- Constantan (58.8 Cu, 40 Ni, 1.2 Mn)
- Manganin (85 Cu, 12 Mn, 3 Ni)
- Nickel silver (65 Cu, 20 Zn, 15 Ni)
- Nickelin (54 Cu, 20 Zn, 26 Ni)
- Nichrome (67.5 Ni, 15 Cr, 16 Fe, 1.5 Mn)
- Rheonate (84Cu, 12Mn, 4 Zn)
- Fechral (80 Fe, 14 Cr, 6 Al)
Nichrome resistivity
Every body through which an electric current is passed automatically exhibits a certain resistance to it. The property of a conductor to resist electric current is called electrical resistance.
Let's consider the electronic theory of this phenomenon. When moving along a conductor, free electrons constantly encounter other electrons and atoms on their way. By interacting with them, a free electron loses part of its charge. Thus, the electrons encounter resistance from the conductor material. Each body has its own atomic structure, which provides different resistance to electric current. The unit of resistance is considered to be Ohm. The resistance of materials is designated R or r.
The lower the resistance of the conductor, the easier it is for electric current to pass through this body. And vice versa: the higher the resistance, the worse body conducts electric current.
The resistance of each individual conductor depends on the properties of the material from which it is made. For precise characteristics The concept of resistivity (nichrome, aluminum, etc.) was introduced to determine the electrical resistance of a particular material. Specific resistance is considered to be the resistance of a conductor up to 1 m long, the cross-section of which is 1 square meter. mm. This indicator is denoted by the letter p. Each material used in the production of a conductor has its own resistivity. For example, consider the resistivity of nichrome and fechral (more than 3 mm):
- Х15Н60 — 1.13 Ohm*mm/m
- Х23У5Т — 1.39 Ohm*mm/m
- Х20Н80 — 1.12 Ohm*mm/m
- ХН70У — 1.30 Ohm*mm/m
- ХН20УС — 1.02 Ohm*mm/m
Resistivity nichrome, fehrali indicates the main scope of their application: the manufacture of devices thermal action, household appliances and electro heating elements industrial furnaces.
Since nichrome and fechral are mainly used in the production of heating elements, the most common products are nichrome thread, tape, strip X15N60 and X20N80, as well as fechral wire X23Yu5T.
Resistivity is an applied concept in electrical engineering. It denotes how much resistance per unit length a material of a unit cross-section has to the current flowing through it - in other words, what resistance a wire of a millimeter cross-section one meter long has. This concept is used in various electrical calculations.
It is important to understand the differences between DC electrical resistivity and AC electrical resistivity. In the first case, resistance is caused solely by action direct current to the conductor. In the second case alternating current(it can be of any shape: sinusoidal, rectangular, triangular or arbitrary) causes an additional vortex field in the conductor, which also creates resistance.
Physical representation
In technical calculations involving the laying of cables of various diameters, parameters are used to calculate the required cable length and its electrical characteristics. One of the main parameters is resistivity. Electrical resistivity formula:
ρ = R * S / l, where:
- ρ is the resistivity of the material;
- R is the ohmic electrical resistance of a particular conductor;
- S - cross section;
- l - length.
The dimension ρ is measured in Ohm mm 2 /m, or, to abbreviate the formula - Ohm m.
The value of ρ for the same substance is always the same. Therefore, this is a constant characterizing the material of the conductor. It is usually indicated in directories. Based on this, it is already possible to calculate technical quantities.
It is important to say about specific electrical conductivity. This value is the inverse of the resistivity of the material, and is used equally with it. It is also called electrical conductivity. The higher this value, the metal is better conducts current. For example, the conductivity of copper is 58.14 m/(Ohm mm2). Or, in SI units: 58,140,000 S/m. (Siemens per meter is the SI unit of electrical conductivity).
We can talk about resistivity only in the presence of elements that conduct current, since dielectrics have infinite or close to infinite electrical resistance. In contrast, metals are very good conductors of current. You can measure the electrical resistance of a metal conductor using a milliohmmeter, or an even more accurate microohmmeter. The value is measured between their probes applied to the conductor section. They allow you to check circuits, wiring, windings of motors and generators.
Metals vary in their ability to conduct current. Resistivity various metals- a parameter characterizing this difference. The data is given at a material temperature of 20 degrees Celsius:
The parameter ρ shows what resistance a meter conductor with a cross section of 1 mm 2 will have. The higher this value, the greater the electrical resistance will be. the right wire a certain length. The smallest ρ, as can be seen from the list, is silver; the resistance of one meter of this material will be equal to only 0.015 Ohms, but this is too expensive a metal to use on an industrial scale. Next comes copper, which is much more common in nature (not a precious metal, but a non-ferrous metal). Therefore, copper wiring is very common.
Copper is not only good guide electric current, but also a very plastic material. Thanks to this property, copper wiring fits better and is resistant to bending and stretching.
Copper is in great demand on the market. Many different products are made from this material:
- A huge variety of conductors;
- Auto parts (eg radiators);
- Clock mechanisms;
- Computer components;
- Parts of electrical and electronic devices.
Specific electrical resistance Copper is one of the best conductive materials, so many electrical industry products are created on its basis. In addition, copper is easy to solder, so it is very common in amateur radio.
The high thermal conductivity of copper allows it to be used in cooling and heating devices, and its plasticity makes it possible to create the smallest parts and the thinnest conductors.
Conductors of electric current are of the first and second kind. Conductors of the first kind are metals. Conductors of the second type are conductive solutions of liquids. The current in the first type is carried by electrons, and the current carriers in conductors of the second type are ions, charged particles of the electrolytic liquid.
We can talk about the conductivity of materials only in the context of temperature environment. With more high temperature conductors of the first type increase their electrical resistance, and the second, on the contrary, decrease. Accordingly, there is a temperature coefficient of resistance of materials. The resistivity of copper Ohm m increases with increasing heating. The temperature coefficient α also depends only on the material; this value has no dimension and for different metals and alloys is equal to the following indicators:
- Silver - 0.0035;
- Iron - 0.0066;
- Platinum - 0.0032;
- Copper - 0.0040;
- Tungsten - 0.0045;
- Mercury - 0.0090;
- Constantan - 0.000005;
- Nickelin - 0.0003;
- Nichrome - 0.00016.
Determination of the electrical resistance value of a conductor section at elevated temperature R (t) is calculated using the formula:
R (t) = R (0) · , where:
- R (0) - resistance at initial temperature;
- α - temperature coefficient;
- t - t (0) - temperature difference.
For example, knowing the electrical resistance of copper at 20 degrees Celsius, you can calculate what it will be equal to at 170 degrees, that is, when heated by 150 degrees. The initial resistance will increase by a factor of 1.6.
As the temperature increases, the conductivity of materials, on the contrary, decreases. Since this is the reciprocal of electrical resistance, it decreases by exactly the same amount. For example, the electrical conductivity of copper when the material is heated by 150 degrees will decrease by 1.6 times.
There are alloys that practically do not change their electrical resistance when temperature changes. This is, for example, constantan. When the temperature changes by one hundred degrees, its resistance increases by only 0.5%.
While the conductivity of materials deteriorates with heat, it improves with decreasing temperature. This is related to the phenomenon of superconductivity. If you lower the temperature of the conductor below -253 degrees Celsius, its electrical resistance will sharply decrease: almost to zero. In this regard, the costs of transmitting electrical energy are falling. The only problem was cooling the conductors to such temperatures. However, due to the recent discoveries of high-temperature superconductors based on copper oxides, materials have to be cooled to acceptable values.
It has been experimentally established that resistance R metal conductor is directly proportional to its length L and inversely proportional to its cross-sectional area A:
R = ρ L/ A (26.4)
where is the coefficient ρ is called resistivity and serves as a characteristic of the substance from which the conductor is made. This is common sense: a thick wire should have less resistance than a thin wire because electrons can move over a larger area in a thick wire. And we can expect an increase in resistance with increasing length of the conductor, as the number of obstacles to the flow of electrons increases.
Typical values ρ for different materials are given in the first column of the table. 26.2. (Actual values depend on the purity of the substance, heat treatment, temperature and other factors.)
|
Table 26.2. Specific resistance and temperature coefficient of resistance (TCR) (at 20 °C) |
||
| Substance | ρ ,Ohm m | TKS α ,°C -1 |
| Conductors | ||
| Silver | 1.59·10 -8 | 0,0061 |
| Copper | 1.68·10 -8 | 0,0068 |
| Aluminum | 2.65·10 -8 | 0,00429 |
| Tungsten | 5.6·10 -8 | 0,0045 |
| Iron | 9.71·10 -8 | 0,00651 |
| Platinum | 10.6·10 -8 | 0,003927 |
| Mercury | 98·10 -8 | 0,0009 |
| Nichrome (alloy of Ni, Fe, Cr) | 100·10 -8 | 0,0004 |
| Semiconductors 1) | ||
| Carbon (graphite) | (3-60)·10 -5 | -0,0005 |
| Germanium | (1-500)·10 -5 | -0,05 |
| Silicon | 0,1 - 60 | -0,07 |
| Dielectrics | ||
| Glass | 10 9 - 10 12 | |
| Hard rubber | 10 13 - 10 15 | |
| 1) Real values strongly depend on the presence of even small amounts of impurities. | ||
Silver has the lowest resistivity, which thus turns out to be the best conductor; however it is expensive. Copper is slightly inferior to silver; It is clear why wires are most often made of copper.
Aluminum has a higher resistivity than copper, but it has a much lower density and is preferred in some applications (for example, in power lines) because the resistance of aluminum wires of the same mass is less than that of copper. The reciprocal of resistivity is often used:
σ = 1/ρ (26.5)
σ called specific conductivity. Specific conductivity is measured in units (Ohm m) -1.
The resistivity of a substance depends on temperature. As a rule, the resistance of metals increases with temperature. This should not be surprising: as temperature increases, atoms move faster, their arrangement becomes less ordered, and we can expect them to interfere more with the flow of electrons. In narrow temperature ranges, the resistivity of the metal increases almost linearly with temperature:
Where ρ T- resistivity at temperature T, ρ 0 - resistivity at standard temperature T 0 , a α - temperature coefficient of resistance (TCR). The values of a are given in table. 26.2. Note that for semiconductors the TCR can be negative. This is obvious, since with increasing temperature the number of free electrons increases and they improve the conductive properties of the substance. Thus, the resistance of a semiconductor may decrease with increasing temperature (although not always).
The values of a depend on temperature, so you should pay attention to the temperature range within which given value(for example, according to a reference book of physical quantities). If the range of temperature changes turns out to be wide, then linearity will be violated, and instead of (26.6) it is necessary to use an expression containing terms that depend on the second and third powers of temperature:
ρ T = ρ 0 (1+αT+ + βT 2 + γT 3),
where are the coefficients β And γ usually very small (we put T 0 = 0°С), but at large T the contributions of these members become significant.
At very low temperatures, the resistivity of some metals, as well as alloys and compounds, drops to zero within the accuracy of modern measurements. This property is called superconductivity; it was first observed by the Dutch physicist Geike Kamerling Onnes (1853-1926) in 1911 when mercury was cooled below 4.2 K. At this temperature, the electrical resistance of mercury suddenly dropped to zero.
Superconductors enter a superconducting state below the transition temperature, which is typically a few degrees Kelvin (just above absolute zero). An electric current was observed in a superconducting ring, which practically did not weaken in the absence of voltage for several years.
One of the most popular metals in industries is copper. It is most widely used in electrical and electronics. Most often it is used in the manufacture of windings for electric motors and transformers. The main reason for using this particular material is that copper has the lowest electrical resistivity of any material currently available. Until it appears new material with a lower value of this indicator, we can say with confidence that there will be no replacement for copper.
Speaking about copper, it must be said that at the dawn of the electrical era it began to be used in the production of electrical equipment. They began to use it largely due to unique properties, which this alloy possesses. By itself, it is a material characterized by high properties in terms of ductility and good malleability.
Along with the thermal conductivity of copper, one of its most important advantages is its high electrical conductivity. It is due to this property that copper and has become widespread in power plants, in which it acts as a universal conductor. The most valuable material is electrolytic copper, which has a high degree of purity of 99.95%. Thanks to this material, it becomes possible to produce cables.
Pros of using electrolytic copper
The use of electrolytic copper allows you to achieve the following:
- Ensure high electrical conductivity;
- Achieve excellent styling ability;
- Provide a high degree of plasticity.
Areas of application
Cable products made from electrolytic copper are widely used in various industries. Most often it is used in the following areas:
- electrical industry;
- electrical appliances;
- automotive industry;
- production of computer equipment.
What is the resistivity?
To understand what copper is and its characteristics, it is necessary to understand the main parameter of this metal - resistivity. It should be known and used when performing calculations.
Resistivity is usually understood as a physical quantity, which is characterized as the ability of a metal to conduct electric current.
It is also necessary to know this value in order to correctly calculate electrical resistance conductor. When making calculations, they are also guided by its geometric dimensions. When carrying out calculations, use the following formula:
This formula is familiar to many. Using it, you can easily calculate the resistance of a copper cable, focusing only on the characteristics of the electrical network. It allows you to calculate the power that is inefficiently spent on heating the cable core. Besides, a similar formula allows you to calculate resistance any cable. It does not matter what material was used to make the cable - copper, aluminum or some other alloy.
A parameter such as electrical resistivity is measured in Ohm*mm2/m. This indicator for copper wiring laid in an apartment is 0.0175 Ohm*mm2/m. If you try to look for an alternative to copper - a material that could be used instead, then only silver can be considered the only suitable one, whose resistivity is 0.016 Ohm*mm2/m. However, when choosing a material, it is necessary to pay attention not only to resistivity, but also to reverse conductivity. This value is measured in Siemens (Cm).
Siemens = 1/ Ohm.
For copper of any weight, this composition parameter is 58,100,000 S/m. As for silver, its reverse conductivity is 62,500,000 S/m.
In our world high technology when every home has a large number of electrical devices and installations, the value of such a material as copper is simply invaluable. This material used to make wiring, without which no room can do. If copper did not exist, then man would have to use wires from other available materials, for example, from aluminum. However, in this case one would have to face one problem. The thing is that this material has a much lower conductivity than copper conductors.
Resistivity
The use of materials with low electrical and thermal conductivity of any weight leads to large losses of electricity. A this affects power loss on the equipment used. Most experts call copper as the main material for making insulated wires. It is the main material from which they are made individual elements equipment powered by electric current.
- Boards installed in computers are equipped with etched copper traces.
- Copper is also used to make a wide variety of components used in electronic devices.
- In transformers and electric motors it is represented by a winding, which is made of this material.
There is no doubt that the expansion of the scope of application of this material will occur with the further development of technological progress. Although, besides copper, there are other materials, but still the designer when creating equipment and various installations use copper. main reason the demand for this material lies in good electrical and thermal conductivity of this metal, which it provides in conditions room temperature.
Temperature coefficient of resistance
All metals with any thermal conductivity have the property of decreasing conductivity with increasing temperature. As the temperature decreases, conductivity increases. Experts call the property of decreasing resistance with decreasing temperature particularly interesting. Indeed, in this case, when the temperature in the room drops to a certain value, the conductor may lose electrical resistance and it will move into the class of superconductors.
In order to determine the resistance value of a particular conductor of a certain weight at room temperature, there is a critical resistance coefficient. It is a value that shows the change in resistance of a section of a circuit when the temperature changes by one Kelvin. To calculate the electrical resistance of a copper conductor in a certain time period, use the following formula:
ΔR = α*R*ΔT, where α is the temperature coefficient of electrical resistance.
Conclusion
Copper is a material that is widely used in electronics. It is used not only in windings and circuits, but also as a metal for manufacturing cable products. For machinery and equipment to work effectively, it is necessary correctly calculate the resistivity of the wiring, laid in the apartment. There is a certain formula for this. Knowing it, you can make a calculation that allows you to find out the optimal size of the cable cross-section. In this case, it is possible to avoid loss of equipment power and ensure its efficient use.
The concept “specific copper” is often found in electrical engineering literature. And you can’t help but wonder, what is this?
The concept of “resistance” for any conductor is continuously associated with an understanding of the process of electric current flowing through it. Since the article will focus on the resistance of copper, we should consider its properties and the properties of metals.
When it comes to metals, you involuntarily remember that they all have a certain structure - a crystal lattice. Atoms are located in the nodes of such a lattice and move relative to them. The distances and location of these nodes depend on the forces of interaction of atoms with each other (repulsion and attraction), and are different for different metals. And electrons revolve around atoms in their orbits. They are also kept in orbit by the balance of forces. Only this is atomic and centrifugal. Can you imagine the picture? You can call it, in some respects, static.
Now let's add dynamics. It begins to act on a piece of copper electric field. What happens inside the conductor? Electrons, torn from their orbits by the force of the electric field, rush to its positive pole. Here you have the directed movement of electrons, or rather, electric current. But on the way of their movement they come across atoms at the nodes of the crystal lattice and electrons that still continue to rotate around their atoms. At the same time, they lose their energy and change the direction of movement. Now does the meaning of the phrase “conductor resistance” become a little clearer? It is the atoms of the lattice and the electrons rotating around them that resist the directional movement of electrons torn from their orbits by the electric field. But the concept of conductor resistance can be called general characteristic. Resistivity characterizes each conductor more individually. Including copper. This characteristic is individual for each metal, since it directly depends only on the shape and size of the crystal lattice and, to some extent, on temperature. As the temperature of the conductor increases, the atoms vibrate more intensely at the lattice sites. And electrons rotate around nodes at higher speeds and in orbits of larger radius. And, naturally, free electrons encounter greater resistance when moving. This is the physics of the process.
For the needs of the electrical engineering sector, widespread production of metals such as aluminum and copper, the resistivity of which is quite low, has been established. These metals are used to make cables and various types wires that are widely used in construction, for the production of household appliances, busbars, transformer windings and other electrical products.
For each conductor there is a concept of resistivity. This value consists of Ohms multiplied by a square millimeter, then divided by one meter. In other words, this is the resistance of a conductor whose length is 1 meter and cross-section is 1 mm2. The same is true for the resistivity of copper, a unique metal that is widely used in electrical engineering and energy.
Properties of copper
Due to its properties, this metal was one of the first to be used in the field of electricity. First of all, copper is a malleable and ductile material with excellent electrical conductivity properties. There is still no equivalent replacement for this conductor in the energy sector.
The properties of special electrolytic copper, which has high purity, are especially appreciated. This material made it possible to produce wires with minimum thickness at 10 microns.
In addition to high electrical conductivity, copper lends itself very well to tinning and other types of processing.
Copper and its resistivity
Any conductor exhibits resistance if an electric current is passed through it. The value depends on the length of the conductor and its cross-section, as well as on the effect of certain temperatures. Therefore, the resistivity of conductors depends not only on the material itself, but also on its specific length and area cross section. The easier a material allows a charge to pass through itself, the lower its resistance. For copper, the resistivity is 0.0171 Ohm x 1 mm2/1 m and is only slightly inferior to silver. However, the use of silver on an industrial scale is not economically profitable, therefore, copper is the best conductor used in energy.
The resistivity of copper is also related to its high conductivity. These values are directly opposite to each other. The properties of copper as a conductor also depend on the temperature coefficient of resistance. This is especially true for resistance, which is influenced by the temperature of the conductor.
Thus, due to its properties, copper has become widespread not only as a conductor. This metal is used in most instruments, devices and units whose operation is associated with electric current.
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 electron movement continuously changes: when electrons collide with atoms, molecules and other electrons, it decreases, then under the influence of an electric field it increases and decreases again during a new collision. As a result, the conductor is installed uniform motion flow of electrons at a speed of several fractions of a centimeter per second. Consequently, electrons passing through a conductor always encounter resistance to their movement from its side. When electric current passes through a conductor, the latter heats up.
Electrical resistance
The electrical resistance of a conductor, which is denoted by a Latin letter r, is the property of a body or medium to transform electrical energy into heat when an electric current passes through it.
In the diagrams, electrical resistance is indicated as shown in Figure 1, A.
Variable electrical resistance, which serves to change the current in a circuit, is called rheostat. In the diagrams, rheostats are designated as shown in Figure 1, b. IN general view A rheostat is made from a wire of one resistance or another, wound on an insulating base. The slider or rheostat lever is placed in a certain position, as a result of which the required resistance is introduced into the circuit.
A long conductor with a small cross-section creates a large resistance to current. Short conductors with a large cross-section offer little resistance to current.
If we take two conductors from different materials, but the same length and cross-section, then the conductors will conduct current differently. This shows that the resistance of a conductor depends on the material of the conductor itself.
The temperature of the conductor also affects its resistance. As temperature increases, the resistance of metals increases, and the resistance of liquids and coal decreases. Only some special metal alloys (manganin, constantan, nickel and others) hardly change their resistance with increasing temperature.
So, we see that the electrical resistance of a conductor depends on: 1) the length of the conductor, 2) the cross-section of the conductor, 3) the material of the conductor, 4) the temperature of the conductor.
The unit of resistance is one ohm. Om is often represented by the Greek capital letter Ω (omega). Therefore, instead of writing “The conductor resistance is 15 ohms,” you can simply write: r= 15 Ω.
1,000 ohms is called 1 kiloohm(1kOhm, or 1kΩ),
1,000,000 ohms is called 1 megaohm(1mOhm, or 1MΩ).
When comparing the resistance of conductors from 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 copper wire with a cross section of 1 mm² it 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, and windings. electric 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 cross section 20 m 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, 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).
Here are the values temperature coefficient 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)
Electrical resistivity is a physical quantity that indicates 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.
Reciprocal of this material is the specific 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 mm 2 /m. To transfer from this system to an international one you will not need to use complex formulas, since 1 Ohm mm 2 /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 in 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. Carriers electric charges 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 generally not applicable for electrical engineering if they have high value 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 | 10 16 |
| Benzene | 10 15 ...10 16 |
| Paper | 10 15 |
| Distilled water | 10 4 |
| Sea water | 0.3 |
| Dry wood | 10 12 |
| The ground is wet | 10 2 |
| Quartz glass | 10 16 |
| Kerosene | 10 1 1 |
| Marble | 10 8 |
| Paraffin | 10 1 5 |
| Paraffin oil | 10 14 |
| Plexiglass | 10 13 |
| Polystyrene | 10 16 |
| Polyvinyl chloride | 10 13 |
| Polyethylene | 10 12 |
| Silicone oil | 10 13 |
| Mica | 10 14 |
| Glass | 10 11 |
| Transformer oil | 10 10 |
| Porcelain | 10 14 |
| Slate | 10 14 |
| Ebonite | 10 16 |
| Amber | 10 18 |
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.
Widespread use has also affected noble metals, which have suitable characteristics for electrical engineering. For critical circuits that require high speed, silver contacts are selected. They have high cost, 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 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 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.