When an electrical circuit is closed, on the terminals of which there is a potential difference, an electric current arises. Free electrons under the influence of electric field forces move along the conductor. In their motion, the electrons collide with the atoms of the conductor and give them a reserve of their kinetic energy. The speed of movement of electrons is constantly changing: when electrons collide with atoms, molecules and other electrons, it decreases, then increases under the influence of an electric field and decreases again with a new collision. As a result, a uniform flow of electrons is established in the conductor at a speed of several fractions of a centimeter per second. Consequently, electrons passing through a conductor always encounter resistance from its side to their movement. When an electric current passes through a conductor, the latter heats up.
Electrical resistance
The electrical resistance of the conductor, which is indicated by the Latin letter r, is the property of a body or medium to convert electrical energy into thermal energy when an electric current passes through it.
In the diagrams, electrical resistance is indicated as shown in Figure 1, A.
Variable electrical resistance, which serves to change the current in the circuit, is called rheostat. In the diagrams, rheostats are designated as shown in Figure 1, b. In general, a rheostat is made from a wire of one or another resistance, wound on an insulating base. The slider or lever of the rheostat is placed in a certain position, as a result of which the desired resistance is introduced into the circuit.
A long conductor of small cross-section creates a high resistance to current. Short conductors of large cross-section have little resistance to current.
If we take two conductors from different materials, but of the same length and section, then the conductors will conduct current in different ways. This shows that the resistance of a conductor depends on the material of the conductor itself.
The temperature of a conductor also affects its resistance. As the temperature rises, the resistance of metals increases, and the resistance of liquids and coal decreases. Only some special metal alloys (manganin, constantan, nickeline and others) almost do not change their resistance with increasing temperature.
So, we see that the electrical resistance of the conductor depends on: 1) the length of the conductor, 2) the cross section of the conductor, 3) the material of the conductor, 4) the temperature of the conductor.
The unit of resistance is one ohm. Om is often denoted by the Greek capital letter Ω (omega). So instead of writing "The resistance of the conductor is 15 ohms", you can simply write: r= 15Ω.
1000 ohm is called 1 kiloohm(1kΩ, or 1kΩ),
1,000,000 ohms is called 1 megaohm(1mgOhm, or 1MΩ).
When comparing the resistance of conductors from different materials, it is necessary to take a certain length and section for each sample. Then we will be able to judge which material conducts electric current better or worse.
Video 1. Conductor resistance
Specific electrical resistance
The resistance in ohms of a conductor 1 m long, with a cross section of 1 mm² is called resistivity and is denoted by the Greek letter ρ (ro).
Table 1 gives the specific resistances of some conductors.
Table 1
Resistivity of various conductors
The table shows that an iron wire with a length of 1 m and a cross section of 1 mm² has a resistance of 0.13 ohms. To get 1 ohm of resistance, you need to take 7.7 m of such 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 precludes its widespread use. After silver in the table comes copper: 1 m of copper wire with a cross section of 1 mm² has a resistance of 0.0175 ohms. To get a resistance of 1 ohm, you need to take 57 m of such wire.
Chemically pure, obtained by refining, copper has found widespread use in electrical engineering for the manufacture of wires, cables, windings of electrical machines and apparatus. Aluminum and iron are also widely used as conductors.
The resistance of a conductor can be determined by the formula:
Where r- conductor resistance in ohms; ρ - specific resistance of the conductor; l is the length of the conductor in m; S– conductor cross-section in mm².
Example 1 Determine the resistance of 200 m of iron wire with a cross section of 5 mm².
Example 2 Calculate the resistance of 2 km of aluminum wire with a cross section of 2.5 mm².
From the resistance formula, you can easily determine the length, resistivity and cross section of the conductor.
Example 3 For a radio receiver, it is necessary to wind a resistance of 30 ohms from nickel wire with a cross section of 0.21 mm². Determine the required wire length.
Example 4 Determine the cross section of 20 m of nichrome wire if its resistance is 25 ohms.
Example 5 A wire with a cross section of 0.5 mm² and a length of 40 m has a resistance of 16 ohms. Determine the material of the wire.
The material of a conductor characterizes its resistivity.
According to the table of resistivity, we find that lead has such resistance.
It was stated above that the resistance of conductors depends on temperature. Let's do the following experiment. We wind several meters of thin metal wire in the form of a spiral and turn this spiral into a battery circuit. To measure the current in the circuit, turn on the ammeter. When heating the spiral in the flame of the burner, you can notice that the ammeter readings will decrease. This shows that the resistance of the metal wire increases with heating.
For some metals, when heated by 100 °, the resistance increases by 40 - 50%. There are alloys that slightly change their resistance with heat. Some special alloys hardly change resistance with temperature. 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 temperature changes is used to construct resistance thermometers. Such a 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 the conductor when it is heated, per 1 ohm of the initial resistance and 1 ° temperature, is called temperature coefficient of resistance and is denoted by the letter α.
If at a temperature t 0 conductor resistance is r 0 , and at temperature t equals r t, then the temperature coefficient of resistance
Note. This formula can only be calculated within a certain temperature range (up to about 200°C).
We give the values of the temperature coefficient of resistance α for some metals (table 2).
table 2
Temperature coefficient values for some metals
From the formula for the temperature coefficient of resistance, we determine r t:
r t = r 0 .
Example 6 Determine the resistance of an iron wire heated to 200°C if its resistance at 0°C was 100 ohms.
r t = r 0 = 100 (1 + 0.0066 × 200) = 232 ohms.
Example 7 A resistance thermometer made of platinum wire in a room with a temperature of 15°C had a resistance of 20 ohms. The thermometer was placed in the furnace and after a while its resistance was measured. It turned out to be equal to 29.6 ohms. Determine the temperature in the oven.
electrical conductivity
Until now, we have considered the resistance of the conductor as an obstacle that the conductor provides to the electric current. However, current flows through the conductor. Therefore, in addition to resistance (obstacles), the conductor also has the ability to conduct electric current, that is, conductivity.
The more resistance a conductor has, the less conductivity it has, the worse it conducts electric current, and, conversely, the lower the resistance of a conductor, the more conductivity it has, the easier it is for current to pass through the conductor. Therefore, the resistance and conductivity of the conductor are reciprocal quantities.
It is known from mathematics that the reciprocal of 5 is 1/5 and, conversely, the reciprocal 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 denoted by the letter g.
Electrical conductivity is measured in (1/ohm) or siemens.
Example 8 Conductor resistance is 20 ohms. Determine its conductivity.
If r= 20 Ohm, then
Example 9 Conductor conductivity is 0.1 (1/ohm). Determine its resistance
If g \u003d 0.1 (1 / Ohm), then r= 1 / 0.1 = 10 (ohm)
Content:The resistivity of metals is their ability to resist the electric current passing through them. The unit of measurement of this value is Ohm * m (Ohm-meter). The Greek letter ρ (rho) is used as a symbol. High resistivity means poor electrical charge conduction by a particular material.
Steel Specifications
Before considering in detail the resistivity of steel, you should familiarize yourself with its basic physical and mechanical properties. Due to its qualities, this material is widely used in the manufacturing sector and other areas of people's lives and activities.
Steel is an alloy of iron and carbon, contained in an amount not exceeding 1.7%. In addition to carbon, steel contains a certain amount of impurities - silicon, manganese, sulfur and phosphorus. In terms of its qualities, it is much better than cast iron, it is easily hardened, forged, rolled and other types of processing. All types of steels are characterized by high strength and ductility.
According to its purpose, steel is divided into structural, tool, and also with special physical properties. Each of them contains a different amount of carbon, due to which the material acquires certain specific qualities, for example, heat resistance, heat resistance, resistance to rust and corrosion.
A special place is occupied by electrical steels produced in sheet format and used in the manufacture of electrical products. To obtain this material, doping with silicon is performed, which can improve its magnetic and electrical properties.
In order for electrical steel to acquire the necessary characteristics, certain requirements and conditions must be met. The material should be easily magnetized and remagnetized, that is, have a high magnetic permeability. Such steels have good, and their magnetization reversal is carried out with minimal losses.
The dimensions and mass of magnetic cores and windings, as well as the efficiency of transformers and their operating temperature, depend on compliance with these requirements. The fulfillment of the conditions is influenced by many factors, including the resistivity of steel.
Resistivity and other indicators
The electrical resistivity value is the ratio of the electric field strength in the metal and the current density flowing in it. For practical calculations, the formula is used: in which ρ is the resistivity of the metal (Ohm * m), E- electric field strength (V/m), and J- the density of the electric current in the metal (A / m 2). With a very high electric field strength and low current density, the resistivity of the metal will be high.
There is another quantity called electrical conductivity, the inverse of resistivity, indicating the degree of conductivity of electric current by a particular material. It is determined by the formula and is expressed in units of Sm / m - Siemens per meter.
Resistivity is closely related to electrical resistance. However, they have differences among themselves. In the first case, this is a property of the material, including steel, and in the second case, the property of the entire object is determined. The quality of a resistor is influenced by a combination of several factors, primarily the shape and resistivity of the material from which it is made. For example, if a thin and long wire was used to make a wire resistor, then its resistance will be greater than that of a resistor made from a thick and short wire of the same metal.
Another example is wire resistors of the same diameter and length. However, if in one of them the material has a high resistivity, and in the other it is low, then, accordingly, the electrical resistance in the first resistor will be higher than in the second.
Knowing the basic properties of the material, you can use the resistivity of steel to determine the resistance value of the steel conductor. For calculations, in addition to electrical resistivity, the diameter and length of the wire itself will be required. Calculations are performed according to the following formula: , in which R is (Ohm), ρ - resistivity of steel (Ohm * m), L- corresponds to the length of the wire, A- area of its cross section.
There is a dependence of the resistivity of steel and other metals on temperature. In most calculations, room temperature is used - 20 0 C. All changes under the influence of this factor are taken into account using the temperature coefficient.
- conductors;
- dielectrics (with insulating properties);
- semiconductors.
Electrons and current
At the heart of the modern concept of electric current is the assumption that it consists of material particles - charges. But various physical and chemical experiments give grounds to assert that these charge carriers can be of different types in the same conductor. And this inhomogeneity of the particles affects the current density. For calculations that are related to the parameters of the electric current, certain physical quantities are used. Among them, an important place is occupied by conductivity along with resistance.
- Conductivity is related to resistance by a mutual inverse relationship.
It is known that when there is a certain voltage applied to an electric circuit, an electric current appears in it, the value of which is related to the conductivity of this circuit. This fundamental discovery was made at the time by the German physicist Georg Ohm. Since then, a law called Ohm's law has been in use. It exists for different circuit options. Therefore, the formulas for them may be different from each other, since they correspond to completely different conditions.
Every electrical circuit has a conductor. If it contains one type of charge carrier particles, the current in the conductor is like a fluid flow that has a certain density. It is determined by the following formula:
Most metals correspond to the same type of charged particles, due to which there is an electric current. For metals, the calculation of electrical conductivity is carried out according to the following formula:
Since the conductivity can be calculated, it is now easy to determine the electrical resistivity. It has already been mentioned above that the resistivity of a conductor is the reciprocal of conductivity. Hence,
In this formula, the Greek letter ρ (rho) is used to denote electrical resistivity. This designation is most often used in technical literature. However, you can also find slightly different formulas with the help of which the resistivity of conductors is calculated. If the classical theory of metals and electronic conductivity in them are used for calculations, the resistivity is calculated by the following formula:
However, there is one "but". The state of atoms in a metal conductor is affected by the duration of the ionization process, which is carried out by an electric field. With a single ionizing effect on the conductor, the atoms in it will receive a single ionization, which will create a balance between the concentration of atoms and free electrons. And the values of these concentrations will be equal. In this case, the following dependencies and formulas take place:
Conductivity and resistance deviations
Next, we consider what determines the specific conductivity, which is inversely related to resistivity. The resistivity of a substance is a rather abstract physical quantity. Each conductor exists in the form of a specific sample. It is characterized by the presence of various impurities and defects in the internal structure. They are taken into account as separate terms in the expression that determines the resistivity in accordance with the Matthiessen rule. This rule also takes into account the scattering of a moving electron stream on the nodes of the crystal lattice of the sample that fluctuate depending on the temperature.
The presence of internal defects, such as inclusions of various impurities and microscopic voids, also increases the resistivity. To determine the amount of impurities in the samples, the resistivity of the materials is measured for two temperature values of the sample material. One temperature value is room temperature, and the other corresponds to liquid helium. From the ratio of the measurement result at room temperature to the result at liquid helium temperature, a coefficient is obtained that illustrates the structural perfection of the material and its chemical purity. The coefficient is denoted by the letter β.
If a metal alloy with a disordered solid solution structure is considered as a conductor of electric current, the value of the residual resistivity can be significantly greater than the resistivity. Such a feature of two-component metal alloys that are not related to rare earth elements, as well as to transition elements, is covered by a special law. It is called Nordheim's law.
Modern technologies in electronics are increasingly moving towards miniaturization. And so much so that the word "nanocircuit" will soon appear instead of a microcircuit. The conductors in such devices are so thin that it would be correct to call them metal films. It is quite clear that the film sample with its resistivity will differ upwards from the larger conductor. The small thickness of the metal in the film leads to the appearance of semiconductor properties in it.
The proportionality between the thickness of the metal and the free path of electrons in this material begins to appear. There is little room for electrons to move. Therefore, they begin to prevent each other from moving in an orderly manner, which leads to an increase in resistivity. For metal films, the resistivity is calculated using a special formula obtained from experiments. The formula is named after Fuchs, a scientist who studied the resistivity of films.
Films are very specific formations that are difficult to repeat so that the properties of several samples are the same. For acceptable accuracy in the evaluation of films, a special parameter is used - the specific surface resistance.
Resistors are formed from metal films on the microcircuit substrate. For this reason, resistivity calculations are a highly demanded task in microelectronics. The value of resistivity, obviously, is influenced by temperature and is related to it by a direct proportionality dependence. For most metals, this dependence has a certain linear section in a certain temperature range. In this case, the resistivity is determined by the formula:
In metals, electric current arises due to the large number of free electrons, the concentration of which is relatively high. Moreover, electrons also determine the high thermal conductivity of metals. For this reason, a connection has been established between the electrical conductivity and thermal conductivity by a special law, which was substantiated experimentally. This Wiedemann-Franz law is characterized by the following formulas:
Tempting prospects for superconductivity
However, the most amazing processes occur at the lowest technically achievable temperature of liquid helium. Under such cooling conditions, all metals practically lose their resistivity. Copper wires cooled to the temperature of liquid helium are capable of conducting currents that are many times greater than under normal conditions. If in practice this became possible, the economic effect would be invaluable.
Even more surprising was the discovery of high-temperature conductors. These varieties of ceramics under normal conditions were very far in their resistivity from metals. But at a temperature of about three dozen degrees above liquid helium, they became superconductors. The discovery of this behavior of non-metallic materials has become a powerful stimulus for research. Due to the enormous economic consequences of the practical application of superconductivity, very significant financial resources were thrown into this direction, and large-scale research began.
But for now, as they say, “things are still there” ... Ceramic materials turned out to be unsuitable for practical use. The conditions for maintaining the state of superconductivity required such large expenses that all the benefits from its use were destroyed. But experiments with superconductivity continue. There is progress. Superconductivity has already been obtained at a temperature of 165 degrees Kelvin, but this requires high pressure. The creation and maintenance of such special conditions again denies the commercial use of this technical solution.
Additional Influencing Factors
At present, everything continues to go its own way, and for copper, aluminum and some other metals, the resistivity continues to provide their industrial use for the manufacture of wires and cables. In conclusion, it is worth adding some more information that not only the resistivity of the conductor material and the ambient temperature affect the losses in it during the passage of an electric current. The geometry of the conductor is very significant when using it at an increased voltage frequency and at high current strength.
Under these conditions, electrons tend to concentrate near the surface of the wire, and its thickness as a conductor loses its meaning. Therefore, it is possible to justifiably reduce the amount of copper in the wire by making only the outer part of the conductor from it. Another factor in increasing the resistivity of a conductor is deformation. Therefore, despite the high performance of some electrically conductive materials, under certain conditions they may not appear. It is necessary to choose the right conductors for specific tasks. The tables below will help you with this.
We know that the cause of the electrical resistance of a conductor is the interaction of electrons with ions of the metal crystal lattice (§ 43). Therefore, it can be assumed that the resistance of a conductor depends on its length and cross-sectional area, as well as on the substance from which it is made.
Figure 74 shows the setup for such an experiment. Various conductors are included in turn in the current source circuit, for example:
- Nickel wires of the same thickness, but different lengths;
- Nickel wires of the same length, but different thicknesses (different cross-sectional area);
- nickel and nichrome wires of the same length and thickness.
The current in the circuit is measured with an ammeter, the voltage with a voltmeter.
Knowing the voltage at the ends of the conductor and the strength of the current in it, according to Ohm's law, you can determine the resistance of each of the conductors.
Rice. 74. Dependence of the resistance of a conductor on its size and type of substance
Having carried out these experiments, we will establish that:
- of two nickel-plated wires of the same thickness, the longer wire has the greater resistance;
- of two nickel wires of the same length, the wire with the smaller cross section has the greater resistance;
- nickel and nichrome wires of the same size have different resistance.
The dependence of the resistance of a conductor on its dimensions and the substance from which the conductor is made was first studied by Ohm in experiments. He found that resistance is directly proportional to the length of the conductor, inversely proportional to its cross-sectional area and depends on the substance of the conductor.
How to take into account the dependence of resistance on the substance from which the conductor is made? For this, the so-called resistivity of matter.
Resistivity is a physical quantity that determines the resistance of a conductor made of a given substance, 1 m long, with a cross-sectional area of 1 m 2.
Let's introduce letter designations: ρ - specific resistance of the conductor, I - length of the conductor, S - area of its cross section. Then the resistance of the conductor R is expressed by the formula
From it we get that:
From the last formula, you can determine the unit of resistivity. Since the unit of resistance is 1 ohm, the unit of cross-sectional area is 1 m2, and the unit of length is 1 m, then the unit of resistivity is:
It is more convenient to express the cross-sectional area of \u200b\u200bthe conductor in square millimeters, since it is most often small. Then the unit of resistivity will be:
Table 8 shows the resistivity values of some substances at 20 °C. Resistivity changes with temperature. Empirically, it was found that in metals, for example, the resistivity increases with increasing temperature.
Table 8. Electrical resistivity of some substances (at t = 20 °C)
Of all metals, silver and copper have the lowest resistivity. Therefore, silver and copper are the best conductors of electricity.
When wiring electrical circuits, aluminum, copper and iron wires are used.
In many cases, devices with high resistance are needed. They are made from specially created alloys - substances with high resistivity. For example, as can be seen from table 8, the nichrome alloy has a resistivity almost 40 times greater than aluminum.
Porcelain and ebonite have such a high resistivity that they almost do not conduct electricity at all, they are used as insulators.
Questions
- How does the resistance of a conductor depend on its length and on the cross-sectional area?
- How to show experimentally the dependence of the resistance of a conductor on its length, cross-sectional area and the substance from which it is made?
- What is the specific resistance of a conductor?
- What formula can be used to calculate the resistance of conductors?
- What is the unit of resistivity of a conductor?
- What materials are the conductors used in practice made of?
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. A 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.
