperature range (up to approximately 200°C).

We present 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 had a resistance of 20 ohms in a room at 15°C. The thermometer was placed in the oven and after some time its resistance was measured. It turned out to be equal to 29.6 Ohms. Determine the temperature in the oven.

Electrical conductivity

So far, we have considered the resistance of a conductor as the obstacle that the conductor provides to the electric current. But still, current passes through the conductor. Therefore, in addition to resistance (obstacle), 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 a conductor are reciprocal quantities.

From mathematics it is known that the inverse of 5 is 1/5 and, conversely, the inverse 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 symbolized by the letter g.

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

Example 8. The conductor resistance is 20 ohms. Determine its conductivity.

If r= 20 Ohm, then

Example 9. The conductivity of the conductor is 0.1 (1/Ohm). Determine its resistance

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

Physical nature of electrical resistance. When free electrons move in a conductor, they collide on their path with positive ions 2 (see Fig. 10, a), atoms and molecules of the substance from which the conductor is made, and transfer part of their energy to them. In this case, the energy of moving electrons as a result of their collision with atoms and molecules is partially released and dissipated in the form of heat, heating the conductor. Due to the fact that electrons, colliding with particles of a conductor, overcome some resistance to movement, it is customary to say that conductors have electrical resistance. If the resistance of the conductor is low, it is relatively weakly heated by the current; if the resistance is high, the conductor may become hot. The wires supplying electric current to the electric stove hardly heat up, since their resistance is low, and the spiral of the stove, which has a high resistance, becomes red-hot. The filament of the electric lamp heats up even more.
The unit of resistance is the ohm. A conductor has a resistance of 1 Ohm through which a current of 1 A passes with a potential difference at its ends (voltage) equal to 1 V. The standard of resistance of 1 Ohm is a column of mercury 106.3 cm long and a cross-sectional area of 1 mm2 at a temperature of 0°C. In practice, resistance is often measured in thousands of ohms - kiloohms (kOhm) or millions of ohms - megaohms (MOhm). Resistance is denoted by the letter R (r).
Conductivity. Any conductor can be characterized not only by its resistance, but also by the so-called conductivity - the ability to conduct electric current. Conductivity is the reciprocal of resistance. The unit of conductivity is called siemens (Sm). 1 cm is equal to 1/1 ohm. Conductivity is designated by the letter G (g). Hence,

G = 1/R(4)

Electrical resistivity and conductivity. Atoms different substances provide unequal resistance to the passage of electric current. The ability of individual substances to conduct electric current can be judged by their electrical resistivity p. The value characterizing resistivity is usually taken to be the resistance of a cube with an edge of 1 m. Electrical resistivity is measured in Ohm*m. To judge the electrical conductivity of materials, the concept of specific electrical conductivity? = 1/? is also used. Specific electrical conductivity is measured in siemens per meter (S/m) (conductivity of a cube with an edge of 1 m). Electrical resistivity is often expressed in ohm-centimeters (Ohm*cm), and electrical conductivity in siemens per centimeter (S/cm). At the same time 1 Ohm*cm = 10 -2 Ohm*m, and 1 S/cm = 10 2 S/m.

Conductor materials are used mainly in the form of wires, bars or tapes, the cross-sectional area of which is usually expressed in square millimeters and the length in meters. Therefore, for the electrical resistivity of such materials and the electrical conductivity, other units of measurement have been introduced: ? measured in Ohm * mm 2 / m (resistance of a conductor 1 m long and cross-sectional area 1 mm 2), huh? - in Sm*m/mm2 (conductivity of a conductor with a length of 1 m and a cross-sectional area of 1 mm2).

Of the metals, silver and copper have the highest electrical conductivity, since the structure of their atoms allows free electrons to easily move, followed by gold, chromium, aluminum, manganese, tungsten, etc. Iron and steel conduct current worse.

Pure metals always conduct electricity better than their alloys. Therefore, in electrical engineering, very pure copper is used predominantly, containing only 0.05% impurities. And vice versa, in cases where a material with high resistance is needed (for various heating devices, rheostats, etc.), special alloys are used: constantan, manganin, nichrome, fechral.

It should be noted that in technology, in addition to metallic conductors, non-metallic ones are also used. Such conductors include, for example, coal, from which brushes of electric machines, electrodes for spotlights, etc. are made. Conductors of electric current are the thickness of the earth, living tissues of plants, animals and humans. Damp wood and many other insulating materials conduct electricity when wet.
The electrical resistance of a conductor depends not only on the material of the conductor, but also on its length l and cross-sectional area s. (Electrical resistance is similar to the resistance offered to the movement of water in a pipe, which depends on the cross-sectional area of the pipe and its length.)
Straight conductor resistance

R= ? l/s (5)

If resistivity? expressed in Ohm*mm/m, then in order to obtain the resistance of the conductor in ohms, its length must be substituted into formula (5) in meters, and the cross-sectional area in square millimeters.

Dependence of resistance on temperature. The electrical conductivity of all materials depends on their temperature. In metal conductors, when heated, the range and speed of vibrations of atoms in the crystal lattice of the metal increase, as a result of which the resistance that they provide to the flow of electrons also increases. When cooling, the opposite phenomenon occurs: disordered oscillatory motion atoms at nodes crystal lattice decreases, their resistance to the flow of electrons decreases and the electrical conductivity of the conductor increases.

In nature, however, there are some alloys: fechral, constantan, manganin, etc., in which the electrical resistance changes relatively little in a certain temperature range. Such alloys are used in technology for the manufacture of various resistors used in electrical measuring instruments and some devices to compensate for the effect of temperature on their operation.

The degree of change in the resistance of conductors with temperature changes is judged by the so-called temperature coefficient of resistance a. This coefficient represents the relative increase in the resistance of the conductor as its temperature increases by 1 °C. In table Table 1 shows the values of the temperature coefficient of resistance for the most commonly used conductor materials.

Resistance of a metal conductor R t at any temperature t

R t = R 0 [ 1 + ? (t - t 0) ] (6)

where R 0 is the resistance of the conductor at a certain initial temperature t 0 (usually at + 20 ° C), which can be calculated using formula (5);

t- t 0 - temperature change.

The property of metal conductors to increase their resistance when heated is often used in modern technology for measuring temperature. For example, when testing traction motors after repair, the heating temperature of their windings is determined by measuring their resistance in a cold state and after operating under load for a specified period (usually 1 hour).

While studying the properties of metals during deep (very strong) cooling, scientists discovered a remarkable phenomenon: near absolute zero (-273.16 °C), some metals almost completely lose electrical resistance. They become ideal guides, capable long time pass current through a closed circuit without any influence from a source of electrical energy. This phenomenon is called superconductivity. Currently created prototypes power lines and electrical machines that use the phenomenon of superconductivity. Such machines have significantly less weight and overall dimensions compared to general purpose machines and operate with a very high efficiency. In this case, power lines can be made of wires with a very small cross-sectional area. In the future, this phenomenon will be used more and more in electrical engineering.

When an electrical circuit is closed, at the terminals of which there is a potential difference, a voltage occurs. Free electrons, under the influence of electric field forces, move along the conductor. In their movement, electrons collide with the atoms of the conductor and give them a supply of their kinetic energy. The speed of electron movement continuously changes: when electrons collide with atoms, molecules and other electrons, it decreases, then under the influence of an electric field it increases and decreases again during 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 to their movement from its side. When electric current passes through a conductor, the latter heats up.

Electrical resistance

The electrical resistance of a conductor, which is denoted by a 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 a circuit, is called rheostat. In the diagrams, rheostats are designated as shown in Figure 1, b. In general, a rheostat is made of a wire of one resistance or another, wound on an insulating base. The slider or rheostat lever is placed in a certain position, as a result of which the required resistance is introduced into the circuit.