Resistivity and temperature coefficient of resistance of metals and alloys

Description

Since the beginning of the electrical age, it has been known that copper, with its unique properties, is usable. Copper is a malleable and ductile material with excellent electrical conductivity. Along with the use of enamelled wires, Elektrisola uses high purity electrolytic copper (Cu-ETP) (99.95%), which allows us to produce ultra-thin wire up to 10 microns in thickness. We sell enameled wires with a diameter of 0.010mm to 0.500mm with any enamel insulation. In addition to enameled wires, ELEKTRISOLA also produces bare wires.

Properties

• Increased electrical conductivity
• Good tinning ability
• High plasticity

Application

• Components for the electrical industry
• Automotive
• electrical appliances
• Consumables
• Computer manufacturing

Typical values

Resistance Calculation

Conductor material resistance (e.g. copper wires)

Resistance R copper wire in length l can be calculated with the following formula

if
R- resistance of the conductor material (ohm)
l- wire length in meters
ρ - electrical resistivity of the material
A- square cross section
π - mathematical number
d - nominal diameter wires in millimeters

Electrical resistivity ρ

Electrical resistivity describes the extent to which this material resists electrical current. Low resistance indicates that the material easily passes an electrical charge. Copper has an electrical resistance of 0.0171 Ohm mm²/m, this resistance is one of the best conductors for electric current(after pure silver).

Conductivity γ

Electrical conductivity or specific conductivity is a material measure of the possibility of conducting an electric current. Conductivity is the opposite of electrical resistance. Annealed copper wire has a minimum conductivity of 58 S*m/mm², equivalent to 100% IACS (International Standard Annealed Copper), actual coil size 58.5-59 S*m/mm²

Temperature coefficient of electrical resistance

The electrical resistance depends on the temperature of the wire. This relationship between resistance and temperature is expressed by the coefficient thermal resistance α . To calculate the resistance of a winding product or wire at a temperature T you can use the following formula:

where
α - temperature coefficient resistance
R T- winding product resistance at temperature T
R 20 - resistance of the winding product at a temperature of 20°C

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

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

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. Formula of electrical resistivity:

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, shortening the formula - Ohm m.

The value of ρ for the same substance is always the same. Therefore, it is a constant that characterizes the material of the conductor. Usually it is indicated in reference books. Based on this, it is already possible to carry out the calculation of technical quantities.

It is important to say about the specific electrical conductivity. This value is the reciprocal of the resistivity of the material, and is used along with it. It is also called electrical conductivity. The higher this value, the better metal conducts current. For example, the conductivity of copper is 58.14 m / (Ohm mm 2). Or, in SI units: 58,140,000 S/m. (Siemens per meter is the SI unit of electrical conductivity).

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

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

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

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

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

• Huge variety of conductors;
• Auto parts (for example, radiators);
• Watch movements;
• Computer components;
• Details of electrical and electronic devices.

The electrical resistivity of copper is one of the best among current-conducting materials, so many products of the electrical industry 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 ductility makes it possible to create the smallest details 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 kind are conductive solutions of liquids. The current in the former is carried by electrons, and the current carriers in conductors of the second kind are ions, charged particles of the electrolytic liquid.

It is possible to talk about the conductivity of materials only in the context of temperature environment. At a higher temperature, the conductors of the first kind increase their electrical resistance, and the second, on the contrary, decrease. Accordingly, there is a temperature coefficient of resistance of materials. The specific resistance 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.

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

R (t) = R (0) , where:

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

For example, knowing the electrical resistance of copper at 20 degrees Celsius, you can calculate what it will be 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 the electrical resistance, then it decreases exactly the same number of times. 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 with a change in temperature. Such, for example, is Constantan. When the temperature changes by one hundred degrees, its resistance increases by only 0.5%.

If 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 decrease sharply: almost to zero. As a result, transmission costs are falling. electrical energy. The only problem was the cooling of the conductors to such temperatures. However, in connection with the recent discoveries of high-temperature superconductors based on copper oxides, materials have to be cooled to acceptable values.

One of the most demanded 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 this moment materials specific electrical resistance. Until it appears new material with a lower value of this indicator, it is safe to say that there will be no replacement for copper.

General characteristics of copper

Speaking about copper, it must be said that even at the dawn of the electrical era, it began to be used in the production of electrical engineering. It was used largely due to the unique properties that this alloy possesses. By itself, it is a material with high ductility properties and good ductility.

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 - 99.95%. Thanks to this material, it becomes possible to produce cables.

Advantages of using electrolytic copper

The use of electrolytic copper allows you to achieve the following:

• Provide high electrical conductivity;
• Achieve excellent laying ability;
• Provide a high degree of plasticity.

Applications

Cable products made from electrolytic copper are widely used in various industries. It is most often 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 understood to mean physical quantity, which is characterized as the ability of a metal to conduct an electric current.

It is also necessary to know this value in order to correctly calculate the electrical resistance conductor. When calculating, they also focus on its geometric dimensions. When making calculations, use the following formula:

This formula is well known to many. Using it, you can easily calculate the resistance of a copper cable, focusing only on the characteristics 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 perform resistance calculations 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 the 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 silver is the only suitable, 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 \u003d 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 house 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 is complete. If copper did not exist, then man would have to use wires from other available materials, for example, 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 big losses electricity. BUT it affects power loss on the equipment being used. Most specialists refer to copper as the main material for the manufacture of insulated wires. It is the main material from which individual elements electrical powered equipment.

• Boards installed in computers are equipped with etched copper tracks.
• Copper is also used to make a wide variety of elements used in electronic devices.
• In transformers and electric motors, it is represented by a winding made from this material.

There is no doubt that the expansion of the scope of this material will occur with further development technical progress. Although, in addition to copper, there are other materials, but still the designer when creating equipment and various installations copper is used. main reason demand for this material is in good electrical and thermal conductivity of this metal, which it provides at 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, the conductivity increases. Specialists call the property of decreasing resistance with decreasing temperature especially interesting. After all, in this case, when the temperature in the room drops to a certain value, the conductor may lose electrical resistance and it will pass into the class of superconductors.

In order to determine the resistance index 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 circuit section with a change in temperature by one Kelvin. To perform the calculation of the electrical resistance of a copper conductor in a certain time interval, 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 the manufacture of cable products. In order 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, the power loss of the equipment can be avoided and the efficiency of its use can be ensured.

During heating, the resistivity of the metal increases due to the activation of the Brownian motion of atoms. Some alloys with a higher resistivity practically do not change it with increasing temperature (manganin, constantan). This is due to the special structure of the alloys and the short mean free time of electrons.

Conductivity change

Temperature coefficient of resistance- reflects the change in conductivity when the material is heated or cooled. If the temperature coefficient is denoted by α, the resistivity at 20 °C by Ro, then during the heating of the material to a temperature t ° its resistivity R1 = Ro (1 + (α (t1 - to))

Let's take an example. The temperature coefficient of fechral = 0.0001 / 1 degree, and for nichrome α = 0.0002 / 1 degree. This means that heating by 100 °C increases the electrical resistance of Fechral by 1% and that of Nichrome by 2%.

Piece of nichrome wire 1 m

The property of conductors to change their resistance depending on temperature is used in thermocouples for measuring the temperature of metallurgical processes, as well as in drying and roasting furnaces.

Provider

Supplier "Auremo" - a recognized expert in the market of non-ferrous and stainless steel - offers to buy at affordable price nichrome, fechral, ​​thermocouples:. Big choice in stock. Compliance with GOST and international standards quality. Nichrome, fechral, ​​thermocouples are always available, the price is optimal from the supplier. To wholesale customers the price is preferential. Contact the phone numbers from the "Contacts" section, we are always open to suggestions. We invite you to partner cooperation.

Buy at a bargain price

The supplier "Auremo" offers to buy nichrome, fechral, ​​thermocouples on favorable terms, the price is determined technological features production without additional costs. The company's website displays the most up-to-date information, there is a product catalog and price lists. Under the order, you can buy products of non-standard parameters. The price of the order depends on the volume and additional terms of delivery.

Material when the temperature changes by 1, expressed in K -1. In electronics, in particular, resistors made of special metal alloys with a low α value, such as manganin or constantan alloys and semiconductor components with large positive or negative valuesα (thermistors). The physical meaning of the temperature coefficient of resistance is expressed by the equation:

where dR- change in electrical resistance R when the temperature changes by dT.

conductors

The temperature dependence of resistance for most metals is close to linear for a wide temperature range and is described by the formula:

At low temperatures the temperature dependence of the resistance of conductors is determined by the Mathiesen rule.

Semiconductors

Temperature dependence of NTC thermistor resistance

For semiconductor devices such as thermistors, the temperature dependence of resistance is mainly determined by the dependence of charge carrier concentration on temperature. This is an exponential relationship:

Taking the logarithm of the left and right sides of the equation, we get:

The temperature coefficient of resistance of the thermistor is given by the equation:

From the dependence of R T on T we have:

Sources

• Theoretical basis electrical engineering: Textbook: In 3 volumes / V. S. Boyko, V. V. Boyko, Yu. F. Vydolob et al.; Under total ed. I. M. Chizhenko, V. S. Boyko. - M.: ShTs "Publishing house" Politekhnika "", 2004. - T. 1: stable modes of linear electrical circuits with lumped parameters. - 272 p: ill. ISBN 966-622-042-3
• Shegedin A.I. Malyar V.S. Theoretical foundations of electrical engineering. Part 1: Tutorial for distance learning students of higher electrotechnical and electromechanical specialties educational institutions. - M.: Magnolia plus, 2004. - 168 p.
• I.M. Kucheruk, I.T. Gorbachuk, P.P. Lutsik (2006). General course of physics: Textbook in 3 volumes. V.2. electricity and magnetism. Kyiv: Technique.

Probably everyone knows about the effect of superconductivity. At least you've heard of him. The essence of this effect is that at minus 273 ° C, the resistance of the conductor to the flowing current disappears. This example alone is enough to understand that there is its dependence on temperature. A describes a special parameter - the temperature coefficient of resistance.

Any conductor impedes the current flowing through it. This resistance is different for each conductive material, it is determined by many factors inherent in a particular material, but this will not be discussed further. Interest in this moment represents its dependence on temperature and the nature of this dependence.

Metals are usually conductors of electric current, their resistance increases with increasing temperature, and decreases with decreasing temperature. The magnitude of this change per 1 °C is called the temperature coefficient of resistance, or TCR for short.

The TCS value can be positive or negative. If it is positive, then it increases with increasing temperature, if it is negative, then it decreases. For most metals used as conductors of electric current, TCR is positive. One of the best conductors is copper, the temperature coefficient of resistance of copper is not exactly the best, but compared to other conductors, it is less. You just need to remember that the TCR value determines what the resistance value will be when the environmental parameters change. Its change will be the greater, the larger this coefficient.

Such a temperature dependence of the resistance must be taken into account when designing electronic equipment. The fact is that the equipment must work under any environmental conditions, the same cars are operated from minus 40 ° C to plus 80 ° C. And there are a lot of electronics in the car, and if you do not take into account the influence of the environment on the operation of the circuit elements, then you may encounter a situation where the electronic unit works fine under normal conditions, but refuses to work when exposed to low or high temperatures.

Here is this dependence on conditions external environment and take into account the hardware developers when designing it, using for this purpose the temperature coefficient of resistance when calculating the parameters of the circuit. There are tables with TCS data for the materials used and calculation formulas, by which, knowing the TCS, you can determine the resistance value under any conditions and take into account its possible change in the operating modes of the circuit. But to understand that, TCS, now neither formulas nor tables are needed.

It should be noted that there are metals with a very small TCR value, and they are used in the manufacture of resistors, the parameters of which depend little on environmental changes.

The temperature coefficient of resistance can be used not only to take into account the influence of fluctuations in environmental parameters, but also for what is enough. Knowing the material that has been exposed, it is possible to determine from the tables what temperature the measured resistance corresponds to. An ordinary copper wire can be used as such a meter, however, you will have to use it a lot and wind it in the form, for example, of a coil.

All of the above does not fully cover all the issues of using the temperature coefficient of resistance. There are very interesting applications associated with this coefficient in semiconductors, in electrolytes, but what has been stated is enough to understand the concept of TCR.

The results of resistivity measurements are strongly affected by shrinkage cavities, gas bubbles, inclusions, and other defects. Moreover, fig. 155 shows that small amounts of impurities entering the solid solution also have big influence to the measured conductivity. Therefore, it is much more difficult to make satisfactory samples for electrical resistance measurements than for

dilatometric study. This has led to another phase diagram method in which the temperature coefficient of resistance is measured.

Temperature coefficient of resistance

Electrical resistance at temperature

Matthiessen found that the increase in the resistance of a metal due to the presence of a small amount of the second component in a solid solution does not depend on temperature; it follows that for such a solid solution, the value does not depend on the concentration. This means that the temperature coefficient of resistance is proportional to, i.e., conductivity, and the graph of the coefficient a, depending on the composition, is similar to the graph of the conductivity of a solid solution. There are many known exceptions to this rule, especially for transition metals, but for most cases it is approximately true.

The temperature coefficient of resistance of intermediate phases is usually of the same order of magnitude as for pure metals, even in cases where the connection itself has a high resistance. There are, however, intermediate phases whose temperature coefficient is zero or negative in a certain temperature range.

Matthiessen's rule applies, strictly speaking, only to solid solutions, but there are many cases where it seems to be true for two-phase alloys as well. If the temperature coefficient of resistance is plotted as a function of composition, the curve usually has the same shape as the conductance curve, so that the phase transformation can be detected in the same way. This method is useful when, due to brittleness or other reasons, it is not possible to prepare samples suitable for conductivity measurements.

In practice, the average temperature coefficient between two temperatures is determined by measuring the electrical resistance of the alloy at those temperatures. If no phase transformation occurs in the temperature range under consideration, then the coefficient is determined by the formula:

will have the same value as if the interval is small. For hardened alloys as temperatures and

It is convenient to take 0° and 100°, respectively, and measurements will give the phase regions at the quenching temperature. However, if measurements are taken at high temperatures, the interval must be much smaller than 100° if the phase boundary can be somewhere between the temperatures

Rice. 158. (see scan) Electrical conductivity and temperature coefficient of electrical resistance in the silver-magic system (Tamman)

The great advantage of this method is that the coefficient a depends on the relative resistance of the sample at the two temperatures, and thus is not affected by cavities and other metallurgical defects of the sample. Conductivity and temperature coefficient curves

resistance in some alloy systems repeat one another. Rice. 158 is taken from Tamman's early work (the curves refer to silver-magnesium alloys); later work showed that the region of the solid solution decreases with decreasing temperature and that a superstructure exists in the region of the phase. Some other phase boundaries have also changed recently, so that the diagram shown in Fig. 158 is of historical interest only and cannot be used for accurate measurements.

Conductor resistance (R) (resistivity) () depends on temperature. This dependence with slight temperature changes () is presented as a function:

where is the specific resistance of the conductor at a temperature equal to 0 o C; - temperature coefficient of resistance.

DEFINITION

temperature coefficient of electrical resistance() is called a physical quantity equal to the relative increment (R) of the circuit section (or the resistivity of the medium ()) that occurs when the conductor is heated by 1 o C. Mathematically, the definition of the temperature coefficient of resistance can be represented as:

The value serves as a characteristic of the relationship between electrical resistance and temperature.

At temperatures within the range, for most metals, the coefficient under consideration remains constant. For pure metals, the temperature coefficient of resistance is often taken equal to

Sometimes they talk about the average temperature coefficient of resistance, defining it as:

where is the average value of the temperature coefficient in a given temperature range ().

Temperature coefficient of resistance for different substances

Most metals have a temperature coefficient of resistance greater than zero. This means that the resistance of metals increases with increasing temperature. This occurs as a result of the scattering of electrons by the crystal lattice, which amplifies thermal vibrations.

At temperatures close to absolute zero(-273 o C) the resistance of a large number of metals drops sharply to zero. Metals are said to go into a superconducting state.

Semiconductors that do not contain impurities have a negative temperature coefficient of resistance. Their resistance decreases with increasing temperature. This is due to the fact that the number of electrons that pass into the conduction band increases, which means that the number of holes per unit volume of the semiconductor increases.

Electrolyte solutions have The resistance of electrolytes decreases with increasing temperature. This is because the increase in the number of free ions as a result of the dissociation of molecules exceeds the increase in the scattering of ions as a result of collisions with solvent molecules. It must be said that the temperature coefficient of resistance for electrolytes is a constant value only in a small temperature range.

Units

The basic unit for measuring the temperature coefficient of resistance in the SI system is:

Examples of problem solving

Exercise	An incandescent lamp with a tungsten spiral is connected to a network with voltage B, current A flows through it. What will be the temperature of the spiral if at a temperature of o C it has a resistance of Ohm? Temperature coefficient of resistance of tungsten .
Solution	As a basis for solving the problem, we use the formula for the dependence of resistance on temperature of the form: where is the resistance of the tungsten filament at a temperature of 0 o C. We express from expression (1.1), we have: According to Ohm's law for the circuit section we have: Compute Let's write the equation relating resistance and temperature: Let's do the calculations:
Answer	K