Electrical resistance, expressed in ohms, is different from resistivity. To understand what resistivity is, one must relate it to the physical properties of the material.
About specific conductivity and specific resistance
The flow of electrons does not travel 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 by mutual repulsion due to a similar charge. Thus, 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 and is characterized by the degree of difficulty that electrons encounter as they move through a material, giving an idea of \u200b\u200bhow good or bad a conductor is.
Important! A high resistivity indicates a poorly conductive material, while a low resistivity indicates a good conductive material.
Specific conductivity is designated by the letter σ and is calculated by the formula:
Resistivity ρ, as a reciprocal, can be found as follows:
In this expression, E is the strength of the generated electric field (V / m), and J is the density of the electric current (A / m²). Then the unit of measurement of ρ will be:
W / mx m² / A \u003d 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:
- Conductors. These include all metals, alloys, solutions dissociated into ions, as well as thermally excited gases, including plasma. Of non-metals, graphite is an example;
- Semiconductors, which are in fact non-conducting materials, whose crystal lattices are purposefully doped with the inclusion of foreign atoms with more or less bound electrons. As a result, quasi-free excess electrons or holes are formed in the lattice structure, which contribute to the current conductivity;
- Dissociated dielectrics or insulators are all materials that do not have free electrons under normal conditions.
For the transportation of electrical energy or in electrical installations for household 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 rest of the materials is expressed as a specific percentage of LACS.
Most metals have a conductivity value of less than 100% LACS. However, there are exceptions such as silver or very high conductivity special copper 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.
The transitions between the three groups are fluid. It is known for sure: there are no absolutely non-conductive media and materials. For example, air is an insulator at room temperature, but in conditions of a strong low frequency signal, it can become a conductor.
Determination of specific conductivity
When comparing the electrical resistivity of different substances, standardized measurement conditions are required:
- In the case of liquids, poor conductors and insulators, use cube specimens with a rib length of 10 mm;
- The values \u200b\u200bof the resistivity 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 the solutions is set at 10%;
- To determine the resistivity of metal conductors, wires of one 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, an electric current will flow through the wire. As the voltage increases, more electrons move through the substance in a unit of time. If all additional parameters (temperature, cross-sectional area, wire length and material) are unchanged, then the ratio of the current to the applied voltage is also constant and is called conductivity:
Accordingly, the electrical resistance will be:
The result is obtained in ohms.
In turn, the conductor can be of different lengths, cross-sectional sizes and be made of different materials, on which the R value depends. Mathematically, this dependence looks like this:
The material factor takes into account the ρ factor.
From here you can derive the formula for the resistivity:
If the values \u200b\u200bof S and l correspond to the given conditions for the comparative calculation of the resistivity, ie, 1 mm² and 1 m, then ρ \u003d R. When the dimensions of the conductor change, the number of ohms also changes.
Specific electrical resistance, or simply resistivity substances - a physical quantity that characterizes the ability of a substance to prevent the passage of electric current.
Resistivity is indicated by the Greek letter ρ. The reciprocal of specific resistance is called conductivity (electrical conductivity). Unlike electrical resistance, which is a property conductor and depending on its material, shape and size, electrical resistivity is a property only substances.
Electrical resistance of a homogeneous conductor with resistivity ρ, length l and cross-sectional area S can be calculated by the formula R \u003d ρ ⋅ l S (\\ displaystyle R \u003d (\\ frac (\\ rho \\ cdot l) (S))) (this assumes that neither the area nor the cross-sectional shape changes along the conductor). Accordingly, ρ satisfies ρ \u003d R ⋅ S l. (\\ displaystyle \\ rho \u003d (\\ frac (R \\ cdot S) (l)).)
From the last formula it follows: the physical meaning of the resistivity of a substance is that it is the resistance of a homogeneous conductor made from this substance of unit length and unit cross-sectional area.
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The unit of measurement of resistivity in the International System of Units (SI) is Ohm ·. From the ratio ρ \u003d R ⋅ S l (\\ displaystyle \\ rho \u003d (\\ frac (R \\ cdot S) (l))) it follows that the unit of resistivity in the SI system is equal to the specific resistance of the substance at which a homogeneous conductor 1 m long with a cross-sectional area of \u200b\u200b1 m2, made of this substance, has a resistance of 1 Ohm. Accordingly, the resistivity of an arbitrary substance, expressed in SI units, is numerically equal to the resistance of a section of an electrical circuit made of this substance, 1 m long and a cross-sectional area of \u200b\u200b1 m2.
The technology also uses the outdated off-system unit Ohm · mm² / m, equal to 10 −6 of 1 Ohm · m. This unit is equal to the specific resistance of the substance at which a uniform conductor 1 m long with a cross-sectional area of \u200b\u200b1 mm², made of this substance, has a resistance of 1 Ohm. Accordingly, the specific resistance of any substance, expressed in these units, is numerically equal to the resistance of a section of an electrical circuit made of this substance, 1 m long and 1 mm² cross-sectional area.
Generalization of the concept of resistivity
Resistivity can also be determined for an inhomogeneous material whose properties vary from point to point. In this case, it is not a constant, but a scalar function of coordinates - a coefficient linking the electric field strength E → (r →) (\\ displaystyle (\\ vec (E)) ((\\ vec (r)))) and current density J → (r →) (\\ displaystyle (\\ vec (J)) ((\\ vec (r)))) at this point r → (\\ displaystyle (\\ vec (r)))... The specified relationship is expressed by Ohm's law in differential form:
E → (r →) \u003d ρ (r →) J → (r →). (\\ displaystyle (\\ vec (E)) ((\\ vec (r))) \u003d \\ rho ((\\ vec (r))) (\\ vec (J)) ((\\ vec (r))).)This formula is valid for an inhomogeneous but isotropic substance. A substance can also be anisotropic (most crystals, magnetized plasma, etc.), that is, its properties can depend on direction. In this case, the resistivity is a coordinate-dependent second-rank tensor containing nine components. In an anisotropic substance, the vectors of current density and electric field strength at each given point of the substance are not codirectional; the connection between them is expressed by the ratio
E i (r →) \u003d ∑ j \u003d 1 3 ρ i j (r →) J j (r →). (\\ displaystyle E_ (i) ((\\ vec (r))) \u003d \\ sum _ (j \u003d 1) ^ (3) \\ rho _ (ij) ((\\ vec (r))) J_ (j) (( \\ vec (r))).)In an anisotropic but homogeneous substance, the tensor ρ i j (\\ displaystyle \\ rho _ (ij)) does not depend on coordinates.
Tensor ρ i j (\\ displaystyle \\ rho _ (ij)) symmetrical, that is, for any i (\\ displaystyle i) and j (\\ displaystyle j) performed ρ i j \u003d ρ j i (\\ displaystyle \\ rho _ (ij) \u003d \\ rho _ (ji)).
As for any symmetric tensor, for ρ i j (\\ displaystyle \\ rho _ (ij)) you can choose an orthogonal Cartesian coordinate system in which the matrix ρ i j (\\ displaystyle \\ rho _ (ij)) becomes diagonal, that is, it takes the form in which of the nine components ρ i j (\\ displaystyle \\ rho _ (ij)) only three are nonzero: ρ 11 (\\ displaystyle \\ rho _ (11)), ρ 22 (\\ displaystyle \\ rho _ (22)) and ρ 33 (\\ displaystyle \\ rho _ (33))... In this case, denoting ρ i i (\\ displaystyle \\ rho _ (ii)) how, instead of the previous formula, we get a simpler
E i \u003d ρ i J i. (\\ displaystyle E_ (i) \u003d \\ rho _ (i) J_ (i).)The quantities ρ i (\\ displaystyle \\ rho _ (i)) called main values resistivity tensor.
Relation to conductivity
In isotropic materials, the relationship between resistivity ρ (\\ displaystyle \\ rho) and conductivity σ (\\ displaystyle \\ sigma) expressed by equality
ρ \u003d 1 σ. (\\ displaystyle \\ rho \u003d (\\ frac (1) (\\ sigma)).)In the case of anisotropic materials, the relationship between the components of the resistivity tensor ρ i j (\\ displaystyle \\ rho _ (ij)) and the conductivity tensor is more complex. Indeed, Ohm's law in differential form for anisotropic materials is:
J i (r →) \u003d ∑ j \u003d 1 3 σ i j (r →) E j (r →). (\\ displaystyle J_ (i) ((\\ vec (r))) \u003d \\ sum _ (j \u003d 1) ^ (3) \\ sigma _ (ij) ((\\ vec (r))) E_ (j) (( \\ vec (r))).)From this equality and the previously given relation for E i (r →) (\\ displaystyle E_ (i) ((\\ vec (r)))) it follows that the resistivity tensor is the reciprocal of the conductivity tensor. With this in mind, for the components of the resistivity tensor, the following is performed:
ρ 11 \u003d 1 det (σ) [σ 22 σ 33 - σ 23 σ 32], (\\ displaystyle \\ rho _ (11) \u003d (\\ frac (1) (\\ det (\\ sigma))) [\\ sigma _ ( 22) \\ sigma _ (33) - \\ sigma _ (23) \\ sigma _ (32)],) ρ 12 \u003d 1 det (σ) [σ 33 σ 12 - σ 13 σ 32], (\\ displaystyle \\ rho _ (12) \u003d (\\ frac (1) (\\ det (\\ sigma))) [\\ sigma _ ( 33) \\ sigma _ (12) - \\ sigma _ (13) \\ sigma _ (32)],)where det (σ) (\\ displaystyle \\ det (\\ sigma)) - determinant of a matrix composed of tensor components σ i j (\\ displaystyle \\ sigma _ (ij))... The remaining components of the resistivity tensor are obtained from the above equations as a result of the cyclic permutation of the indices 1 , 2 and 3 .
Specific electrical resistance of some substances
Metallic single crystals
The table shows the main values \u200b\u200bof the resistivity tensor of single crystals at a temperature of 20 ° C.
Crystal ρ 1 \u003d ρ 2, 10 −8 Ohm m ρ 3, 10 −8 Ohm · m Tin 9,9 14,3 Bismuth 109 138 Cadmium 6,8 8,3 Zinc 5,91 6,13 When an electric circuit is closed, at the terminals of which there is a potential difference, an electric current arises. Free electrons under the influence of electric field forces move along the conductor. In their motion, the electrons collide with the atoms of the conductor and give them a supply of their kinetic energy. The speed of movement of electrons is constantly changing: when electrons collide with atoms, molecules and other electrons, it decreases, then under the action of an electric field it increases and again decreases with a new collision. As a result, a uniform motion of the electron flow 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 an electric current passes through a conductor, the latter heats up.
Electrical resistance
The electrical resistance of the conductor, which is indicated by a Latin letter r, is called the property of a body or medium to convert electrical energy into heat when an electric current passes through it.
In the diagrams, the electrical resistance is indicated as shown in Figure 1, and.
Variable electrical resistance, which serves to change the current in the circuit, is called rheostat... In the diagrams, rheostats are indicated 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 lever of the rheostat is placed in a certain position, as a result of which the required resistance is introduced into the circuit.
A long conductor of small cross-section creates a high current resistance. Short conductors with a large cross-section have little resistance to current.
If you take two conductors of different materials, but of the same length and cross-section, then the conductors will conduct current in different ways. This shows that the resistance of a conductor depends on the material of the conductor itself.
The temperature of a conductor also affects its resistance. As the temperature rises, the resistance of metals increases, while the resistance of liquids and coal decreases. Only some special metal alloys (manganin, konstaitan, nickelin, and others) hardly change their resistance with an increase in temperature.
So, we see that the electrical resistance of the conductor depends on: 1) the length of the conductor, 2) the cross-section of the conductor, 3) the material of the conductor, 4) the temperature of the conductor.
One Ohm is taken as a unit of resistance. Om is often indicated by the Greek capital letter Ω (omega). Therefore, instead of writing "Conductor resistance is 15 ohms", you can write simply: r \u003d 15 Ω.
1000 Ohm is called 1 kilo (1kΩ, or 1kΩ),
1,000,000 Ohm is called 1 megaohm (1mgΩ, or 1MΩ).When comparing the resistance of conductors from different materials, it is necessary to take a certain length and section for each sample. Then we will be able to judge which material conducts electric current better or worse.
Video 1. Resistance of conductors
Specific electrical resistance
The resistance in ohms of a conductor 1 m long, with a cross section of 1 mm² is called resistivity and is denoted by the Greek letter ρ (ro).
Table 1 shows the specific resistances of some conductors.
Table 1
Resistivity of various conductors
The table shows that an iron wire with a length of 1 m and a cross-section of 1 mm² has a resistance of 0.13 ohms. To get 1 Ohm of resistance, you need to take 7.7 m of such a wire. Silver has the lowest specific resistance. 1 Ohm of resistance can be obtained by taking 62.5 m of silver wire with a cross section of 1 mm². Silver is the best conductor, but the cost of silver precludes its 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 a wire.
Chemically pure, obtained by refining, copper has found widespread use in electrical engineering for the manufacture of wires, cables, windings of electrical machines and devices. Aluminum and iron are also widely used as conductors.
Conductor resistance can be determined by the formula:
where r - conductor resistance in ohms; ρ - the 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 resistance of 30 Ohm from nickelin 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 a conductor characterizes its resistivity.
According to the table of specific resistances, we find that lead has such resistance.
It was stated above that the resistance of the conductors depends on the temperature. Let's do the following experiment. We will wind several meters of thin metal wire in the form of a spiral and include this spiral in the battery circuit. To measure the current in the circuit, turn on the ammeter. When the coil is heated in the burner flame, you will notice that the ammeter reading will decrease. This shows that the resistance of the metal wire increases with heating.
For some metals, when heated to 100 °, the resistance increases by 40 - 50%. There are alloys that change their resistance slightly with heating. Some special alloys practically do not change the resistance when the temperature changes. The resistance of metal conductors increases with increasing temperature, the resistance of electrolytes (liquid conductors), coal and some solids, on the contrary, decreases.
The ability of metals to change their resistance with changing temperature is used to design resistance thermometers. Such a thermometer is a platinum wire wound on a mica frame. By placing a thermometer in an oven, for example, and measuring the resistance of the platinum wire before and after heating, the oven temperature can be determined.
The change in the resistance of a conductor when it is heated, per 1 Ohm of the initial resistance and 1 ° of temperature, is called temperature coefficient of resistance and denoted by the letter α.
If at temperature t 0 conductor resistance is r 0, and at a temperature t equally r t, then the temperature coefficient of resistance
Note. This formula can only be calculated within a certain temperature range (up to about 200 ° C).
We give the values \u200b\u200bof the temperature coefficient of resistance α for some metals (table 2).
table 2
Temperature coefficient values \u200b\u200bfor 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 \u003d 100 (1 + 0.0066 × 200) \u003d 232 ohms.
Example 7. A resistance thermometer made of platinum wire had a resistance of 20 ohms in a room with a temperature of 15 ° C. The thermometer was placed in an oven and after a while its resistance was measured. It turned out to be equal to 29.6 ohms. Determine the oven temperature.
Electrical conductivity
So far, we have considered the resistance of a conductor as an obstacle that a conductor exerts on electric current. But still the current passes through the conductor. Therefore, in addition to resistance (obstacles), the conductor also has the ability to conduct electric current, that is, conductivity.
The more resistance a conductor has, the less conductivity it has, the worse it conducts electric current, and, conversely, the lower the resistance of the conductor, the more conductivity it has, the easier it is for the current to pass through the conductor. Therefore, the resistance and conductivity of the conductor are inverse quantities.
It is known from mathematics that the inverse of 5 is 1/5 and, conversely, the inverse of 1/7 is 7. Therefore, if the resistance of the conductor is denoted by the letter r, then the conductivity is defined as 1 / r... Usually conductivity is indicated by the letter g.
Electrical conductivity is measured in (1 / Ohm) or siemens.
Example 8. Conductor resistance is 20 ohms. Determine its conductivity.
If r \u003d 20 Ohm, then
Example 9. The conductivity of the conductor is 0.1 (1 / ohm). Determine his resistance,
If g \u003d 0.1 (1 / Ohm), then r \u003d 1 / 0.1 \u003d 10 (Ohm)
- active - or ohmic, resistive - resulting from the consumption of electricity for heating a conductor (metal) when an electric current passes through it, and
- reactive - capacitive or inductive, - which comes 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 is of two types:
Resistivity of popular conductors (metals and alloys). Steel resistivity
Resistivity of iron, aluminum and other conductors
The transmission of electricity over long distances requires taking care of minimizing losses resulting from the current overcoming the resistance of the conductors that make up the electric line. Of course, this does not mean that such losses, already occurring 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 most productive, that is, with high efficiency, to bring energy to the consumer, both the economy 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 the location 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 chosen for each structural element. , its work and operating costs. In addition, in the lines that transmit electricity, the requirements for ensuring the safety of both the lines themselves and the entire environment where they pass are higher. And this adds costs to both the provision of electricity wiring and an additional margin of safety for all structures.
For comparison, the data are usually reduced to a single, comparable form. Often, the epithet "specific" is added to such characteristics, and the values \u200b\u200bthemselves are considered on some standards unified in terms of physical parameters. For example, electrical resistivity is the resistance (ohm) of a conductor made of some kind of metal (copper, aluminum, steel, tungsten, gold) that has a unit length and a unit cross-section in the system of units used (usually in SI). In addition, the temperature is negotiated, since when heated, the resistance of the conductors can behave differently. It is based on normal average operating conditions - at 20 degrees Celsius. And where properties are important when changing the parameters of the medium (temperature, pressure), coefficients are introduced and additional tables and graphs of dependences are drawn up.
Resistivity types
Since resistance happens:
- Specific electrical resistance to direct current (having a resistive character) and
- Specific electrical resistance to alternating current (having a reactive character).
Here, type 2 resistivity is a complex value, it consists of two TP 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, which are associated with the inclusion of current (current change from 0 to nominal) or off (drop from nominal to 0). And they are usually taken into account only when designing overload protection.
In alternating current circuits, the phenomena associated with reactances are much more diverse. They depend not only on the actual passage of the current through a certain section, but also on the shape of the conductor, and the dependence is not linear.
The fact is that the 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 depth of the entire 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 layer close to the surface, the rest of the conductor thickness remains unused, it does not reduce its resistance, and there is simply no point in increasing the conductor thickness. Especially at high frequencies. Therefore, for alternating current, resistances are measured in such conductor cross-sections, where its entire cross-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, the effective conduction of alternating current is not exhausted by the reduction in the thickness of the wires that are round in cross-section. The conductor can be thinned, but at the same time make it flat in the form of a tape, then the cross section will be higher than that of a round wire, respectively, and the resistance is lower. In addition, simply increasing the surface area will have the effect of increasing the effective section. The same can be achieved by using a stranded wire instead of a single-core one, moreover, a multi-core wire is superior in flexibility to a single-core wire, which is often also valuable. On the other hand, taking into account the skin effect in the wires, it is possible to make the wires composite by making the core of a metal with good strength characteristics, such as steel, but low electrical. At the same time, an aluminum braid is made over the steel, which has a lower specific resistance.
In addition to the skin effect, the flow of alternating current in conductors is affected by the excitation of eddy currents in the 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 conducting complex - playing the role of wires of other phases, zero, grounding.
All of these phenomena are found in all structures associated with electricity, this further enhances the importance of having at your disposal a summary of reference information on a variety of materials.
The resistivity for conductors is measured with very sensitive and accurate instruments, since metals with the lowest resistance are selected for wiring - of the order of ohms * 10-6 per meter of length and sq. mm. section. To measure the specific resistance of insulation, devices are needed, on the contrary, having ranges of very high resistance values \u200b\u200b- usually megohms. It is clear that conductors must conduct well, and insulators must be well insulated.
Table
Iron as a conductor in electrical engineering
Iron is the most widespread 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 due to the appropriate cross section.
Having a table of specific resistances 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, nickelin and iron wire. For the original, we take an aluminum wire with a cross section of 2.5 mm.
We need the resistance of the wire made of all these metals to be equal to the resistance of the original one over a length of 1 m. The resistance of aluminum per 1 m of length and 2.5 mm of section will be equal
, where R is the resistance, ρ is the resistivity of the metal from the table, S is the sectional area, L is the length.Substituting the initial values, we get the resistance of a meter piece of aluminum wire in ohms.
After that we solve the formula for S
, we will substitute the values \u200b\u200bfrom 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 micro-ohms per 1 mm2 of cross-section, we got it in micro-ohms. To get it in ohms, you need to multiply the value by 10-6. But the number of ohms with 6 zeros after the decimal point is not at all necessary for us, since the final result is still found in mm2.
As you can see, the resistance of iron is large enough, the wire is thick.
But there are materials that have even more of it, for example, nickeline or constantan.
Similar articles:
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Table of electrical resistivity of metals and alloys in electrical engineering
Home\u003e y\u003e
Resistivity of metals.
Resistivity of alloys.
The values \u200b\u200bare given at t \u003d 20 ° C. The resistances of the alloys depend on their exact composition. Comments powered by HyperCommentstab.wikimassa.org
Specific electrical resistance | The world of welding
Specific electrical resistance of materials
Specific electrical resistance (specific resistance) - the ability of a substance to prevent the passage of electric current.
Measurement unit (SI) - Ohm m; also measured in Ohm cm and Ohm mm2 / m.
Material Temperature, ° С Specific electrical resistance, Ohm m Metals Aluminum 20 0.028 10-6 Beryllium 20 0.036 10-6 Phosphorous 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 Glass fiber laminate 20 1011–1012 Textolite 20 107–1010 Celluloid 20 109 Ebonite 20 1012–1014 Rubber 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 guide / Tallinn: Printtest, 1991 - 448 p.
- Handbook of elementary physics / N.N. Koshkin, M.G. Shirkevich. M., Science. 1976.256 s.
- Reference book on welding of non-ferrous metals / S.M. Gurevich. Kiev .: Naukova Dumka. 1990.512 s.
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Resistivity of metals, electrolytes and substances (Table)
Resistivity of metals and insulators
The reference table gives the values \u200b\u200bof the resistivity p of some metals and insulators at a temperature of 18-20 ° C, expressed in ohm cm. The value of p for metals is highly dependent on impurities, the table gives the values \u200b\u200bof p for chemically pure metals, for insulators they are given approximately. Metals and insulators are listed in the table in order of increasing p values.
Resistivity table of metals
Pure metals
104 ρ (ohm cm)
Pure metals
104 ρ (ohm cm)
Aluminum
Duralumin
Platinum 2)
Argentan
Manganese
Manganin
Tungsten
Constantan
Molybdenum
Wood alloy 3)
Alloy Rose 4)
Palladium
Fechral 6)
Resistivity table 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 values \u200b\u200bof the resistivity (in ohm cm) of some pure metals at low temperatures (0 ° C).
The ratio of resistance 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
Tungsten
Molybdenum
Resistivity of electrolytes
The table gives the values \u200b\u200bof the specific resistance of electrolytes in ohm · cm at a temperature of 18 ° C. The concentration of solutions with is given in percent, which determine the number of grams of anhydrous salt or acid in 100 g of solution.
Source of information: A BRIEF PHYSICAL AND TECHNICAL REFERENCE / Volume 1, - M .: 1960.
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Specific electrical resistance - steel
Page 1
The electrical resistivity of steel increases with increasing temperature, and the greatest changes are observed when heated to the Curie point temperature. After the Curie point, the resistivity value changes insignificantly and at temperatures above 1000 C is practically constant.
Due to the high electrical resistivity of the steel, these iuKii create a HcO large slowdown in the decay of the flux. For 100 A contactors the dropout time is 0 07 sec, and for 600 A-0 contactors it is 23 sec. Due to the special requirements for contactors of the KMV series, which are designed to turn on and off the electromagnets of the drives of oil switches, 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 tear-off spring. Contactors of the KMV type must operate with a deep voltage dip. Therefore, the minimum pick-up voltage of these contactors can drop down to 65% UH. This low pick-up voltage causes a current to flow through the winding at rated voltage, causing the coil to heat up.
The addition of silicon increases the electrical resistivity of the steel almost proportionally to the silicon content and thereby helps to reduce the eddy current losses that arise in the steel when it is operated in an alternating magnetic field.
The addition of silicon increases the electrical resistivity of the steel, which helps to reduce eddy current losses, but at the same time silicon impairs the mechanical properties of the steel and 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 CM-19 alloy. The specific electrical resistance of steel differs little from the specific resistance of the alloy, and the cg of steel is about an order of magnitude higher. The thickness of the screen is chosen according to the penetration depth of the first-order tooth harmonics and is equal to d e 0 8 mm. For comparison, additional losses, W, are given for a basic squirrel-cage rotor and a two-layer rotor with a massive cylinder made of CM-19 alloy and with copper end rings.
The main magnetically conductive material is alloyed electrical steel sheet containing from 2 to 5% silicon. The addition of silicon increases the electrical resistivity of the steel, as a result of which eddy current losses are reduced, the steel becomes resistant to oxidation and aging, but becomes more brittle. In recent years, cold rolled grain steel with higher magnetic properties in the rolling direction has been widely used. To reduce losses from eddy currents, the core of the magnetic circuit is made in the form of a package assembled from sheets of stamped steel.
Electrical steel is a low carbon steel. To improve the magnetic characteristics, silicon is introduced into it, which causes an increase in the specific electrical resistance of the steel. This leads to a decrease in eddy current losses.
After machining, the magnetic core is annealed. Since eddy currents in steel participate in the creation of deceleration, one should focus on the value of the specific electrical resistance of steel of the order of Pc (10 -15) 10 - 6 ohm cm.In the attracted position of the armature, the magnetic system is quite saturated, therefore the initial induction in various magnetic systems fluctuates within very insignificant limits and is for steel grade E VN1 6 - 1 7 hl. The indicated induction value maintains the field strength in steel on the order of Yang.
For the manufacture of magnetic systems (magnetic cores) of transformers, special thin-sheet electrical steels are used, which have an increased (up to 5%) silicon content. Silicon contributes to the decarburization of steel, which leads to an increase in magnetic permeability, decreases hysteresis losses and increases its electrical resistivity. An increase in the electrical resistivity of steel makes it possible to reduce losses in it from eddy currents. In addition, silicon weakens the aging of steel (an increase in losses in steel over time), reduces its magnetostriction (changes in the shape and size of the body during magnetization) and, consequently, the noise of transformers. At the same time, the presence of silicon in steel leads to an increase in its brittleness and complicates its mechanical processing.
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Resistivity | Wikitronic Wiki
Resistivity is a characteristic of a material that determines its ability to conduct electric current. It is defined as the ratio of the electric field to the current density. In the general case, it is a tensor; however, for most materials that do not exhibit anisotropic properties, it is assumed to be a scalar value.
Designation - ρ
$ \\ vec E \u003d \\ rho \\ vec j, $
$ \\ vec E $ is the electric field strength, $ \\ vec j $ is the current density.
The SI unit of measurement is ohm-meter (ohm m, Ω m).
The resistance of a cylinder or prism (between the ends) made of material with a length l, and a section S in terms of resistivity is determined as follows:
$ R \u003d \\ frac (\\ rho l) (S). $
In technology, the definition of resistivity is used as the resistance of a conductor of a single cross-section and a single length.
Resistivity of some materials used in electrical engineering Edit
Material ρ at 300 K, Ohm m TCR, 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 tin white 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 distilled water 5 · 10³ ebonite 10⁸ hard paper 10¹⁰ transformer oil 10¹¹ ordinary glass 5 10¹¹ polyvinyl 10¹² porcelain 10¹² wood 10¹² PTFE (Teflon) \u003e 10¹³ rubber 5 · 10¹³ quartz glass 10¹⁴ waxed paper 10¹⁴ polystyrene \u003e 10¹⁴ mica 5 10¹⁴ paraffin 10¹⁵ polyethylene 3 10¹⁵ acrylic resin 10¹⁹ ru.electronics.wikia.com
Specific electrical resistance | formula, volumetric, table
Resistivity is a physical quantity that indicates the degree to which a material can resist the passage of an electric current through it. Some people may confuse this characteristic with ordinary electrical resistance. Despite the similarity of the concepts, the difference between them lies in the fact that the specific refers to substances, and the second term refers exclusively to conductors and depends on the material of their manufacture.
The reciprocal of a given material is electrical conductivity. The higher this parameter, the better the current passes through the substance. Accordingly, the higher the resistance, the more losses are expected at the output.
Calculation formula and measurement value
Considering what the specific electrical resistance is measured in, it is also possible to trace the connection with the non-specific, since the units of Ohm m are used to designate the parameter. The quantity itself is denoted as ρ. With this value, you can 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 options can also be found. In technology, you can periodically see the outdated designation Ohm · mm2 / m. To transfer from this system to the international one, you will not need to use complex formulas, since 1 Ohm · mm2 / m is equal to 10-6 Ohm · m.
The resistivity formula is as follows:
R \u003d (ρ l) / S, where:
- R is the resistance of the conductor;
- Ρ - material resistivity;
- l is the length of the conductor;
- S - conductor cross-section.
Temperature dependence
Resistivity is temperature dependent. But all groups of substances manifest themselves in different ways when it changes. This must be taken into account when calculating the wires that will work in certain conditions. For example, outdoors, where the temperature values \u200b\u200bdepend on the season, the required materials are less susceptible to changes in the range from -30 to +30 degrees Celsius. If you plan to use it in a technique that will work in the same conditions, then here you also need to optimize the wiring for specific parameters. The material is always selected taking into account the operation.
In the nominal table, electrical resistivity is taken at a temperature of 0 degrees Celsius. An 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. Carriers of electric charges are chaotically scattered in all directions, which leads to the creation of obstacles in the movement of particles. The magnitude of the electric flux decreases.
As the temperature decreases, the conditions for the passage of current become better. When a certain temperature is reached, which will differ for each metal, superconductivity appears, at which the considered characteristic almost reaches zero.
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 generally not applicable for electrical engineering if they have a high value of this parameter. Other properties can interfere with this. For example, the specific electrical conductivity of water will not matter much for a given area. Here are the values \u200b\u200bof some substances with high values.
High resistivity materials ρ (Ohm m) Bakelite 1016 Benzene 1015...1016 Paper 1015 Distilled water 104 Sea water 0.3 Dry wood 1012 The earth is wet 102 Quartz glass 1016 Kerosene 1011 Marble 108 Paraffin 1015 Paraffin oil 1014 Plexiglass 1013 Polystyrene 1016 PVC 1013 Polyethylene 1012 Silicone oil 1013 Mica 1014 Glass 1011 Transformer oil 1010 Porcelain 1014 Slate 1014 Ebonite 1016 Amber 1018 Substances with low rates are more actively used in electrical engineering. Often these are metals that serve as conductors. There are also many differences in them. To find out the electrical resistivity of copper or other materials, look 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 Nickelin 0.4 10-6 Specific volumetric electrical resistance
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, the product from which will be included in the electrical circuit. It is supplied with rated current. After passing, the output data is measured.
Use in electrical engineering
Changing the parameter at different temperatures is widely used in electrical engineering. The simplest example is an incandescent lamp using a nichrome filament. When heated, it starts to glow. When a current passes through it, it begins to heat up. As heating increases, so does the resistance. Accordingly, the initial current that was needed to obtain illumination is limited. The nichrome spiral, using the same principle, can become a regulator on various devices.
Precious metals have also been widely used, which have suitable characteristics for electrical engineering. For critical circuits that require performance, silver contacts are selected. They have a high cost, but given the relatively small amount of materials, their use is quite justified. Copper is inferior to silver in conductivity, but has a more affordable price, which makes it more often used to create wires.
In conditions where extremely low temperatures can be used, superconductors are used. For room temperature and outdoor use, they are not always appropriate, since as the temperature rises, their conductivity will begin to drop, therefore, for such conditions, aluminum, copper and silver remain the leaders.
In practice, many parameters are taken into account and this one is one of the most important. All calculations are carried out at the design stage, for which reference materials are used.
Electric current arises as a result of closing a circuit with a potential difference at the terminals. The field forces act on free electrons and they move along the conductor. During this journey, electrons meet with atoms and transfer to them part of their accumulated energy. As a result, their speed decreases. But, due to the influence of the electric field, it is gaining momentum again. Thus, electrons constantly experience resistance, which is why the electric current heats up.
The property of a substance, to convert electricity into heat during exposure to current, is electrical resistance and is denoted as R, its measuring unit is Ohm. The amount of resistance depends mainly on the ability of various materials to conduct current.
For the first time, the German researcher G. Ohm stated about resistance.In order to find out the dependence of the current strength on resistance, the famous physicist conducted many experiments. For the experiments, he used various conductors and received different indicators.
The first thing that G. Ohm determined is that the resistivity depends on the length of the conductor. That is, if the length of the conductor increased, the resistance also increased. As a result, this relationship was determined to be directly proportional.The second relationship is the cross-sectional area. It could be determined by cross-cutting the conductor. The area of \u200b\u200bthe figure that formed on the cut is the cross-sectional area. Here the relationship is inversely proportional. That is, the larger the cross-sectional area, the less the conductor resistance becomes.
And the third, important quantity on which the resistance depends is the material. As a result of the fact that Ohm used different materials in experiments, he discovered different properties of resistance. All these experiments and indicators were summarized in a table from which you can see the different values \u200b\u200bof the specific resistance of various substances.
It is known that the best conductors are metals. Which metals are the best conductors? The table shows that copper and silver have the least resistance. Copper is used more often because of its lower cost, and silver is used in the most important and critical devices.
Substances with high resistivity in the table do not conduct electric current well, which means they can be excellent insulating materials. Substances with this property to the greatest extent are porcelain and ebonite.
In general, electrical resistivity is a very important factor, because, having determined its indicator, we can find out from what substance the conductor is made. To do this, you need to measure the cross-sectional area, find out the current strength using a voltmeter and ammeter, and measure the voltage. Thus, we find out the value of resistivity and, using the table, we can easily go to the substance. It turns out that resistivity is a kind of fingerprint substance. In addition, resistivity is important when planning long electrical circuits: we need to know this indicator in order to maintain a balance between length and area.
There is a formula that determines that the resistance is 1 Ohm, if at a voltage of 1V, its current strength is 1A. That is, the resistance of a unit area and unit length made from a certain substance is the resistivity.
It should also be noted that the resistivity index directly depends on the frequency of the substance. That is, whether it has impurities. That, the addition of only one percent of manganese increases the resistance of the conductive substance itself - copper, three times.
This table shows the resistivity of some substances.
Highly conductive materialsCopper
As we said, copper is most often used as a conductor. This is due not only to its low resistance. Copper has advantages such as high strength, corrosion resistance, ease of use, and good machinability. Good grades of copper are M0 and M1. The amount of impurities in them does not exceed 0.1%.The high cost of metal and its prevailing scarcity in recent years prompts manufacturers to use aluminum as a conductor. Also, copper alloys with various metals are used.
Aluminum
This metal is much lighter than copper, but aluminum has a high heat capacity and melting point. In this regard, in order to bring it to a molten state, more energy is required than copper. Nevertheless, one must take into account the fact of copper deficiency.
In the production of electrical products, as a rule, aluminum grade A1 is used. It contains no more than 0.5% impurities. And the metal of the highest frequency is AB0000 aluminum.
Iron
The cheapness and availability of iron is overshadowed by its high resistivity. Moreover, it corrodes quickly. For this reason, steel conductors are often zinc plated. The so-called bimetal is widely used - it is steel covered with copper for protection.
Sodium
Sodium is also an affordable and promising material, but its resistance is almost three times that of copper. In addition, metallic sodium has a high chemical activity, which obliges to cover such a conductor with a hermetic protection. It should also protect the conductor from mechanical damage, since sodium is a very soft and rather fragile material.Superconductivity
The table below shows the specific resistance of substances at a temperature of 20 degrees. The indication of the temperature is not accidental, because the resistivity directly depends on this indicator. This is due to the fact that when heated, the speed of atoms also increases, which means that the probability of meeting them with electrons will also increase.
I wonder what happens to the resistance under cooling conditions. The behavior of atoms at very low temperatures was first noticed by G. Kamerling-Onnes in 1911. He cooled the mercury wire to 4K and found its resistance to drop to zero. The change in the resistivity index of some alloys and metals at low temperatures, the physicist called superconductivity.Superconductors pass into a state of superconductivity upon cooling, and their optical and structural characteristics do not change. The main discovery is that the electrical and magnetic properties of metals in a superconducting state are very different from their own properties in the ordinary state, as well as from the properties of other metals, which cannot pass into this state with decreasing temperature.
The use of superconductors is carried out mainly in obtaining a superstrong magnetic field, the strength of which reaches 107 A / m. Superconducting power line systems are also being developed.Similar materials.