How to find the resistivity of a metal. Electrical resistance and conductivity

Therefore, it is important to know the parameters of all elements and materials used. And not only electrical, but also mechanical. And have at your disposal some convenient reference materials that allow you to compare the characteristics of different materials and choose for design and work exactly what will be optimal in a particular situation.
In energy transmission lines, where the task is to deliver energy to the consumer in the most productive way, that is, with high efficiency, both the economics of losses and the mechanics of the lines themselves are taken into account. The final result depends on the mechanics - that is, the device and arrangement of conductors, insulators, supports, step-up/step-down transformers, the weight and strength of all structures, including wires stretched over long distances, as well as the materials selected for each structural element. economic efficiency line, its operation and operating costs. In addition, in lines transmitting electricity, there are higher requirements for ensuring the safety of both the lines themselves and everything around them where they pass. And this adds costs both for providing electricity wiring and for an additional margin of safety of all structures.

For comparison, data are usually reduced to a single, comparable form. Often, the epithet “specific” is added to such characteristics, and the values ​​themselves are considered based on certain standards unified by physical parameters. For example, specific electrical resistance- this is the resistance (ohms) of a conductor made of some metal (copper, aluminum, steel, tungsten, gold), having a unit length and a unit cross-section in the system of units of measurement used (usually in SI). In addition, the temperature is specified, since when heated, the resistance of the conductors can behave differently. Normal average operating conditions are taken as a basis - at 20 degrees Celsius. And where properties are important when changing environmental parameters (temperature, pressure), coefficients are introduced and additional tables and dependency graphs are compiled.

Types of resistivity

Since resistance happens:

• active - or ohmic, resistive - resulting from the expenditure of electricity on heating the conductor (metal) when an electric current passes through it, and
• reactive - capacitive or inductive - which occurs from the inevitable losses due to the creation of any changes in the current passing through the conductor of electric fields, then resistivity There are two types of conductor:

1. Specific electrical resistance to direct current (having a resistive nature) and
2. Specific electrical resistance to alternating current (having a reactive nature).

Here, type 2 resistivity is a complex value; it consists of two TC components - active and reactive, since resistive resistance always exists when current passes, regardless of its nature, and reactive resistance occurs only with any change in current in the circuits. In DC circuits, reactance occurs only during transient processes that are associated with turning on the current (change in current from 0 to nominal) or turning off (difference from nominal to 0). And they are usually taken into account only when designing overload protection.

In alternating current circuits, the phenomena associated with reactance are much more diverse. They depend not only on the actual passage of current through a certain cross section, but also on the shape of the conductor, and the dependence is not linear.

The fact is that alternating current induces an electric field both around the conductor through which it flows and in the conductor itself. And from this field, eddy currents arise, which give the effect of “pushing” the actual main movement of charges, from the depths of the entire cross-section of the conductor to its surface, the so-called “skin effect” (from skin - skin). It turns out that eddy currents seem to “steal” its cross-section from the conductor. The current flows in a certain layer close to the surface, the remaining thickness of the conductor remains unused, it does not reduce its resistance, and there is simply no point in increasing the thickness of the conductors. Especially at high frequencies. Therefore, for alternating current, resistance is measured in such sections of conductors where its entire section can be considered near-surface. Such a wire is called thin; its thickness is equal to twice the depth of this surface layer, where eddy currents displace the useful main current flowing in the conductor.

Of course, reducing the thickness of round wires does not exhaust the effective conduction of alternating current. The conductor can be thinned, but at the same time made flat in the form of a tape, then the cross-section will be higher than that of a round wire, and accordingly, the resistance will be lower. In addition, simply increasing the surface area will have the effect of increasing the effective cross-section. The same can be achieved by using stranded wire instead of single-core; moreover, stranded wire is more flexible than single-core wire, which is often valuable. On the other hand, taking into account the skin effect in wires, it is possible to make the wires composite by making the core from a metal that has good strength characteristics, for example, steel, but low electrical characteristics. In this case, an aluminum braid is made over the steel, which has a lower resistivity.

In addition to the skin effect, the flow of alternating current in conductors is affected by the excitation of eddy currents in surrounding conductors. Such currents are called induction currents, and they are induced both in metals that do not play the role of wiring (load-bearing structural elements), and in the wires of the entire conductive complex - playing the role of wires of other phases, neutral, grounding.

All of these phenomena occur in all electrical structures, making it even more important to have a comprehensive reference for a wide variety of materials.

The resistivity for conductors is measured with very sensitive and precise instruments, since metals with the lowest resistance are selected for wiring - on the order of ohms * 10 -6 per meter of length and sq. m. mm. sections. To measure the specific insulation resistance, you need instruments, on the contrary, that have ranges very large values resistance - usually megohms. It is clear that conductors must conduct well, and insulators must insulate well.

Table

Table of resistivity of conductors (metals and alloys)
Conductor material	Composition (for alloys)	Resistivity ρ mΩ × mm 2/m
	copper, zinc, tin, nickel, lead, manganese, iron, etc.
Aluminum
Tungsten
Molybdenum
	copper, tin, aluminum, silicon, beryllium, lead, etc. (except zinc)
	iron, carbon
	copper, nickel, zinc
Manganin	copper, nickel, manganese
Constantan	copper, nickel, aluminum
	nickel, chromium, iron, manganese
	iron, chromium, aluminum, silicon, manganese

Iron as a conductor in electrical engineering

Iron is the most common metal in nature and technology (after hydrogen, which is also a metal). It is the cheapest and has excellent strength characteristics, therefore it is used everywhere as the basis for the strength of various structures.

In electrical engineering, iron is used as a conductor in the form of flexible steel wires where physical strength and flexibility are needed, and the required resistance can be achieved through the appropriate cross-section.

Having a resistivity table various metals and alloys, you can calculate the cross-sections of wires made from different conductors.

As an example, let's try to find the electrically equivalent cross-section of conductors made of different materials: copper, tungsten, nickel and iron wire. Let's take aluminum wire with a cross-section of 2.5 mm as the initial one.

We need that over a length of 1 m the resistance of the wire made of all these metals is equal to the resistance of the original one. The resistance of aluminum per 1 m length and 2.5 mm section will be equal to

Where R- resistance, ρ – resistivity of the metal from the table, S– cross-sectional area, L- length.

Substituting the original values, we get the resistance of a meter-long piece of aluminum wire in ohms.

After this, let us solve the formula for S

We will substitute the values ​​from the table and obtain the cross-sectional areas for different metals.

Since the resistivity in the table is measured on a wire 1 m long, in microohms per 1 mm 2 section, then we got it in microohms. To get it in ohms, you need to multiply the value by 10 -6. But we don’t necessarily need to get the number ohm with 6 zeros after the decimal point, since end result we still find it in mm 2.

As you can see, the resistance of the iron is quite high, the wire is thick.

But there are materials for which it is even greater, for example, nickel or constantan.

Many people have heard about Ohm's law, but not everyone knows what it is. The study begins with a school physics course. They are taught in more detail at the Faculty of Physics and Electrodynamics. This knowledge is unlikely to be useful to the average person, but it is necessary for general development, and for some for a future profession. On the other hand, basic knowledge about electricity, its structure, and its features at home will help protect yourself from harm. It is not for nothing that Ohm’s law is called the fundamental law of electricity. A home handyman needs to have knowledge in the field of electricity to prevent overvoltage, which can lead to an increase in load and a fire.

Concept of electrical resistance

Relationship between basic physical quantities electrical circuit– resistance, voltage, current were 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, some of the electrons under the influence of electric current on the conductor leave their place in the crystal lattice and are directed to the positive pole of the conductor. Some electrons remain in the lattice, continuing to rotate around the nuclear atom. These electrons and atoms form electrical resistance that prevents the movement of released particles.

The above process applies to all metals, but resistance occurs differently in them. This is due to the difference in size, shape, and material of which the conductor is made. Accordingly, the dimensions of the crystal lattice have different shapes 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 (SER) 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 using the formula, where one of 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 of iron, as one of the available materials, equal to 0.1 Ohm, then for 1 Ohm you will need 10 meters. Silver has the lowest electrical resistance; for its value of 1 ohm it will be 66.7 meters. A significant difference, but silver is an expensive metal that is not practical to use everywhere. The next best indicator is copper, where 57.14 meters are required per 1 ohm. Due to its availability and cost compared to silver, copper is one of the popular materials for use in electrical networks. The low resistivity of copper wire or the resistance of copper wire makes it possible to use copper conductor in many branches of science, technology, as well as for industrial and domestic purposes.

Resistivity value

The resistivity value is not constant; it varies depending on the following factors:

• Size. The larger the diameter of the conductor, the more electrons it passes through. 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 making calculations, it is necessary to take into account the length and size of the wire, because the longer or 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 a fire.
• Temperature. It is known that temperature regime has great value on the behavior of substances differently. 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 the impact environment, ingress of moisture, salt, dirt, etc. manifestations. It is recommended to insulate and protect all connections, terminals, twists, install protection for equipment located on the street, and promptly replace damaged wires, components, and assemblies.

Resistance calculation

Calculations are made when designing objects for various purposes and uses, because everyone’s life support is provided by electricity. Everything is taken into account, from lighting fixtures to technically complex equipment. At home, it would also be useful to make a calculation, especially if it is planned to replace the electrical wiring. For private housing construction, it is necessary to calculate the load, otherwise the “makeshift” 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 using the formula R=p*l/S, where:

R – calculated result;

p – resistivity indicator from the table;

l – length of wire (conductor);

S – section diameter.

Units of measurement

In the international system of units physical quantities(SI) electrical resistance is measured in Ohms (ohms). The unit of measurement of resistivity according to the SI system is equal to the 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 for different metals is clearly shown in the table.

Significance of resistivity

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

Advantages of Electrolytic Copper

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

Dependence of resistance index on temperature

The temperature coefficient is a value that is equal to 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 resistivity of copper wire and at temperatures from 0 to 100°C is 4.1 10− 3 (1/Kelvin). For silver, under the same conditions, this indicator has a value of 3.8, and for iron, 6.0. This once again proves the effectiveness of using copper as a conductor.

Content:

The resistivity of metals is their ability to resist electric current passing through them. The unit of measurement for this quantity is Ohm*m (Ohm-meter). The symbol used is the Greek letter ρ (rho). High resistivity values ​​mean poor conductivity of electrical charge by a particular material.

Steel Specifications

Before considering the resistivity of steel in detail, you should familiarize yourself with its basic physical and mechanical properties. Due to its qualities, this material is widely used in the manufacturing sector and other areas of people’s lives and activities.

Steel is an alloy of iron and carbon, contained in an amount not exceeding 1.7%. In addition to carbon, steel contains a certain amount of impurities - silicon, manganese, sulfur and phosphorus. In terms of its qualities, it is much better than cast iron; it can easily be hardened, forged, rolled and other types of processing. All types of steels are characterized by high strength and ductility.

According to its purpose, steel is divided into structural, tool, and also with special physical properties. Each of them contains a different amount of carbon, thanks to which the material acquires certain specific qualities, for example, heat resistance, heat resistance, resistance to rust and corrosion.

A special place is occupied by electrical steels, produced in sheet format and used in the production of electrical products. To obtain this material, silicon is doped, which can improve its magnetic and electrical properties.

In order for electrical steel to acquire the necessary characteristics, certain requirements and conditions must be met. The material must be easily magnetized and remagnetized, that is, have high magnetic permeability. Such steels have good , and their magnetization reversal is carried out with minimal losses.

The dimensions and weight of magnetic cores and windings, as well as the coefficient, depend on compliance with these requirements. useful action transformers and their sizes operating temperature. The fulfillment of the conditions is influenced by many factors, including the resistivity of steel.

Resistivity and other indicators

The electrical resistivity value is the ratio of the voltage electric field in the metal and the current density flowing in it. For practical calculations, the formula is used: in which ρ is the resistivity of the metal (Ohm*m), E- electric field strength (V/m), and J- electric current density in the metal (A/m2). At very high electric field strength and low current density, the resistivity of the metal will be high.

There is another quantity called electrical conductivity, the inverse of resistivity, indicating the degree to which a material conducts electrical current. It is determined by the formula and expressed in units of S/m - siemens per meter.

Resistivity is closely related to electrical resistance. However, they have differences among themselves. In the first case, this is a property of the material, including steel, and in the second case, the property of the entire object is determined. The quality of a resistor is influenced by a combination of several factors, primarily the shape and resistivity of the material from which it is made. For example, if a thin and long wire was used to make a wirewound resistor, then its resistance will be greater than that of a resistor made from a thick and short wire of the same metal.

Another example is resistors made of wires of the same diameter and length. However, if in one of them the material has a high resistivity, and in the other it is low, then, accordingly, the electrical resistance in the first resistor will be higher than in the second.

Knowing the basic properties of the material, you can use the resistivity of steel to determine the resistance value of a steel conductor. For calculations, in addition to the electrical resistivity, you will need the diameter and length of the wire itself. Calculations are performed using the following formula: , in which R is (Ohm), ρ - resistivity of steel (Ohm*m), L- corresponds to the length of the wire, A- its cross-sectional area.

There is a dependence of the resistivity of steel and other metals on temperature. In most calculations, room temperature is used - 20 0 C. All changes under the influence of this factor are taken into account using the temperature coefficient.

Resistivity is an applied concept in electrical engineering. It denotes how much resistance per unit length a material of a unit cross-section has to the current flowing through it - in other words, what resistance a wire of a millimeter cross-section one meter long has. This concept is used in various electrical calculations.

It is important to understand the differences between DC electrical resistivity and AC electrical resistivity. In the first case, the resistance is caused solely by the action of direct current on the conductor. In the second case, alternating current (it can be of any shape: sinusoidal, rectangular, triangular or arbitrary) causes an additional vortex field in the conductor, which also creates resistance.

Physical representation

In technical calculations involving the laying of cables of various diameters, parameters are used to calculate the required cable length and its electrical characteristics. One of the main parameters is resistivity. Electrical resistivity formula:

ρ = R * S / l, where:

• ρ is the resistivity of the material;
• R is the ohmic electrical resistance of a particular conductor;
• S - cross section;
• l - length.

The dimension ρ is measured in Ohm mm 2 /m, or, to abbreviate the formula - Ohm m.

The value of ρ for the same substance is always the same. Therefore, this is a constant characterizing the material of the conductor. It is usually indicated in directories. Based on this, it is already possible to calculate technical quantities.

It is important to say about specific electrical conductivity. This value is the inverse of the resistivity of the material, and is used equally with it. It is also called electrical conductivity. The higher this value, the metal is better conducts current. For example, the conductivity of copper is 58.14 m/(Ohm mm2). Or, in SI units: 58,140,000 S/m. (Siemens per meter is the SI unit of electrical conductivity).

We can talk about resistivity only in the presence of elements that conduct current, since dielectrics have infinite or close to infinite electrical resistance. In contrast, metals are very good conductors of current. You can measure the electrical resistance of a metal conductor using a milliohmmeter, or an even more accurate microohmmeter. The value is measured between their probes applied to the conductor section. They allow you to check circuits, wiring, windings of motors and generators.

Metals vary in their ability to conduct current. The resistivity of various metals is a parameter that characterizes this difference. The data is given at a material temperature of 20 degrees Celsius:

The parameter ρ shows what resistance a meter conductor with a cross section of 1 mm 2 will have. The higher this value, the greater the electrical resistance of the desired wire of a certain length. The smallest ρ, as can be seen from the list, is silver; the resistance of one meter of this material will be equal to only 0.015 Ohms, but this is too expensive a metal to use on an industrial scale. Next comes copper, which is much more common in nature (not a precious metal, but a non-ferrous metal). Therefore, copper wiring is very common.

Copper is not only a good conductor of electric current, but also a very ductile material. Thanks to this property, copper wiring fits better and is resistant to bending and stretching.

Copper is in great demand on the market. Many different products are made from this material:

• A huge variety of conductors;
• Auto parts (eg radiators);
• Clock mechanisms;
• Computer components;
• Parts of electrical and electronic devices.

The electrical resistivity of copper is one of the best among current-conducting materials, so many electrical industry products are created based on it. In addition, copper is easy to solder, so it is very common in amateur radio.

The high thermal conductivity of copper allows it to be used in cooling and heating devices, and its plasticity makes it possible to create the smallest parts and the thinnest conductors.

Conductors of electric current are of the first and second kind. Conductors of the first kind are metals. Conductors of the second type are conductive solutions of liquids. The current in the first type is carried by electrons, and the current carriers in conductors of the second type are ions, charged particles of the electrolytic liquid.

We can only talk about the conductivity of materials in the context of ambient temperature. With more high temperature conductors of the first type increase their electrical resistance, and the second, on the contrary, decrease. Accordingly, there is a temperature coefficient of resistance of materials. The resistivity of copper Ohm m increases with increasing heating. The temperature coefficient α also depends only on the material; this value has no dimension and for different metals and alloys is equal to the following indicators:

• Silver - 0.0035;
• Iron - 0.0066;
• Platinum - 0.0032;
• Copper - 0.0040;
• Tungsten - 0.0045;
• Mercury - 0.0090;
• Constantan - 0.000005;
• Nickelin - 0.0003;
• Nichrome - 0.00016.

Determination of the electrical resistance value of a conductor section at elevated temperature R(t), calculated by the formula:

R (t) = R (0) · , where:

• R (0) - resistance at initial temperature;
• α - temperature coefficient;
• t - t (0) - temperature difference.

For example, knowing the electrical resistance of copper at 20 degrees Celsius, you can calculate what it will be equal to at 170 degrees, that is, when heated by 150 degrees. The initial resistance will increase by a factor of 1.6.

As the temperature increases, the conductivity of materials, on the contrary, decreases. Since this is the reciprocal of electrical resistance, it decreases by exactly the same amount. For example, the electrical conductivity of copper when the material is heated by 150 degrees will decrease by 1.6 times.

There are alloys that practically do not change their electrical resistance when temperature changes. This is, for example, constantan. When the temperature changes by one hundred degrees, its resistance increases by only 0.5%.

While the conductivity of materials deteriorates with heat, it improves with decreasing temperature. This is related to the phenomenon of superconductivity. If you lower the temperature of the conductor below -253 degrees Celsius, its electrical resistance will sharply decrease: almost to zero. In this regard, the costs of transmitting electrical energy are falling. The only problem was cooling the conductors to such temperatures. However, due to the recent discoveries of high-temperature superconductors based on copper oxides, materials have to be cooled to acceptable values.

Electrical resistance, expressed in ohms, is different from the concept of resistivity. To understand what resistivity is, we need to relate it to the physical properties of the material.

About conductivity and resistivity

The flow of electrons does not move unimpeded through the material. At constant temperature elementary particles swing around a state of rest. In addition, electrons in the conduction band interfere with each other through mutual repulsion due to similar charge. This is how resistance arises.

Conductivity is an intrinsic characteristic of materials and quantifies the ease with which charges can move when a substance is exposed to an electric field. Resistivity is the reciprocal of the material and describes the degree of difficulty electrons encounter as they move through a material, giving an indication of how good or bad a conductor is.

Important! An electrical resistivity with a high value indicates that the material is poorly conductive, and with low value– defines a good conductive substance.

Specific conductivity is designated by the letter σ and is calculated by the formula:

Resistivity ρ, as an inverse indicator, can be found as follows:

In this expression, E is the intensity of the generated electric field (V/m), and J is the electric current density (A/m²). Then the unit of measurement ρ will be:

V/m x m²/A = ohm m.

For conductivity σ, the unit in which it is measured is S/m or Siemens per meter.

Types of materials

According to the resistivity of materials, they can be classified into several types:

1. Conductors. These include all metals, alloys, solutions dissociated into ions, as well as thermally excited gases, including plasma. Among non-metals, graphite can be cited as an example;
2. Semiconductors, which are essentially non-conducting materials, crystal lattices which are purposefully doped with the inclusion of foreign atoms with a greater or lesser number of bound electrons. As a result, quasi-free excess electrons or holes are formed in the lattice structure, which contribute to the conductivity of the current;
3. Dielectrics or dissociated insulators are all materials that normal conditions have no free electrons.

For the transport of electrical energy or in electrical installations for domestic and industrial purposes, a frequently used material is copper in the form of single-core or multi-core cables. An alternative metal is aluminum, although the resistivity of copper is 60% of that of aluminum. But it is much lighter than copper, which predetermined its use in high-voltage power lines. Gold is used as a conductor in special-purpose electrical circuits.

Interesting. The electrical conductivity of pure copper was adopted by the International Electrotechnical Commission in 1913 as the standard for this value. By definition, the conductivity of copper measured at 20° is 0.58108 S/m. This value is called 100% LACS, and the conductivity of the remaining materials is expressed as a certain percentage of LACS.

Most metals have a conductivity value less than 100% LACS. There are exceptions, however, such as silver or special copper with very high conductivity, designated C-103 and C-110, respectively.

Dielectrics do not conduct electricity and are used as insulators. Examples of insulators:

• glass,
• ceramics,
• plastic,
• rubber,
• mica,
• wax,
• paper,
• dry wood,
• porcelain,
• some fats for industrial and electrical use and bakelite.

Between the three groups the transitions are fluid. It is known for sure: there are no absolutely non-conducting media and materials. For example, air is an insulator at room temperature, but when exposed to a strong low-frequency signal, it can become a conductor.

Determination of conductivity

If we compare the electrical resistivity various substances, standardized measurement conditions are required:

1. In the case of liquids, poor conductors and insulators, cubic samples with an edge length of 10 mm are used;
2. The resistivity values ​​of soils and geological formations are determined on cubes with a length of each edge of 1 m;
3. The conductivity of a solution depends on the concentration of its ions. A concentrated solution is less dissociated and has fewer charge carriers, which reduces conductivity. As the dilution increases, the number of ion pairs increases. The concentration of solutions is set to 10%;
4. To determine the resistivity of metal conductors, wires of a meter length and a cross-section of 1 mm² are used.

If a material, such as a metal, can provide free electrons, then when a potential difference is applied, electrons will flow through the wire. electric current. As the voltage increases, more electrons move through the substance into the time unit. If all additional parameters (temperature, cross-sectional area, length and wire material) are unchanged, then the ratio of current to applied voltage is also constant and is called conductivity:

Accordingly, the electrical resistance will be:

The result is in ohms.

In turn, the conductor can be of different lengths, cross-sectional sizes and made of different materials, which determines the value of R. Mathematically, this relationship looks like this:

The material factor takes into account the coefficient ρ.

From this we can derive the formula for resistivity:

If the values ​​of S and l correspond to the given conditions for the comparative calculation of resistivity, i.e. 1 mm² and 1 m, then ρ = R. When the dimensions of the conductor change, the number of ohms also changes.