Specific electrical resistance of brass. Resistivity of aluminum

Electrical resistance is the main characteristic of conductive materials. Depending on the scope of the conductor, the value of its resistance can play both a positive and a negative role in the functioning of an electrical system. Also, the features of the use of the conductor may cause the need to take into account additional characteristics, the influence of which in a particular case cannot be neglected.

Conductors are pure metals and their alloys. In a metal, atoms fixed in a single "strong" structure have free electrons (the so-called "electron gas"). It is these particles in this case that are charge carriers. Electrons are in constant random movement from one atom to another. When an electric field appears (a voltage source is connected to the ends of the metal), the movement of electrons in the conductor becomes ordered. Moving electrons encounter obstacles in their path caused by the peculiarities of the molecular structure of the conductor. When colliding with the structure, charge carriers lose their energy, giving it to the conductor (heating it). The more obstacles the conductive structure creates for charge carriers, the higher the resistance.

With an increase in the cross section of the conducting structure for one number of electrons, the “transmission channel” will become wider, and the resistance will decrease. Accordingly, with an increase in the length of the wire, there will be more such obstacles and the resistance will increase.

Thus, the basic formula for calculating the resistance includes the length of the wire, the cross-sectional area and a certain coefficient that relates these dimensional characteristics to the electrical values ​​of voltage and current (1). This coefficient is called resistivity.
R=r*L/S (1)

Resistivity

Resistivity unchanged and is a property of the substance from which the conductor is made. Units of measurement r - ohm * m. Often, the resistivity value is given in ohm * mm sq. / m. This is due to the fact that the cross section of the most commonly used cables is relatively small and is measured in mm square. Let's take a simple example.

Task number 1. Copper wire length L = 20 m, section S = 1.5 mm. sq. Calculate the wire resistance.
Solution: specific resistance of copper wire r = 0.018 ohm*mm. sq./m. Substituting the values ​​into formula (1) we get R=0.24 ohm.
When calculating the resistance of the power system, the resistance of one wire must be multiplied by the number of wires.
If aluminum with a higher resistivity (r = 0.028 ohm * mm sq. / m) is used instead of copper, then the resistance of the wires will increase accordingly. For the example above, the resistance would be R = 0.373 ohm (55% more). Copper and aluminum are the main materials for wires. There are metals with lower resistivity than copper, such as silver. However, its use is limited due to the obvious high cost. The table below lists the resistances and other basic characteristics of conductor materials.
Table - the main characteristics of the conductors

Thermal losses of wires

If, using the cable from the above example, a load of 2.2 kW is connected to a single-phase 220 V network, then the current I \u003d P / U or I \u003d 2200/220 \u003d 10 A will flow through the wire. The formula for calculating the power loss in the conductor:
Ppr \u003d (I ^ 2) * R (2)
Example No. 2. Calculate active losses during power transmission of 2.2 kW in a network with a voltage of 220 V for the mentioned wire.
Solution: by substituting the values ​​of the current and resistance of the wires into the formula (2), we get Ppr \u003d (10 ^ 2) * (2 * 0.24) \u003d 48 W.
Thus, when transferring energy from the network to the load, the losses in the wires will be slightly more than 2%. This energy is converted into heat released by the conductor into the environment. According to the condition of heating the conductor (according to the magnitude of the current), its cross section is selected, guided by special tables.
For example, for the above conductor, the maximum current is 19 A or 4.1 kW in a 220 V network.

Increased voltage is used to reduce active losses in power lines. In this case, the current in the wires decreases, the losses fall.

Temperature effect

An increase in temperature leads to an increase in the oscillations of the crystal lattice of the metal. Accordingly, the electrons encounter more obstacles, which leads to an increase in resistance. The value of the "sensitivity" of the resistance of the metal to a rise in temperature is called the temperature coefficient α. The formula for taking into account the temperature is as follows
R=Rн*, (3)
where Rn is the resistance of the wire under normal conditions (at temperature t°n); t° is the temperature of the conductor.
Usually t°n = 20°C. The value of α is also indicated for the temperature t°n.
Task 4. Calculate the resistance of a copper wire at a temperature of t ° \u003d 90 ° C. α copper \u003d 0.0043, Rn \u003d 0.24 Ohm (task 1).
Solution: substituting the values ​​in formula (3) we get R = 0.312 Ohm. The resistance of the analyzed heated wire is 30% greater than its resistance at room temperature.

Frequency effect

With an increase in the frequency of the current in the conductor, the process of displacing charges closer to its surface occurs. As a result of an increase in the concentration of charges in the surface layer, the resistance of the wire also increases. This process is called the “skin effect” or surface effect. Skin coefficient– the effect also depends on the size and shape of the wire. For the above example, with an AC frequency of 20 kHz, the resistance of the wire will increase by approximately 10%. Note that high-frequency components can have a current signal of many modern industrial and domestic consumers (energy-saving lamps, switching power supplies, frequency converters, and so on).

Influence of adjacent conductors

Around any conductor through which current flows, there is a magnetic field. The interaction of the fields of neighboring conductors also causes energy losses and is called the "proximity effect". Also note that any metal conductor has an inductance created by a conductive core, and a capacitance created by insulation. These parameters also have a proximity effect.

Technology

High voltage zero resistance wires

This type of wire is widely used in car ignition systems. The resistance of high-voltage wires is quite small and amounts to a few fractions of an ohm per meter of length. Recall that the resistance of such a value cannot be measured with a general-purpose ohmmeter. Often, measuring bridges are used for the task of measuring low resistances.
Structurally, such wires have a large number of copper conductors with insulation based on silicone, plastics or other dielectrics. The peculiarity of the use of such wires is not only in operation at high voltage, but also in the transfer of energy in a short period of time (pulse mode).

Bimetal cable

The main scope of the mentioned cables is the transmission of high-frequency signals. The core of the wire is made of one type of metal, the surface of which is coated with another type of metal. Since only the surface layer of the conductor is conductive at high frequencies, it is possible to replace the inside of the wire. This saves expensive material and improves the mechanical characteristics of the wire. Examples of such wires are silver-plated copper, copper-plated steel.

Conclusion

Wire resistance is a value that depends on a group of factors: type of conductor, temperature, current frequency, geometric parameters. The significance of the influence of these parameters depends on the operating conditions of the wire. Optimization criteria depending on the tasks for wires can be: reduction of active losses, improvement of mechanical characteristics, price reduction.

Specific electrical resistance, or simply the specific resistance of a substance, is a physical quantity that characterizes the ability of a substance to prevent the passage of an electric current.

Resistivity is denoted by the Greek letter ρ. The reciprocal of resistivity is called specific conductivity (electrical conductivity). Unlike electrical resistance, which is a property of a conductor and depends on its material, shape and size, electrical resistivity is a property of a substance only.

The electrical resistance of a homogeneous conductor with resistivity ρ, length l and cross-sectional area S can be calculated by the formula (it is assumed that neither the area nor the cross-sectional shape changes along the conductor). Accordingly, for ρ,

It follows from the last formula: the physical meaning of the specific resistance of a substance lies in the fact that it is the resistance of a homogeneous conductor made of this substance of unit length and with a unit cross-sectional area.

The unit of resistivity in the International System of Units (SI) is Ohm m.

It follows from the ratio that the unit of measurement of resistivity in the SI system is equal to such a resistivity of a substance at which a homogeneous conductor 1 m long with a cross-sectional area of ​​​​1 m², made from this substance, has a resistance equal to 1 Ohm. Accordingly, the specific resistance of an arbitrary substance, expressed in SI units, is numerically equal to the resistance of an electrical circuit section made of this substance, 1 m long and with a cross-sectional area of ​​1 m².

The technique also uses an outdated off-system unit Ohm mm² / m, equal to 10 −6 of 1 Ohm m. This unit is equal to such a specific resistance of a substance at which a homogeneous conductor 1 m long with a cross-sectional area of ​​\u200b\u200b1 mm², made from this substance, has a resistance equal to 1 Ohm. Accordingly, the resistivity of a substance, expressed in these units, is numerically equal to the resistance of an electrical circuit section made of this substance, 1 m long and with a cross-sectional area of ​​1 mm².

Electromotive force (EMF) is a scalar physical quantity that characterizes the work of external forces, that is, any forces of non-electric origin acting in quasi-stationary DC or AC circuits. In a closed conducting circuit, the EMF is equal to the work of these forces in moving a single positive charge along the entire circuit.

By analogy with the strength of the electric field, the concept of intensity of external forces is introduced, which is understood as a vector physical quantity equal to the ratio of the external force acting on the test electric charge to the magnitude of this charge. Then in a closed loop, the EMF will be equal to:

where is the contour element.

EMF, like voltage, is measured in volts in the International System of Units (SI). We can talk about the electromotive force in any part of the circuit. This is the specific work of external forces not in the entire circuit, but only in this section. The EMF of a galvanic cell is the work of external forces when moving a single positive charge inside the cell from one pole to another. The work of external forces cannot be expressed in terms of the potential difference, since external forces are non-potential and their work depends on the shape of the trajectory. So, for example, the work of external forces when moving a charge between the current terminals is outside of itself? source is zero.

The resistance of copper does change with temperature, but first we need to decide whether we mean the electrical resistivity of the conductors (ohmic resistance), which is important for power over Ethernet using direct current, or we are talking about signals in data networks, and then we we are talking about the insertion loss during the propagation of an electromagnetic wave in a twisted pair medium and about the dependence of attenuation on temperature (and frequency, which is no less important).

Resistivity of copper

In the international SI system, the resistivity of conductors is measured in Ohm∙m. In the field of IT, the off-system dimension Ohm ∙ mm 2 /m is more often used, which is more convenient for calculations, since the cross-sections of conductors are usually indicated in mm 2. The value of 1 Ohm∙mm 2 /m is a million times less than 1 Ohm∙m and characterizes the resistivity of a substance, a homogeneous conductor of which is 1 m long and with a cross-sectional area of ​​​​1 mm 2 gives a resistance of 1 Ohm.

The resistivity of pure electrical copper at 20°C is 0.0172 Ohm∙mm2/m. In various sources, you can find values ​​\u200b\u200bup to 0.018 Ohm ∙ mm 2 / m, which can also apply to electrical copper. The values ​​vary depending on the processing that the material is subjected to. For example, annealing after drawing ("drawing") the wire reduces the resistivity of copper by a few percent, although it is carried out primarily to change the mechanical rather than electrical properties.

The resistivity of copper has a direct bearing on power-over-Ethernet applications. Only a portion of the original DC current applied to the conductor will reach the far end of the conductor - some loss along the way is unavoidable. For example, PoE Type 1 requires at least 12.95 watts of 15.4 watts supplied by the source to reach the far-end powered device.

The resistivity of copper changes with temperature, but for IT temperatures these changes are small. The change in resistivity is calculated by the formulas:

ΔR = α R ΔT

R 2 \u003d R 1 (1 + α (T 2 - T 1))

where ΔR is the change in resistivity, R is the resistivity at a temperature taken as a baseline (usually 20°C), ΔT is the temperature gradient, α is the temperature coefficient of resistivity for a given material (dimension °C -1). In the range from 0°C to 100°C for copper, a temperature coefficient of 0.004 °C -1 is adopted. Calculate the resistivity of copper at 60°C.

R 60°С = R 20°С (1 + α (60°С - 20°С)) = 0.0172 (1 + 0.004 40) ≈ 0.02 Ohm∙mm2/m

The resistivity increased by 16% with an increase in temperature by 40°C. When operating cable systems, of course, twisted pair should not be at high temperatures, this should not be allowed. With a properly designed and installed system, the temperature of the cables differs little from the usual 20°C, and then the change in resistivity will be small. According to the requirements of telecommunications standards, the resistance of a copper conductor 100 m long in a twisted pair of categories 5e or 6 should not exceed 9.38 ohms at 20 ° C. In practice, manufacturers fit this value with a margin, so even at temperatures of 25 ° C ÷ 30 ° C, the resistance of the copper conductor does not exceed this value.

Twisted Pair Attenuation / Insertion Loss

When an electromagnetic wave propagates through a twisted-pair copper medium, part of its energy is dissipated along the path from the near end to the far end. The higher the temperature of the cable, the more the signal attenuates. At high frequencies, the attenuation is stronger than at low frequencies, and for higher categories, insertion loss testing limits are tighter. In this case, all limit values ​​are set for a temperature of 20°C. If at 20°C the original signal arrived at the far end of a 100 m long segment with power level P, then at elevated temperatures such signal power will be observed at shorter distances. If it is necessary to provide the same signal strength at the output of the segment, then either you will have to install a shorter cable (which is not always possible), or choose cable brands with lower attenuation.

• For shielded cables at temperatures above 20°C, a temperature change of 1 degree leads to a change in attenuation of 0.2%
• For all types of cables and any frequencies at temperatures up to 40 ° C, a change in temperature by 1 degree leads to a change in attenuation by 0.4%
• For all types of cables and any frequencies at temperatures from 40°C to 60°C, a change in temperature by 1 degree leads to a change in attenuation by 0.6%
• Category 3 cables may experience attenuation variation of 1.5% per degree Celsius

Already at the beginning of 2000. TIA/EIA-568-B.2 recommended that the maximum allowable length of a permanent Category 6 link/channel be reduced if the cable was installed in elevated temperatures, and the higher the temperature, the shorter the segment should be.

Considering that the frequency ceiling in Category 6A is twice that of Category 6, the temperature limits for such systems will be even tighter.

To date, when implementing applications PoE we are talking about a maximum of 1-gigabit speeds. When 10 Gb applications are used, Power over Ethernet is not used, at least not yet. So depending on your needs, when changing temperature, you need to take into account either the change in copper resistivity or the change in attenuation. It is most reasonable in both cases to ensure that the cables are at temperatures close to 20 ° C.

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 electrical resistivity currently available. Until a new material with a lower value of this indicator appears, 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 widely used 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 usually understood as a 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 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 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 of 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 is complete. If copper did not exist, then man would have to use wires made from other available materials, such as 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. 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 of equipment powered by electric current are made.

• 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 the further development of technical progress. Although, in addition to copper, there are other materials, but still the designer uses copper to create equipment and various installations. The main reason for the 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.

Despite the fact that this topic may seem quite banal, in it I will answer one very important question regarding the calculation of voltage loss and the calculation of short circuit currents. I think for many of you this will be as much of a revelation as it was for me.

Recently I studied one very interesting GOST:

GOST R 50571.5.52-2011 Low-voltage electrical installations. Part 5-52. Selection and installation of electrical equipment. Wiring.

This document provides a formula for calculating voltage loss and states:

p is the resistivity of conductors under normal conditions, taken equal to the resistivity at temperature under normal conditions, that is, 1.25 resistivity at 20 ° C, or 0.0225 Ohm mm 2 / m for copper and 0.036 Ohm mm 2 / m for aluminum;

I didn't understand anything =) Apparently, when calculating voltage losses and when calculating short-circuit currents, we must take into account the resistance of the conductors, as under normal conditions.

It is worth noting that all tabular values ​​\u200b\u200bare given at a temperature of 20 degrees.

What are the normal conditions? I thought 30 degrees Celsius.

Let's remember physics and calculate at what temperature the resistance of copper (aluminum) will increase by 1.25 times.

R1=R0

R0 - resistance at 20 degrees Celsius;

R1 - resistance at T1 degrees Celsius;

T0 - 20 degrees Celsius;

α \u003d 0.004 per degree Celsius (copper and aluminum are almost the same);

1.25=1+α (T1-T0)

Т1=(1.25-1)/α+Т0=(1.25-1)/0.004+20=82.5 degrees Celsius.

As you can see, it's not 30 degrees at all. Apparently, all calculations must be performed at the maximum allowable cable temperatures. The maximum operating temperature of the cable is 70-90 degrees, depending on the type of insulation.

To be honest, I do not agree with this, because. this temperature corresponds to almost the emergency mode of the electrical installation.

In my programs, I laid down the specific resistance of copper - 0.0175 Ohm mm 2 / m, and for aluminum - 0.028 Ohm mm 2 / m.

If you remember, I wrote that in my program for calculating short-circuit currents, the result is about 30% less than the tabular values. There, the resistance of the phase-zero loop is calculated automatically. I tried to find the error but couldn't. Apparently, the inaccuracy of the calculation lies in the resistivity, which is used in the program. And everyone can ask the resistivity, so there should be no questions for the program if you specify the resistivity from the above document.

But I most likely will have to make changes to the programs for calculating voltage losses. This will increase the calculation results by 25%. Although in the ELECTRIC program, the voltage losses are almost the same as mine.

If this is your first time on this blog, then you can get acquainted with all my programs on the page

What do you think, at what temperature should voltage losses be considered: at 30 or 70-90 degrees? Are there any regulations that will answer this question?