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Specific resistance of aluminum wire. Electrical resistance

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, 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 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 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 current. Short conductors with a large cross-section offer 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 denoted in Greek capital letterΩ (omega). Therefore, instead of writing “The conductor resistance is 15 ohms,” you can simply write: r= 15 Ω.
1,000 ohms is called 1 kiloohms(1kOhm, or 1kΩ),
1,000,000 ohms is called 1 megaohm(1mOhm, or 1MΩ).

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 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.

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.

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 resistance 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.

Based on the resistivity table, we find that lead has this 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. 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° 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 flows 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)

Therefore, it is important to know the parameters of all elements and materials used. And not only electrical, but also mechanical. And have some convenient ones at your disposal reference materials, allowing you to compare the characteristics of different materials and choose for design and operation exactly what will be optimal in a particular situation.
In energy transmission lines, where the goal 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, electrical resistivity 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 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 the resistivity of the conductor comes in two varieties:

Specific electrical resistance to direct current (having a resistive nature) and
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 insulation resistivity, you need instruments, on the contrary, that have ranges of very large resistance values - 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
Conductor material	Composition (for alloys)



	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 table of resistivities of 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 final 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.

The term “resistivity” refers to a parameter possessed by copper or any other metal, and is quite often found in the specialized literature. It is worth understanding what is meant by this.

One of the types of copper cable

General information about electrical resistance

First, we should consider the concept of electrical resistance. As is known, under the influence of electric current on a conductor (and copper is one of the best conductor metals), some of the electrons in it leave their place in the crystal lattice and rush towards the positive pole of the conductor. However, not all electrons leave the crystal lattice; some of them remain in it and continue to rotate around the atomic nucleus. It is these electrons, as well as atoms located at the nodes of the crystal lattice, that create electrical resistance that prevents the movement of released particles.

This process, which we briefly outlined, is typical for any metal, including copper. Naturally, different metals, each of which has a special shape and size of the crystal lattice, resist the passage of electric current through them in different ways. It is precisely these differences that characterize resistivity - an indicator individual for each metal.

Applications of copper in electrical and electronic systems

In order to understand the reason for the popularity of copper as a material for the manufacture of electrical and electronic systems, just look at the value of its resistivity in the table. For copper, this parameter is 0.0175 Ohm*mm2/meter. In this regard, copper is second only to silver.

It is the low resistivity, measured at a temperature of 20 degrees Celsius, that is the main reason that almost no electronic and electrical device can do without copper today. Copper is the main material for the production of wires and cables, printed circuit boards, electric motors and power transformer parts.

The low resistivity that copper is characterized by allows it to be used for the manufacture of electrical devices characterized by high energy-saving properties. In addition, the temperature of copper conductors increases very little when electric current passes through them.

What affects the resistivity value?

It is important to know that there is a dependence of the resistivity value on the chemical purity of the metal. When copper contains even a small amount of aluminum (0.02%), the value of this parameter can increase significantly (up to 10%).

This coefficient is also affected by the temperature of the conductor. This is explained by the fact that as the temperature increases, the vibrations of metal atoms in the nodes of its crystal lattice intensify, which leads to the fact that the resistivity coefficient increases.

That is why in all reference tables the value of this parameter is given taking into account a temperature of 20 degrees.

How to calculate the total resistance of a conductor?

Knowing what the resistivity is is important in order to carry out preliminary calculations of the parameters of electrical equipment when designing it. In such cases, the total resistance of the conductors of the designed device, having a certain size and shape, is determined. Having looked at the resistivity value of the conductor using a reference table, determining its dimensions and cross-sectional area, you can calculate the value of its total resistance using the formula:

This formula uses the following notation:

R is the total resistance of the conductor, which must be determined;
p is the resistivity of the metal from which the conductor is made (determined from the table);
l is the length of the conductor;
S is its cross-sectional area.

Resistivity of popular conductors (metals and alloys). Steel resistivity

Resistivity of iron, aluminum and other conductors

Transmitting electricity over long distances requires taking care to minimize losses resulting from current overcoming the resistance of the conductors that make up the electrical line. Of course, this does not mean that such losses, which occur specifically in circuits and consumer devices, do not play a role.

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 operation exactly what will be optimal in a particular situation. In energy transmission lines, where the task is set to be most productive, that is, with high efficiency, to bring energy to the consumer, both the economics of losses and the mechanics of the lines themselves are taken into account. The final economic efficiency of the line 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. , its work 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.

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 the resistivity of the conductor comes in two varieties:

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

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.

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 insulation resistivity, you need instruments, on the contrary, that have ranges of very large resistance values - usually megohms. It is clear that conductors must conduct well, and insulators must insulate well.

Table

Iron as a conductor in electrical engineering

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

, where R is the resistance, ρ is the resistivity of the metal from the table, S is the cross-sectional area, L is the 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 mm2 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 we still find the final result in mm2.

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.

Table of electrical resistivity of metals and alloys in electrical engineering

Home > y >

Specific resistance of metals.

Specific resistance of alloys.

The values are given at a temperature of t = 20° C. The resistances of the alloys depend on their exact composition. comments powered by HyperComments

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Electrical resistivity | Welding world

Electrical resistivity of materials

Electrical resistivity (resistivity) is the ability of a substance to prevent the passage of electric current.

Unit of measurement (SI) - Ohm m; also measured in Ohm cm and Ohm mm2/m.

Material Temperature, °C Electrical resistivity, Ohm m

Metals
Aluminum	20	0.028·10-6
Beryllium	20	0.036·10-6
Phosphor bronze	20	0.08·10-6
Vanadium	20	0.196·10-6
Tungsten	20	0.055·10-6
Hafnium	20	0.322·10-6
Duralumin	20	0.034·10-6
Iron	20	0.097 10-6
Gold	20	0.024·10-6
Iridium	20	0.063·10-6
Cadmium	20	0.076·10-6
Potassium	20	0.066·10-6
Calcium	20	0.046·10-6
Cobalt	20	0.097 10-6
Silicon	27	0.58 10-4
Brass	20	0.075·10-6
Magnesium	20	0.045·10-6
Manganese	20	0.050·10-6
Copper	20	0.017 10-6
Magnesium	20	0.054·10-6
Molybdenum	20	0.057 10-6
Sodium	20	0.047 10-6
Nickel	20	0.073 10-6
Niobium	20	0.152·10-6
Tin	20	0.113·10-6
Palladium	20	0.107 10-6
Platinum	20	0.110·10-6
Rhodium	20	0.047 10-6
Mercury	20	0.958 10-6
Lead	20	0.221·10-6
Silver	20	0.016·10-6
Steel	20	0.12·10-6
Tantalum	20	0.146·10-6
Titanium	20	0.54·10-6
Chromium	20	0.131·10-6
Zinc	20	0.061·10-6
Zirconium	20	0.45·10-6
Cast iron	20	0.65·10-6
Plastics
Getinax	20	109–1012
Capron	20	1010–1011
Lavsan	20	1014–1016
Organic glass	20	1011–1013
Styrofoam	20	1011
Polyvinyl chloride	20	1010–1012
Polystyrene	20	1013–1015
Polyethylene	20	1015
Fiberglass	20	1011–1012
Textolite	20	107–1010
Celluloid	20	109
Ebonite	20	1012–1014
Rubbers
Rubber	20	1011–1012
Liquids
Transformer oil	20	1010–1013
Gases
Air	0	1015–1018
Tree
Dry wood	20	109–1010
Minerals
Quartz	230	109
Mica	20	1011–1015
Various materials
Glass	20	109–1013

LITERATURE

Alpha and Omega. Quick reference book / Tallinn: Printest, 1991 – 448 p.
Guide to elementary physics/ N.N. Koshkin, M.G. Shirkevich. M., Science. 1976. 256 p.
Handbook on welding of non-ferrous metals / S.M. Gurevich. Kyiv: Naukova Dumka. 1990. 512 p.

weldworld.ru

Resistivity of metals, electrolytes and substances (Table)

Resistivity of metals and insulators

The reference table gives the resistivity p values of some metals and insulators at a temperature of 18-20 ° C, expressed in ohm cm. The value of p for metals strongly depends on impurities; the table shows the values of p for chemically pure metals, and for insulators they are given approximately. Metals and insulators are arranged in the table in order of increasing p values.

Metal resistivity table

Pure metals	104 ρ (ohm cm)	Pure metals	104 ρ (ohm cm)



Aluminum
Duralumin
		Platinit 2)

		Argentan
Manganese
		Manganin
Tungsten		Constantan
Molybdenum		Wood alloy 3)

		Alloy Rose 4)






Palladium		Fechral 6)

Table of resistivity of insulators

Insulators		Insulators


Dry wood

Celluloid
		Rosin
Getinax		Quartz _\|_ axis

Soda glass		Polystyrene
Pyrex glass
Quartz \|\| axes
Fused quartz

Resistivity of pure metals at low temperatures

The table gives the resistivity values (in ohm cm) of some pure metals at low temperatures (0°C).

Resistance ratio Rt/Rq of pure metals at temperatures T ° K and 273 ° K.

The reference table gives the ratio Rt/Rq of the resistances of pure metals at temperatures T ° K and 273 ° K.

Pure metals
Aluminum
Aluminum


Tungsten
Tungsten






Molybdenum
Molybdenum

Specific resistance of electrolytes

The table gives the values of the resistivity of electrolytes in ohm cm at a temperature of 18 ° C. The concentration of solutions is given in percentages, which determine the number of grams of anhydrous salt or acid in 100 g of solution.

Source of information: BRIEF PHYSICAL AND TECHNICAL GUIDE / Volume 1, - M.: 1960.

infotables.ru

Electrical resistivity - steel

Page 1

The electrical resistivity of steel increases with increasing temperature, with the greatest changes observed when heated to the Curie point temperature. After the Curie point, the electrical resistivity changes slightly and at temperatures above 1000 C remains virtually constant.

Due to the high electrical resistivity of steel, these iuKii create a very large slowdown in the flow decline. In 100 A contactors, the drop-off time is 0 07 sec, and in 600 A contactors - 0 23 sec. Due to the special requirements for contactors of the KMV series, which are designed to turn on and off the electromagnets of oil switch drives, the electromagnetic mechanism of these contactors allows adjustment of the actuation voltage and release voltage by adjusting the force of the return spring and a special break-off spring. Contactors of the KMV type must operate with a deep voltage drop. Therefore, the minimum operating voltage for these contactors can drop to 65% UH. Such a low operating voltage results in current flowing through the winding at rated voltage, resulting in increased heating of the coil.

The silicon additive increases the electrical resistivity of steel almost proportionally to the silicon content and thereby helps reduce losses due to eddy currents that occur in steel when it operates in an alternating magnetic field.

The silicon additive increases the electrical resistivity of steel, which helps reduce eddy current losses, but at the same time silicon worsens mechanical properties steel, makes it brittle.

Ohm - mm2/m - electrical resistivity of steel.

To reduce eddy currents, cores are used made of steel grades with increased electrical resistivity of steel, containing 0 5 - 4 8% silicon.

To do this, a thin screen made of soft magnetic steel was put on a massive rotor made of the optimal SM-19 alloy. The electrical resistivity of steel differs little from the resistivity of the alloy, and the CG of steel is approximately an order of magnitude higher. The screen thickness is selected according to the penetration depth of first-order tooth harmonics and is equal to 0 8 mm. For comparison, the additional losses, W, are given for a basic squirrel-cage rotor and a two-layer rotor with a massive cylinder made of SM-19 alloy and with copper end rings.

The main magnetically conductive material is sheet alloy electrical steel containing from 2 to 5% silicon. The silicon additive increases the electrical resistivity of steel, as a result of which eddy current losses are reduced, the steel becomes resistant to oxidation and aging, but becomes more brittle. IN last years Cold-rolled grain-oriented steel with higher magnetic properties in the rolling direction is widely used. To reduce losses from eddy currents, the magnetic core is made in the form of a package assembled from sheets of stamped steel.

Electrical steel is low carbon steel. To improve the magnetic characteristics, silicon is introduced into it, which causes an increase in the electrical resistivity of the steel. This leads to a reduction in eddy current losses.

After mechanical treatment, the magnetic core is annealed. Since eddy currents in steel participate in the creation of deceleration, one should focus on the value of the electrical resistivity of steel on the order of Pc (Iu-15) 10 - 6 ohm cm. In the attracted position of the armature, the magnetic system is quite highly saturated, therefore the initial induction in different magnetic systems fluctuates within very small limits and for steel grade E Vn1 6 - 1 7 ch. The indicated induction value maintains the field strength in the steel on the order of Yang.

For the manufacture of magnetic systems (magnetic cores) of transformers, special thin-sheet electrical steels with a high (up to 5%) silicon content are used. Silicon promotes the decarburization of steel, which leads to an increase in magnetic permeability, reduces hysteresis losses and increases its electrical resistivity. Increasing the electrical resistivity of steel makes it possible to reduce losses in it from eddy currents. In addition, silicon weakens the aging of steel (increasing losses in steel over time), reduces its magnetostriction (changes in the shape and size of a body during magnetization) and, consequently, the noise of transformers. At the same time, the presence of silicon in steel increases its brittleness and complicates its machining.

Pages: 1 2

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Resistivity | Wikitronics wiki

Resistivity is a characteristic of a material that determines its ability to conduct electric current. Defined as the ratio of the electric field to the current density. IN general case is a tensor, but for most materials that do not exhibit anisotropic properties, it is accepted as a scalar quantity.

Designation - ρ

$ \vec E = \rho \vec j, $

$ \vec E $ - electric field strength, $ \vec j $ - current density.

The SI unit of measurement is the ohm meter (ohm m, Ω m).

The resistivity resistance of a cylinder or prism (between the ends) of a material with length l and section S is determined as follows:

$ R = \frac(\rho l)(S). $

In technology, the definition of resistivity is used as the resistance of a conductor of a unit cross-section and unit length.

Resistivity of some materials used in electrical engineering Edit

Material ρ at 300 K, Ohm m TKS, K⁻¹

silver	1.59·10⁻⁸	4.10·10⁻³
copper	1.67·10⁻⁸	4.33·10⁻³
gold	2.35·10⁻⁸	3.98·10⁻³
aluminum	2.65·10⁻⁸	4.29·10⁻³
tungsten	5.65·10⁻⁸	4.83·10⁻³
brass	6.5·10⁻⁸	1.5·10⁻³
nickel	6.84·10⁻⁸	6.75·10⁻³
iron (α)	9.7·10⁻⁸	6.57·10⁻³
tin gray	1.01·10⁻⁷	4.63·10⁻³
platinum	1.06·10⁻⁷	6.75·10⁻³
white tin	1.1·10⁻⁷	4.63·10⁻³
steel	1.6·10⁻⁷	3.3·10⁻³
lead	2.06·10⁻⁷	4.22·10⁻³
duralumin	4.0·10⁻⁷	2.8·10⁻³
manganin	4.3·10⁻⁷	±2·10⁻⁵
constantan	5.0·10⁻⁷	±3·10⁻⁵
mercury	9.84·10⁻⁷	9.9·10⁻⁴
nichrome 80/20	1.05·10⁻⁶	1.8·10⁻⁴
Cantal A1	1.45·10⁻⁶	3·10⁻⁵
carbon (diamond, graphite)	1.3·10⁻⁵
germanium	4.6·10⁻¹
silicon	6.4·10²
ethanol	3·10³
water, distilled	5·10³
ebonite	10⁸
hard paper	10¹⁰
transformer oil	10¹¹
regular glass	5·10¹¹
polyvinyl	10¹²
porcelain	10¹²
wood	10¹²
PTFE (Teflon)	>10¹³
rubber	5·10¹³
quartz glass	10¹⁴
wax paper	10¹⁴
polystyrene	>10¹⁴
mica	5·10¹⁴
paraffin	10¹⁵
polyethylene	3·10¹⁵
acrylic resin	10¹⁹

en.electronics.wikia.com

Electrical resistivity | formula, volumetric, table

Electrical resistivity is physical quantity, which shows the extent to which a material can resist the passage of electric current through it. Some people may get confused this characteristic with ordinary electrical resistance. Despite the similarity of concepts, the difference between them is that specific refers to substances, and the second term refers exclusively to conductors and depends on the material of their manufacture.

The reciprocal value of this material is the electrical conductivity. The higher this parameter, the better the current flows through the substance. Accordingly, the higher the resistance, the more losses are expected at the output.

Calculation formula and measurement value

Considering how specific electrical resistance is measured, it is also possible to trace the connection with non-specific, since units of Ohm m are used to denote the parameter. The quantity itself is denoted as ρ. With this value, it is possible to determine the resistance of a substance in a particular case, based on its size. This unit of measurement corresponds to the SI system, but other variations may occur. In technology you can periodically see the outdated designation Ohm mm2/m. To convert from this system to the international one, you will not need to use complex formulas, since 1 Ohm mm2/m equals 10-6 Ohm m.

The formula for electrical resistivity is as follows:

R= (ρ l)/S, where:

R – conductor resistance;
Ρ – resistivity of the material;
l – conductor length;
S – conductor cross-section.

Temperature dependence

Electrical resistivity depends on temperature. But all groups of substances manifest themselves differently when it changes. This must be taken into account when calculating wires that will operate under certain conditions. For example, outdoors, where temperature values depend on the time of year, necessary materials with less susceptibility to changes in the range from -30 to +30 degrees Celsius. If you plan to use it in equipment that will operate under the same conditions, then you also need to optimize the wiring for specific parameters. The material is always selected taking into account the use.

In the nominal table, electrical resistivity is taken at a temperature of 0 degrees Celsius. The increase in the indicators of this parameter when the material is heated is due to the fact that the intensity of the movement of atoms in the substance begins to increase. Electric charge carriers scatter randomly in all directions, which leads to the creation of obstacles to the movement of particles. The amount of electrical flow decreases.

As the temperature decreases, the conditions for current flow become better. Upon reaching a certain temperature, which will be different for each metal, superconductivity appears, at which the characteristic in question almost reaches zero.

The differences in parameters sometimes reach very large values. Those materials that have high performance can be used as insulators. They help protect wiring from short circuits and unintentional human contact. Some substances are not applicable at all for electrical engineering if they have a high value of this parameter. Other properties may interfere with this. For example, the electrical conductivity of water will not have of great importance for this area. Here are the values of some substances with high indicators.

High resistivity materials	ρ (Ohm m)
Bakelite	1016
Benzene	1015...1016
Paper	1015
Distilled water	104
Sea water	0.3
Dry wood	1012
The ground is wet	102
Quartz glass	1016
Kerosene	1011
Marble	108
Paraffin	1015
Paraffin oil	1014
Plexiglass	1013
Polystyrene	1016
Polyvinyl chloride	1013
Polyethylene	1012
Silicone oil	1013
Mica	1014
Glass	1011
Transformer oil	1010
Porcelain	1014
Slate	1014
Ebonite	1016
Amber	1018

Substances with low performance are used more actively in electrical engineering. These are often metals that serve as conductors. There are also many differences between them. To find out the electrical resistivity of copper or other materials, it is worth looking at the reference table.

Low resistivity materials	ρ (Ohm m)
Aluminum	2.7·10-8
Tungsten	5.5·10-8
Graphite	8.0·10-6
Iron	1.0·10-7
Gold	2.2·10-8
Iridium	4.74 10-8
Constantan	5.0·10-7
Cast steel	1.3·10-7
Magnesium	4.4·10-8
Manganin	4.3·10-7
Copper	1.72·10-8
Molybdenum	5.4·10-8
Nickel silver	3.3·10-7
Nickel	8.7 10-8
Nichrome	1.12·10-6
Tin	1.2·10-7
Platinum	1.07 10-7
Mercury	9.6·10-7
Lead	2.08·10-7
Silver	1.6·10-8
Gray cast iron	1.0·10-6
Carbon brushes	4.0·10-5
Zinc	5.9·10-8
Nikelin	0.4·10-6

Specific volumetric electrical resistivity

This parameter characterizes the ability to pass current through the volume of a substance. To measure, it is necessary to apply a voltage potential from different sides of the material from which the product will be included in the electrical circuit. It is supplied with current with rated parameters. After passing, the output data is measured.

Use in electrical engineering

Changing the parameter when different temperatures widely used in electrical engineering. Most simple example is an incandescent lamp that uses a nichrome filament. When heated, it begins to glow. When current passes through it, it begins to heat up. As heating increases, resistance also increases. Accordingly, the initial current that was needed to obtain lighting is limited. A nichrome spiral, using the same principle, can become a regulator on various devices.

Precious metals, which have suitable characteristics for electrical engineering, are also widely used. For critical circuits that require high speed, silver contacts are selected. They are expensive, but given the relatively small amount of materials, their use is quite justified. Copper is inferior to silver in conductivity, but has more affordable price, due to which it is more often used to create wires.

In conditions where maximum use can be made low temperatures, superconductors are used. For room temperature and outdoor use they are not always appropriate, since as the temperature rises their conductivity will begin to fall, so for such conditions aluminum, copper and silver remain the leaders.

In practice, many parameters are taken into account and this is one of the most important. All calculations are carried out at the design stage, for which reference materials are used.

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

About conductivity and resistivity

The flow of electrons does not move unimpeded through the material. At a 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 a poor conductor, while a resistivity with a low value indicates a good conductor.

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 conductivityσ 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:

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;
Semiconductors, which are actually non-conducting materials, whose crystal lattices 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;
Dielectrics or dissociated insulators are all materials that normal conditions have no free electrons.

For transportation 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 has been accepted by the International Electrotechnical Commission in 1913 as a 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

When comparing the electrical resistivity of different substances, standardized measurement conditions are required:

In the case of liquids, poor conductors and insulators, cubic samples with an edge length of 10 mm are used;
The resistivity values of soils and geological formations are determined on cubes with a length of each edge of 1 m;
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%;
To determine the resistivity of metal conductors, wires are used meter long and cross-section 1 mm².

If a material, such as a metal, can provide free electrons, then when a potential difference is applied, an electric current will flow through the wire. As the voltage increases large quantity electrons move through matter into a 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 different lengths, cross-sectional dimensions and made from various materials, on which the R value depends. 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 given conditions 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.

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