Specific resistance of aluminum wire. Aluminum resistivity

Every substance is capable of conducting current varying degrees, this value is affected by the resistance of the material. The resistivity of copper, aluminum, steel and any other element is denoted by the letter ρ of the Greek alphabet. This value does not depend on such characteristics of the conductor as size, shape and physical state, ordinary electrical resistance takes these parameters into account. Resistivity is measured in Ohms multiplied by mm² and divided by meter.

Categories and their descriptions

Any material is capable of exhibiting two types of resistance depending on the electricity supplied to it. The current can be variable or constant, which significantly affects the technical performance of the substance. So, there are such resistances:

1. Ohmic. Appears under the influence of direct current. Characterizes friction, which is created by the movement of electrically charged particles in a conductor.
2. Active. Determined according to the same principle, but created under the influence alternating current.

In this regard, there are also two definitions of specific value. For direct current, it is equal to the resistance exerted by a unit length of conductive material of a unit fixed cross-sectional area. The potential electric field affects all conductors, as well as semiconductors and solutions capable of conducting ions. This value determines the conductive properties of the material itself. The shape of the conductor and its dimensions are not taken into account, so it can be called basic in electrical engineering and materials science.

Subject to passing alternating current specific value calculated taking into account the thickness of the conductive material. Here there is already an impact not only of potential, but also eddy current, in addition, the frequency of electric fields is taken into account. Resistivity of this type more than with DC, since this is where accounting takes place positive value resistance vortex field. Also, this value depends on the shape and size of the conductor itself. It is these parameters that determine the nature of the vortex motion of charged particles.

Alternating current causes certain electromagnetic phenomena. They are very important for the electrical characteristics of the conductive material:

1. The skin effect is characterized by a weakening of the electrical magnetic field the more, the further it penetrates into the medium of the conductor. This phenomenon is also called the surface effect.
2. The proximity effect reduces current density due to the proximity of adjacent wires and their influence.

These effects are very important when calculating the optimal thickness of the conductor, since when using a wire whose radius is greater than the depth of current penetration into the material, the rest of its mass will remain unused, and therefore this approach will be ineffective. In accordance with the calculations carried out, the effective diameter of the conductive material in some situations will be as follows:

• for a current of 50 Hz - 2.8 mm;
• 400 Hz - 1 mm;
• 40 kHz - 0.1 mm.

In view of this, the use of flat multicore cables, consisting of many thin wires, is actively used for high-frequency currents.

Characteristics of metals

Specific indicators of metal conductors are contained in special tables. Using these data, you can make the necessary further calculations. An example of such a resistivity table can be seen in the image.

The table shows that silver has the greatest conductivity - it is an ideal conductor among all existing metals and alloys. If you calculate how much wire from this material is required to obtain a resistance of 1 ohm, you will get 62.5 m. Iron wire for the same value will require as much as 7.7 m.

Whatever remarkable properties no matter what silver has, it is too expensive a material for mass use in electrical networks, therefore copper has found wide application in everyday life and industry. In terms of specific indicator, it is in second place after silver, and in terms of prevalence and ease of extraction, it is much better than it. Copper has other advantages that have allowed it to become the most common conductor. These include:

For use in electrical engineering, refined copper is used, which, after smelting from sulfide ore, goes through the processes of roasting and blowing, and then necessarily undergoes electrolytic purification. After such processing, it is possible to obtain a material that is very High Quality(grades M1 and M0), which will contain from 0.1 to 0.05% impurities. An important nuance is the presence of oxygen in extremely small quantities, since it negatively affects the mechanical characteristics of copper.

Often this metal is replaced by cheaper materials - aluminum and iron, as well as various bronzes (alloys with silicon, beryllium, magnesium, tin, cadmium, chromium and phosphorus). Such compositions have higher strength compared to pure copper, although they have lower conductivity.

Advantages of aluminum

Although aluminum is more resistant and more fragile, its widespread use is due to the fact that it is not as scarce as copper and therefore costs less. The resistivity of aluminum is 0.028, and its low density provides it with a weight 3.5 times less than copper.

For electrical work use purified aluminum grade A1, containing no more than 0.5% impurities. The higher grade AB00 is used for the manufacture of electrolytic capacitors, electrodes and aluminum foil. The impurity content in this aluminum is no more than 0.03%. There is also pure metal AB0000, including no more than 0.004% additives. The impurities themselves also matter: nickel, silicon and zinc have a slight effect on the conductivity of aluminum, and the content of copper, silver and magnesium in this metal has a noticeable effect. Thallium and manganese reduce conductivity the most.

Aluminum has good anti-corrosion properties. Upon contact with air, it becomes covered with a thin film of oxide, which protects it from further destruction. For improvement mechanical characteristics the metal is alloyed with other elements.

Indicators of steel and iron

The resistivity of iron compared to copper and aluminum is very high performance However, due to its availability, strength and resistance to deformation, the material is widely used in electrical production.

Although iron and steel, whose resistivity is even higher, have significant disadvantages, manufacturers of conductor materials have found methods to compensate for them. In particular, low corrosion resistance is overcome by coating the steel wire with zinc or copper.

Properties of sodium

Sodium metal is also very promising in conductor production. In terms of resistance, it significantly exceeds copper, but has a density 9 times less than that. This allows the material to be used in the manufacture of ultra-light wires.

Sodium metal is very soft and completely unstable to any kind of deformation, which makes its use problematic - a wire made of this metal must be covered with a very strong sheath with extremely little flexibility. The shell must be sealed, since sodium exhibits strong chemical activity under the most neutral conditions. It instantly oxidizes in air and exhibits a violent reaction with water, including water contained in the air.

Another benefit of using sodium is its availability. It can be obtained through the electrolysis of molten sodium chloride, of which there is an unlimited amount in the world. Other metals are clearly inferior in this regard.

To calculate the performance of a specific conductor, it is necessary to divide the product of the specific number and length of the wire by its cross-sectional area. The result will be the resistance value in Ohms. For example, to determine the resistance of 200 m of iron wire with a nominal cross-section of 5 mm², you need to multiply 0.13 by 200 and divide the result by 5. The answer is 5.2 Ohms.

Rules and features of calculation

Microohmmeters are used to measure the resistance of metallic media. Today they are produced in a digital version, so the measurements taken with their help are accurate. It can be explained by the fact that metals have high level conductivity and have extremely low resistance. For example, the lower threshold of measuring instruments has a value of 10 -7 Ohms.

Using microohmmeters, you can quickly determine how good the contact is and what resistance is exhibited by the windings of generators, electric motors and transformers, as well as electrical buses. It is possible to calculate the presence of inclusions of another metal in the ingot. For example, a piece of tungsten plated with gold exhibits half the conductivity of all gold. The same method can be used to determine internal defects and cavities in the conductor.

The resistivity formula is as follows: ρ = Ohm mm 2 /m. In words it can be described as the resistance of 1 meter of conductor, having a cross-sectional area of ​​1 mm². The temperature is assumed to be standard - 20 °C.

Effect of temperature on measurement

Heating or cooling of some conductors has a significant effect on the performance of measuring instruments. An example is the following experiment: it is necessary to connect a spirally wound wire to the battery and connect an ammeter to the circuit.

The more the conductor heats up, the lower the readings on the device become. The current has the opposite proportional dependence from resistance. Therefore, we can conclude that as a result of heating, the conductivity of the metal decreases. To a greater or lesser extent, all metals behave this way, but in some alloys there is practically no change in conductivity.

It is noteworthy that liquid conductors and some solid nonmetals tend to decrease their resistance as temperature increases. But scientists have also turned this ability of metals to their advantage. Knowing the temperature coefficient of resistance (α) when heating some materials, it is possible to determine the external temperature. For example, a platinum wire placed on a mica frame is placed in a furnace and the resistance is measured. Depending on how much it has changed, a conclusion is drawn about the temperature in the oven. This design is called a resistance thermometer.

If at temperature t 0 conductor resistance is r 0, and at temperature t equals rt, then the temperature coefficient of resistance is equal to

Calculation using this formula can only be done in a certain temperature range (up to approximately 200 °C).

Most laws of physics are based on experiments. The names of the experimenters are immortalized in the names of these laws. One of them was Georg Ohm.

Georg Ohm's experiments

He established during experiments on the interaction of electricity with various substances, including metals fundamental relationship density, electric field strength and properties of the substance, which is called “specific conductivity”. The formula corresponding to this pattern, called “Ohm’s Law,” is as follows:

j= λE , wherein

• j— electric current density;
• λ — specific conductivity, also called “electrical conductivity”;
• E – electric field strength.

In some cases, to indicate conductivity another letter of the Greek alphabet is used - σ . Specific conductivity depends on certain parameters of the substance. Its value is influenced by temperature, substances, pressure, if it is a gas, and most importantly, the structure of this substance. Ohm's law is observed only for homogeneous substances.

For more convenient calculations, the reciprocal of specific conductivity is used. It is called “specific resistance”, which is also related to the properties of the substance in which it flows. electricity, denoted Greek letter ρ and has the dimension Ohm*m. But since for different physical phenomena different ones apply theoretical justifications, alternative formulas may be used for resistivity. They are a reflection of the classic electron theory metals, as well as quantum theory.

Formulas

In these formulas, which are tedious for ordinary readers, factors such as Boltzmann constant, Avogadro's constant and Planck's constant. These constants are used for calculations that take into account the free path of electrons in a conductor, their speed during thermal movement, the degree of ionization, concentration and density of the substance. In short, everything is quite complicated for a non-specialist. In order not to be unfounded, below you can familiarize yourself with how everything actually looks:

Features of metals

Since the movement of electrons depends on the homogeneity of the substance, the current in a metal conductor flows according to its structure, which affects the distribution of electrons in the conductor, taking into account its heterogeneity. It is determined not only by the presence of impurity inclusions, but also by physical defects - cracks, voids, etc. The heterogeneity of the conductor increases its resistivity, which is determined by Matthiesen's rule.

This easy-to-understand rule essentially says that several separate resistivities can be distinguished in a current-carrying conductor. And the resulting value will be their sum. The terms will be the resistivity crystal lattice metal, impurities and conductor defects. Since this parameter depends on the nature of the substance, corresponding laws have been defined to calculate it, including for mixed substances.

Despite the fact that alloys are also metals, they are considered as solutions with a chaotic structure, and for calculating the resistivity, it matters which metals are included in the alloy. Basically, most alloys of two components that do not belong to transition, as well as rare earth metals fall under the description of Nodheim's law.

How separate topic The resistivity of metal thin films is considered. It is quite logical to assume that its value should be greater than that of a bulk conductor made of the same metal. But at the same time, a special empirical formula Fuchs, which describes the interdependence of resistivity and film thickness. It turns out that metals in films exhibit semiconductor properties.

And the process of charge transfer is influenced by electrons, which move in the direction of the film thickness and interfere with the movement of “longitudinal” charges. At the same time, they are reflected from the surface of the film conductor, and thus one electron oscillates between its two surfaces for quite a long time. Another significant factor in increasing resistivity is the temperature of the conductor. The higher the temperature, the greater the resistance. Conversely, the lower the temperature, the lower the resistance.

Metals are the substances with the lowest resistivity at so-called “room” temperature. The only non-metal that justifies its use as a conductor is carbon. Graphite, which is one of its varieties, is widely used for making sliding contacts. It has a very successful combination of properties such as resistivity and sliding friction coefficient. Therefore, graphite is an indispensable material for electric motor brushes and other sliding contacts. The resistivity values ​​of the main substances used for industrial purposes are given in the table below.

Superconductivity

At temperatures corresponding to the liquefaction of gases, that is, up to the temperature of liquid helium, which is equal to -273 degrees Celsius, the resistivity decreases almost to complete disappearance. And not just good metal conductors such as silver, copper and aluminum. Almost all metals. Under such conditions, which are called superconductivity, the structure of the metal has no inhibitory effect on the movement of charges under the influence of an electric field. Therefore, mercury and most metals become superconductors.

But, as it turned out, relatively recently in the 80s of the 20th century, some types of ceramics are also capable of superconductivity. Moreover, you do not need to use liquid helium for this. Such materials were called high-temperature superconductors. However, several decades have already passed, and the range of high-temperature conductors has expanded significantly. But mass use of such high-temperature superconducting elements has not been observed. In some countries, single installations have been made with the replacement of conventional copper conductors with high-temperature superconductors. To maintain normal routine high temperature superconductivity necessary a liquid nitrogen. And this turns out to be a too expensive technical solution.

Therefore, the low resistivity value given by Nature to copper and aluminum still makes them irreplaceable materials for the manufacture of various electrical conductors.

Electric current occurs as a result of closing a circuit with a potential difference across the terminals. Field forces act on free electrons and they move along the conductor. During this journey, electrons meet atoms and transfer some of their accumulated energy to them. As a result, their speed decreases. But, due to the influence of the electric field, it is gaining momentum again. Thus, electrons constantly experience resistance, which is why the electric current heats up.

The property of a substance to convert electricity into heat when exposed to current is electrical resistance and is denoted as R, its measuring unit is Om. The amount of resistance depends mainly on the ability various materials conduct current.
For the first time, the German researcher G. Ohm spoke about resistance.

In order to find out the dependence of current on resistance, famous physicist conducted many experiments. For experiments he used various conductors and obtained various indicators.
The first thing that G. Ohm determined was that the resistivity depends on the length of the conductor. That is, if the length of the conductor increased, the resistance also increased. As a result, this relationship was determined to be directly proportional.

The second relationship is area cross section. It could be determined by cross-sectioning the conductor. The area of ​​the figure formed on the cut is the cross-sectional area. Here the relationship is inversely proportional. That is, the larger the cross-sectional area, the lower the conductor resistance became.

And the third, important quantity on which resistance depends is the material. As a result of the fact that Om used various materials in experiments, he discovered various properties resistance. All these experiments and indicators were summarized in a table from which it can be seen different meaning specific resistance of various substances.

It is known that the best conductors are metals. Which metals are the best conductors? The table shows that copper and silver have the least resistance. Copper is used more often due to its lower cost, and silver is used in the most important and critical devices.

Substances with high resistivity in the table do not conduct electricity well, which means they can be excellent insulating materials. Substances that have this property to the greatest extent, this is porcelain and ebonite.

In general, specific electrical resistance is very important factor, after all, by determining its indicator, we can find out what substance the conductor is made of. To do this, you need to measure the cross-sectional area, find out the current using a voltmeter and ammeter, and also measure the voltage. This way we will find out the value of the resistivity and, using the table, we can easily identify the substance. It turns out that resistivity is like a substance's fingerprint. In addition, resistivity is important when planning long electrical circuits: we need to know this indicator in order to maintain a balance between length and area.

There is a formula that determines that resistance is 1 ohm if, at a voltage of 1V, its current is 1A. That is, the resistance of a unit area and a unit length made of a certain substance and there is specific resistance.

It should also be noted that the resistivity indicator directly depends on the frequency of the substance. That is, whether it has impurities. However, adding just one percent of manganese increases the resistance of the most conductive substance, copper, by three times.

This table shows the electrical resistivity of some substances.

Highly conductive materials

Copper
As we have already said, copper is most often used as a conductor. This is explained not only by its low resistance. Copper has the advantages of high strength, corrosion resistance, ease of use and good machinability. Good brands copper is considered M0 and M1. The amount of impurities in them does not exceed 0.1%.

The high cost of the metal and its predominance in Lately scarcity encourages manufacturers to use aluminum as a conductor. Also, alloys of copper with various metals are used.
Aluminum
This metal is much lighter than copper, but aluminum has large values heat capacity and melting point. In this regard, in order to bring it to a molten state, more energy is required than copper. However, the fact of copper deficiency must be taken into account.
In the production of electrical products, as a rule, A1 grade aluminum is used. It contains no more than 0.5% impurities. And metal highest frequency- this is aluminum grade AB0000.
Iron
The cheapness and availability of iron is overshadowed by its high resistivity. In addition, it corrodes quickly. For this reason, steel conductors are often coated with zinc. The so-called bimetal is widely used - this is steel coated with copper for protection.
Sodium
Sodium is also an accessible and promising material, but its resistance is almost three times that of copper. In addition, metallic sodium has high chemical activity, which requires covering such a conductor with hermetically sealed protection. It should also protect the conductor from mechanical damage, since sodium is a very soft and rather fragile material.

Superconductivity
The table below shows the resistivity of substances at a temperature of 20 degrees. The indication of temperature is not accidental, because resistivity directly depends on this indicator. This is explained by the fact that when heated, the speed of atoms also increases, which means the probability of them meeting electrons will also increase.

It is interesting what happens to resistance under cooling conditions. For the first time, the behavior of atoms at very low temperatures noted by G. Kamerlingh Onnes in 1911. He cooled the mercury wire to 4K and found that its resistance dropped to zero. The change in the resistivity index of some alloys and metals under low temperature conditions is called superconductivity by the physicist.

Superconductors go into a state of superconductivity when cooled, and, at the same time, their optical and structural characteristics don't change. The main discovery is that electrical and magnetic properties metals in a superconducting state are very different from their properties in the normal state, as well as from the properties of other metals that cannot transition to this state when the temperature decreases.
The use of superconductors is carried out mainly in obtaining an ultra-strong magnetic field, the strength of which reaches 107 A/m. Superconducting power line systems are also being developed.

Similar materials.

In practice, it is often necessary to calculate the resistance of various wires. This can be done using formulas or using the data given in table. 1.

The effect of the conductor material is taken into account using the resistivity, denoted by the Greek letter? and having a length of 1 m and a cross-sectional area of ​​1 mm2. Lowest resistivity? = 0.016 Ohm mm2/m has silver. Let us give the average value of the resistivity of some conductors:

At various quantities impurities and different ratios components included in rheostatic alloys, the resistivity may change slightly.

Resistance is calculated using the formula:

where R is resistance, Ohm; resistivity, (Ohm mm2)/m; l - wire length, m; s - cross-sectional area of ​​the wire, mm2.

If the wire diameter d is known, then its cross-sectional area is equal to:

It is best to measure the diameter of the wire using a micrometer, but if you don’t have one, you should wind 10 or 20 turns of wire tightly onto a pencil and measure the length of the winding with a ruler. Dividing the length of the winding by the number of turns, we find the diameter of the wire.

To determine the length of a wire of a known diameter made of a given material necessary to obtain the required resistance, use the formula

Table 1.

Note. 1. Data for wires not listed in the table should be taken as some average values. For example, for a nickel wire with a diameter of 0.18 mm, we can approximately assume that the cross-sectional area is 0.025 mm2, the resistance of one meter is 18 Ohms, and the permissible current is 0.075 A.

2. For a different value of current density, the data in the last column must be changed accordingly; for example, at a current density of 6 A/mm2, they should be doubled.

Example 1. Find the resistance of 30 m copper wire with a diameter of 0.1 mm.

Solution. We determine according to the table. 1 resistance of 1 m of copper wire, it is equal to 2.2 Ohms. Therefore, the resistance of 30 m of wire will be R = 30 2.2 = 66 Ohms.

Calculation using the formulas gives the following results: cross-sectional area of ​​the wire: s = 0.78 0.12 = 0.0078 mm2. Since the resistivity of copper is 0.017 (Ohm mm2)/m, we get R = 0.017 30/0.0078 = 65.50 m.

Example 2. How much nickel wire with a diameter of 0.5 mm is needed to make a rheostat with a resistance of 40 Ohms?

Solution. According to the table 1, we determine the resistance of 1 m of this wire: R = 2.12 Ohm: Therefore, to make a rheostat with a resistance of 40 Ohms, you need a wire whose length is l = 40/2.12 = 18.9 m.

Let's do the same calculation using the formulas. We find the cross-sectional area of ​​the wire s = 0.78 0.52 = 0.195 mm2. And the length of the wire will be l = 0.195 40/0.42 = 18.6 m.

When closed electrical circuit, at the terminals of which there is a potential difference, an electric current arises. Free electrons influenced electrical forces fields 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 designated 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 denoted in Greek capital letterΩ (omega). Therefore, instead of writing “The conductor resistance is 15 ohms,” you can simply write: r= 15 Ω.
1,000 ohms is called 1 kiloohms(1kOhm, or 1kΩ),
1,000,000 ohms is called 1 megaohm(1mOhm, or 1MΩ).

When comparing the resistance of conductors from different 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 of copper wire with a cross section of 1 mm² has a resistance of 0.0175 Ohm. To get a resistance of 1 ohm, you need to take 57 m of such wire.

Chemically pure copper, obtained by refining, has found widespread use in electrical engineering for the manufacture of wires, cables, windings of electrical machines and devices. Aluminum and iron are also widely used as conductors.

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 the cross-section of 20 m of nichrome wire if its resistance is 25 Ohms.

Example 5. A wire with a cross section of 0.5 mm² and a length of 40 m has a resistance of 16 Ohms. Determine the wire material.

The material of the conductor characterizes its resistivity.

Using 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 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 passes through the conductor. Therefore, in addition to resistance (obstacle), the conductor also has the ability to conduct electric current, that is, conductivity.

The greater the resistance a conductor has, the less conductivity it has, the worse it conducts electric current, and, conversely, the less less resistance 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)