Appearance electric current occurs when the circuit is closed when a potential difference occurs across the terminals. The movement of free electrons in a conductor is carried out under the influence of an electric field. As they move, electrons collide with atoms and partially transfer their accumulated energy to them. This leads to a decrease in their speed of movement. Subsequently, under the influence of the electric field, the speed of electron movement increases again. The result of this resistance is heating of the conductor through which the current flows. Exist various ways calculations of this value, including the resistivity formula used for materials with individual physical properties.

Electrical resistivity

The essence of electrical resistance lies in the ability of a substance to convert electrical energy into thermal energy during the action of current. This quantity is denoted by the symbol R, and the unit of measurement is Ohm. The value of resistance in each case is associated with the ability of one or another.

During the research, a dependence on resistance was established. One of the main qualities of the material is its resistivity, which varies depending on the length of the conductor. That is, as the length of the wire increases, the resistance value also increases. This dependence is defined as directly proportional.

Another property of a material is its cross-sectional area. It represents the dimensions of the cross section of the conductor, regardless of its configuration. In this case, an inversely proportional relationship is obtained when with increasing cross-sectional area it decreases.

Another factor influencing resistance is the material itself. During research, different resistance was found in different materials. Thus, the electrical resistivity values ​​for each substance were obtained.

It turned out that metals are the best conductors. Among them, silver also has the lowest resistance and high conductivity. They are used in the most critical places electronic circuits Moreover, copper has a relatively low cost.

Substances whose resistivity is very high are considered poor conductors of electric current. Therefore they are used as insulating materials. Dielectric properties are most characteristic of porcelain and ebonite.

Thus, the resistivity of a conductor is of great importance because it can be used to determine the material from which the conductor was made. To do this, the cross-sectional area is measured, the current and voltage are determined. This allows you to set the value of the electrical resistivity, after which, using a special table, you can easily determine the substance. Consequently, resistivity is one of the most characteristic features of a particular material. This indicator allows you to determine the most optimal length electrical circuit so that balance is maintained.

Formula

Based on the data obtained, we can conclude that resistivity will be considered the resistance of any material with unit area and unit length. That is, a resistance equal to 1 ohm occurs at a voltage of 1 volt and a current of 1 ampere. This indicator is influenced by the degree of purity of the material. For example, if you add just 1% manganese to copper, its resistance will increase 3 times.

Resistivity and conductivity of materials

Conductivity and resistivity are generally considered at a temperature of 20 0 C. These properties will differ for different metals:

• Copper. Most often used for the manufacture of wires and cables. It has high strength, corrosion resistance, easy and simple processing. In good copper, the proportion of impurities is no more than 0.1%. If necessary, copper can be used in alloys with other metals.
• Aluminum. Its specific gravity is lower than that of copper, but it has a higher heat capacity and melting point. Melting aluminum requires significantly more energy than copper. Impurities in high-quality aluminum do not exceed 0.5%.
• Iron. Along with its availability and low cost, this material has high resistivity. In addition, it has low corrosion resistance. Therefore, it is practiced to coat steel conductors with copper or zinc.

The formula for resistivity at low temperatures is considered separately. In these cases, the properties of the same materials will be completely different. For some of them, resistance may drop to zero. This phenomenon is called superconductivity, in which the optical and structural characteristics of the material remain unchanged.

The effect of the conductor material is taken into account using resistivity, which is usually denoted by the letter of the Greek alphabet ρ and is conductor resistance cross section 1 mm2 and length 1 m. Silver has the lowest resistivity ρ = 0.016 Ohm.mm2/m. Below are the values resistivity for multiple conductors:

• Cable resistance for silver - 0.016,
• Cable resistance for lead - 0.21,
• Cable resistance for copper - 0.017,
• Cable resistance for nickel - 0.42,
• Cable resistance for aluminum - 0.026,
• Cable resistance for manganin - 0.42,
• Cable resistance for tungsten - 0.055,
• Cable resistance for constantan - 0.5,
• Cable resistance for zinc - 0.06,
• Cable resistance for mercury - 0.96,
• Cable resistance for brass - 0.07,
• Cable resistance for nichrome - 1.05,
• Cable resistance for steel - 0.1,
• Cable resistance for fechral -1.2,
• Cable resistance for phosphor bronze - 0.11,
• Cable resistance for chromal - 1.45

Since alloys contain different amounts of impurities, the resistivity may change.

To calculate the conductor resistance, you can use the conductor resistance calculator.

Cable resistance calculated using the formula below:

R=(ρ?l)/S

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

The cross-sectional area is calculated as follows:

S=(π?d^2)/4=0.78?d^2≈0.8?d^2

• where d is the diameter of the wire.

You can measure the diameter of the wire with a micrometer or caliper, but if you don’t have them on hand, you can tightly wrap about 20 turns of wire around a pen (pencil), then measure the length of the wound wire and divide by the number of turns.

To determine the cable length needed to achieve the required resistance, you can use the formula:

l=(S?R)/ρ

Notes:

1. If the data for the wire is not in the table, then some average value is taken. As an example, a nickel wire with a diameter of 0.18 mm, the cross-sectional area is approximately 0.025 mm2, the resistance of one meter is 18 Ohms, and the permissible current is 0.075 A.

2.The data in the last column, for a different current density, must be changed. For example, with a current density of 6 A/mm2, the value must be doubled.

Example 1. Let's find the resistance of 30 m of copper wire with a diameter of 0.1 mm.

Solution. Using the table, we take the resistance of 1 m of copper wire, which is equal to 2.2 Ohms. This means that the resistance of 30 m of wire will be R = 30.2.2 = 66 Ohms.

The calculation using the formulas will look like this: cross-sectional area: s = 0.78.0.12 = 0.0078 mm2. Since the resistivity of copper is ρ = 0.017 (Ohm.mm2)/m, we get R = 0.017.30/0.0078 = 65.50 m.

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

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

The calculation using the formulas will look like this. Wire cross-sectional area s= 0.78.0.52 = 0.195 mm2. Wire length l = 0.195.40/0.42 = 18.6 m.

In his work, an electrician often encounters the calculation of various quantities and transformations. So, to select the cable correctly, you have to select the required cross-section. The logic for choosing the cross-section is based on the dependence of the resistance on the length of the line and the cross-sectional area of ​​the conductor. In this article we will look at how the resistance of a wire is calculated based on its geometric dimensions.

Formula for calculation

Any calculation begins with a formula. The basic formula for calculating conductor resistance is:

R=(ρ*l)/S

Where R is the resistance in Ohms, ρ is the resistivity, l is the length in m, S is the cross-sectional area of ​​the wire in mm2.

This formula is suitable for calculating the resistance of a wire by cross-section and length. It follows from it that the resistance changes depending on the length; the longer, the greater. And on the contrary, depending on the cross-sectional area, the thicker the wire (large cross-section), the lower the resistance. However, the quantity designated by the letter ρ (Po) remains unclear.

Resistivity

Specific resistance is a tabular value; it is different for each metal. It is needed for calculations and depends on the crystal lattice of the metal and the structure of the atoms.

The table shows that silver has the lowest resistance; for a copper cable it is 0.017 Ohm*mm 2 /m. This dimension tells us how many ohms there are for a cross section of 1 square millimeter and a length of 1 meter.

By the way, silver coating is used in contacts of switching devices, circuit breakers, relays and other things. This reduces, increases service life and reduces. At the same time, gold-plated contacts are used in contacts of measuring and precision equipment due to the fact that they are slightly oxidized or do not oxidize at all.

Aluminum, which was often used in electrical wiring in the past, has a resistance 1.8 times greater than copper, equal to 2.82 * 10 -8 Ohm * mm 2 /m. The greater the resistance of the conductor, the more it heats up. Therefore, with the same cross-section, an aluminum cable can transmit less current than a copper cable, this has become the main reason why all modern electricians use. For nichrome, which is used in heating devices, it is 100 times greater than for copper 1.1 * 10 -6 Ohm * mm 2 /m.

Calculation by diameter

In practice, it often happens that the cross-sectional area of ​​the core is unknown. Without this value nothing can be calculated. To find out, you need to measure the diameter. If the wire is thin, you can take a nail or any other rod, wind 10 turns of wire around it, use a regular ruler to measure the length of the resulting spiral and divide by 10, this way you will find out the diameter.

Well, or just measure it with a caliper. The cross section is calculated using the formula:

Are calculations required?

As we have already said, the cross-section of the wire is selected based on the expected current and the resistance of the metal from which the wires are made. The logic of the choice is as follows: the cross-section is selected in such a way that the resistance at a given length does not lead to significant voltage drops. In order not to carry out a series of calculations, for short lines (up to 10-20 meters) there are fairly accurate tables:

This table shows the typical cross-sectional values ​​of copper and aluminum conductors and the rated currents through them. For convenience, the load power that this line will withstand is indicated. Please note the difference in currents and power at a voltage of 380V; naturally, this assumes a three-phase power supply.

Calculating wire resistance comes down to using a couple of formulas, and you can download ready-made calculators from the Play Market for your smartphone, for example, “Electrodroid” or “Mobile Electrician”. This knowledge will be useful for calculating heating devices, cable lines, fuses and even today's popular coils for electronic cigarettes.

Materials

Electrical resistance is the main characteristic of conductor materials. Depending on the area of ​​application of the conductor, the value of its resistance can play both a positive and negative role in the functioning of the electrical system. Also, the peculiarities of using a conductor may require taking 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 that in this case are the charge carriers. Electrons are in constant, random motion from one atom to another. When an electric field appears (connecting a voltage source to the ends of the metal), the movement of electrons in the conductor becomes ordered. Moving electrons encounter obstacles on their path caused by the peculiarities of the molecular structure of the conductor. When they collide with a structure, charge carriers lose their energy, giving it to the conductor (heating it). The more obstacles a conductive structure creates to charge carriers, the higher the resistance.

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

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

Resistivity

Resistivity is 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-sectional area of ​​the most commonly used cables is relatively small and is measured in mm2. Let's give a simple example.

Task No. 1. Copper wire length L = 20 m, cross-section S = 1.5 mm. sq. Calculate the wire resistance.
Solution: resistivity of copper wire r = 0.018 ohm*mm. sq./m. Substituting the values ​​into formula (1) we get R=0.24 ohms.
When calculating the resistance of the power system, the resistance of one wire must be multiplied by the number of wires.
If instead of copper you use aluminum with a higher resistivity (r = 0.028 ohm * mm sq. / m), then the resistance of the wires will increase accordingly. For the example above, the resistance will be R = 0.373 ohms (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 its obvious high cost. The table below shows the resistance and other basic characteristics of conductor materials.
Table - main characteristics of conductors

Heat losses of wires

If using the cable from the above example to single-phase network 220 V connect a load of 2.2 kW, then current I = P / U or I = 2200/220 = 10 A will flow through the wire. Formula for calculating power losses in the conductor:
Ppr=(I^2)*R (2)
Example No. 2. Calculate active losses when transmitting power of 2.2 kW in a network with a voltage of 220 V for the mentioned wire.
Solution: substituting the values ​​of current and resistance of the wires into formula (2), we obtain Ppr=(10^2)*(2*0.24)=48 W.
Thus, when transmitting energy from the network to the load, 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 heating condition of the conductor (according to the current value), 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.

To reduce active losses in power lines, increased voltage is used. At the same time, the current in the wires decreases, losses fall.

Effect of temperature

An increase in temperature leads to an increase in vibrations of the metal crystal lattice. Accordingly, electrons meet large quantity obstacles, which leads to increased resistance. The magnitude of the “sensitivity” of the metal resistance to an increase in temperature is called the temperature coefficient α. The formula for calculating temperature is as follows
R=Rн*, (3)
where Rн – wire resistance under normal conditions (at temperature t°н); t° is the temperature of the conductor.
Usually t°n = 20° C. The value of α is also indicated for temperature t°n.
Task 4. Calculate the resistance of a copper wire at a temperature t° = 90° C. α copper = 0.0043, Rн = 0.24 Ohm (task 1).
Solution: substituting the values ​​into formula (3) we get R = 0.312 Ohm. The resistance of the heated wire being analyzed is 30% greater than its resistance at room temperature.

Effect of frequency

As the frequency of the current in the conductor increases, 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, at frequency alternating current 20 kHz wire resistance will increase by approximately 10%. Note that high-frequency components can have a current signal from many modern industrial and household consumers (energy-saving lamps, pulsed sources power supply, frequency converters and so on).

Influence of neighboring conductors

There is a magnetic field around any conductor through which current flows. The interaction of the fields of neighboring conductors also causes energy loss and is called the “proximity effect”. Also note that any metal conductor has inductance created by the conductive core and capacitance created by the insulation. These parameters are also characterized by the proximity effect.

Technologies

High voltage wires with zero resistance

This type of wire is widely used in car ignition systems. The resistance of high-voltage wires is quite low and amounts to several fractions of an ohm per meter of length. Let us remember that resistance of this magnitude 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 cores with insulation based on silicone, plastics or other dielectrics. The peculiarity of the use of such wires lies not only in working with high voltage, but also the transfer of energy in a short period of time (pulse mode).

Bimetallic cable

The main area of ​​application 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 on high frequencies Only the surface layer of the conductor is conductive, that is, the inside of the wire can be replaced. This saves expensive material and improves the mechanical characteristics of the wire. Examples of such wires: silver-plated copper, copper-plated steel.

Conclusion

Wire resistance is a value that depends on a group of factors: conductor type, 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: reducing active losses, improving mechanical characteristics, reducing prices.