Resistance of a meter of copper wire. Cable resistance

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

The influence of the conductor material is accounted for using the resistivity, denoted by the Greek letter? and representing a length of 1 m and a cross-sectional area of ​​1 mm2. The lowest resistivity? = 0.016 Ohm mm2 / m silver has. Let us give the average value of the specific resistance of some conductors:

With different amounts of impurities and with different ratios of the components that make up the rheostat alloys, the resistivity may change slightly.

Resistance is calculated by the formula:

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

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

It is best to measure the diameter of the wire with a micrometer, but if it is not there, then you should wind tightly 10 or 20 turns of wire on 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 from a given material, necessary to obtain the desired 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 wire made of nickel with a diameter of 0.18 mm, it can be approximately assumed 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 current density value, 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 a 30 m copper wire with a diameter of 0.1 mm.

Solution. 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 the wire will be R = 30 2.2 = 66 Ohm.

Calculation by the formulas gives the following results: wire cross-sectional area: 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, in order to make a rheostat with a resistance of 40 Ohm, 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.

We know that the cause of the electrical resistance of a conductor is the interaction of electrons with ions of the crystal lattice of the metal (§ 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 the current source circuit in turn, for example:

1. nickel wires of the same thickness but different lengths;
2. nickel wires of the same length, but different thicknesses (different cross-sectional areas);
3. 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 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 performed the indicated experiments, we will establish that:

1. of two nickel wires of the same thickness, the longer wire has more resistance;
2. of two nickelin wires of the same length, a wire with a smaller cross-section has a greater resistance;
3. nickel and nichrome wires of the same size have different resistance.

The dependence of the resistance of a conductor on its size and the substance from which the conductor is made was first studied experimentally by Ohm. 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 substance resistivity.

Resistivity is a physical quantity that determines the resistance of a conductor made of a given substance with a length of 1 m and a cross-sectional area of ​​1 m 2.

Let us introduce letter designations: ρ is the resistivity of the conductor, I is the length of the conductor, S is its cross-sectional area. Then the resistance of the conductor R will be 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 will be:

It is more convenient to express the cross-sectional area of ​​the conductor in square millimeters, since it is usually small. Then the unit of resistivity will be:

Table 8 shows the values ​​of the specific resistance of some substances at 20 ° C. Resistivity changes with temperature. It was experimentally found that in metals, for example, the resistivity increases with increasing temperature.

Table 8. Specific electrical resistance of some substances (at t = 20 ° С)

Of all metals, silver and copper have the lowest resistivity. Hence, 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 of almost 40 times that of aluminum.

Porcelain and ebonite have such a high resistivity that they almost do not conduct electric current at all; they are used as insulators.

Questions

1. How does the resistance of a conductor depend on its length and cross-sectional area?
2. 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?
3. What is called the resistivity of a conductor?
4. What formula can be used to calculate the resistance of the conductors?
5. what units is the resistivity of the conductor expressed in?
6. What substances are used for making conductors used in practice?

When designing electrical circuits, it is important to choose the right material and wire cross-section. Most often, copper is used for these purposes, which has less resistance.

What determines the resistance of the metal

Electric current is the directed movement of charged particles. In metals, these are free electrons. They move between the atoms of the crystal lattice. The resistance to their movement depends on the metal or alloy, as well as its temperature - as it rises, the resistance of the wire to electric current increases.

An exception is made for special alloys used in measuring instruments. Resistors are made of them that do not change their parameters when the temperature changes. In addition, two-wire wires are used to connect thermocouples, the resistance of one of which increases with increasing temperature, and the other decreases. As a result, the parameters of the cable do not change.

Resistivity of various metals

Different metals have different properties and are used for different purposes.

Copper and aluminum

The most common wires are copper and aluminum. Copper has a lower electrical resistance than the resistance of an aluminum wire; cables made of it have a smaller cross-section. It is stronger, which allows the cables to be made thinner, as well as flexible and stranded. In addition, copper is brazed with tin solders.

But aluminum has one advantage: it's much cheaper. Therefore, it is used for winding transformers and routing wiring that does not bend, move, or vibrate.

Other metals

• Gold. It has the lowest electrical resistance, but because of its price it is used only in certain places in military and space technology;
• Silver. It has a better price / quality ratio than gold, but it is also used to a limited extent, mainly for the manufacture of contacts and connectors - it does not oxidize;
• Nichrome (an alloy of nickel and chromium) and fechral (iron, chromium and aluminum). They have a high melting point. The resistance of nichrome and nichrome wire is large enough for the manufacture of heaters and wire resistances;
• Tungsten. It has a high resistivity and is very refractory - 3422 degrees. It is used to make filaments in light bulbs;
• Constantan. An alloy of copper, nickel and manganese, which does not change its properties with changes in temperature. It is used for the manufacture of resistors in measuring instruments;
• Compensatory. These alloys are used to make cables for connecting thermocouples and other sensors. As the temperature rises, the electrical resistance of one conductor increases, while the other decreases. As a result, the overall value remains unchanged.

Interesting. In the 50s, transformers for high-voltage substations with silver windings were designed. Taking into account the reduced losses, this was beneficial. But due to the increase in the price of silver on the world market, these projects were not implemented.

Selection of cable cross-section

When calculating the cross-section of a conductor, heating and voltage drop in long cables are taken into account. You can calculate the resistance of the wire using special tables or using online calculators.

The cross section calculated from losses can be greater or less than that calculated from heating. It depends on the length of the cable. A larger value is selected for the spacer.

Selection of conductor cross-section for permissible heating

When an electric current flows through the cable, it heats up. This heating can melt the insulation, which will lead to its destruction and short-circuit of adjacent wires to each other or to grounded parts of structures.

Important! Destruction of insulation and short circuit (short circuit) may cause fire.

In order to prevent this situation, the cable cross-section must correspond to the load current, the type of insulation and the installation conditions. Open conductors or cables with heat-resistant insulation can carry more current than cables routed through vinyl or rubber sheathed pipes.

Choice of cross-section for voltage losses

When an electric current flows through the cable, the voltage near the load decreases. This is due to the fact that, although the resistance of a small piece of wire and the voltage drop across it are small, over a long length it can reach a significant value.

For example, the specific resistance of a copper wire is 0.017 Ohm mm² / m. But in a single-core cable 100 m long with a cross section of 10 mm², it will be 0.17 Ohm. At a current of 80A (permissible for heating), the voltage drop in the 220V network will be 27V (100 m of the phase wire and 100 m of the zero wire with a drop of 13V in each conductor). Therefore, with a permissible voltage drop of 2% or 5V, the cable cross-section must be no less than 66 mm², or the nearest higher standard value - 75 mm².

If the calculation of the cross-section for heating is carried out according to the operating current of the electric motor and in the section from the input machine to the device, then the calculation of losses must be made according to the starting current, taking into account the entire length of the cables: from the main to the electric machine.

The resistance of a copper wire is a quantity that affects the choice of cables and wires for winding coils when designing electrical circuits, as well as electric motors and transformers. Knowing how to calculate the resistance of a conductor and the necessary formulas will help to correctly design the wiring and avoid emergency situations.

Video

When designing electrical networks in apartments or private houses, the calculation of the cross-section of wires and cables is mandatory. For calculations, indicators such as the value of power consumption and the strength of the current that will pass through the network are used. Resistance is not taken into account due to the short length of cable lines. However, this indicator is necessary with a large length of power lines and voltage drops in different sections. The resistance of the copper wire is of particular importance. These wires are increasingly used in modern networks, so their physical properties must be taken into account when designing.

Concepts and meaning of resistance

The electrical resistance of materials is widely used and taken into account in electrical engineering. This value allows you to establish the basic parameters of wires and cables, especially with a hidden method of laying them. First of all, the exact length of the laid line and the material used to produce the wire are established. Having calculated the initial data, it is quite possible the measured cable.

Compared to conventional electrical wiring, in electronics, resistance parameters are decisive. It is considered and compared in conjunction with other indicators present in electronic circuits. In these cases, an incorrectly selected wire resistance can cause a failure in the operation of all elements of the system. This can happen if you use a wire that is too thin to connect to the computer's power supply. There will be a slight decrease in the voltage in the conductor, which will cause the computer to malfunction.

The resistance in a copper wire depends on many factors, and primarily on the physical properties of the material itself. In addition, the diameter or cross-section of the conductor is taken into account, determined by the formula or a special table.

table

The resistance of a copper conductor is influenced by several additional physical quantities. First of all, the ambient temperature must be taken into account. Everyone knows that with an increase in the temperature of a conductor, an increase in its resistance is observed. Simultaneously with this, there is a decrease in the current strength due to the inversely proportional dependence of both quantities. This primarily concerns metals with a positive temperature coefficient. An example of a negative factor is the tungsten alloy used in incandescent lamps. In this alloy, the current strength does not decrease even at very high heating.

How to calculate resistance

There are several ways to calculate the resistance of a copper wire. The simplest is the tabular version, where the interrelated parameters are indicated. Therefore, in addition to resistance, the current strength, diameter or cross-section of the wire is determined.

In the second case, various are used. A set of physical quantities of copper wire is inserted into each of them, with the help of which accurate results are obtained. Most similar calculators use 0.0172 Ohm * mm 2 / m. In some cases, this average value can affect the accuracy of the calculations.

The most difficult option is considered manual calculations, using the formula: R = p x L / S, in which p is the resistivity of copper, L is the length of the conductor and S is the cross-section of this conductor. It should be noted that the table defines the resistance of a copper wire as one of the lowest. Only silver has a lower value.

The lesson reveals in detail the previously announced parameters of the conductor, on which its resistance depends. It turns out that for calculating the resistance of a conductor, its length, cross-sectional area and the material from which it is made are important. The concept of the resistivity of a conductor is introduced, which characterizes the substance of a conductor.

Topic:Electromagnetic phenomena

Lesson: Calculating the resistance of a conductor. Resistivity

In previous lessons, we have already raised the question of how electrical resistance affects the current in a circuit, but we did not discuss on what specific factors the resistance of the conductor depends. In today's lesson, we will learn about the parameters of a conductor that determine its resistance, and we will learn how Georg Ohm investigated the resistance of conductors in his experiments.

To obtain the dependence of the current in the circuit on the resistance, Ohm had to conduct a huge number of experiments in which it was necessary to change the resistance of the conductor. In this regard, he faced the problem of studying the resistance of a conductor, depending on its individual parameters. First of all, Georg Ohm drew attention to the dependence of the resistance of the conductor on its length, which was already casually discussed in the previous lessons. He concluded that with an increase in the length of the conductor, its resistance also increases in direct proportion. In addition, it was found that the resistance is also influenced by the cross-section of the conductor, that is, the area of ​​the figure, which is obtained with a cross-section. Moreover, the larger the cross-sectional area, the lower the resistance. From this we can conclude that the thicker the wire, the lower its resistance. All these facts were obtained empirically.

In addition to geometric parameters, the resistance of a conductor is also influenced by a quantity that describes the type of substance that makes up the conductor. In his experiments, Ohm used conductors made of various materials. When using copper wires, the resistance was some one, silver - another, iron - a third, etc. The value that characterizes the kind of substance in this case is called resistivity.

Thus, you can get the following dependences for the resistance of the conductor (Fig. 1):

1. Resistance is directly proportional to the length of the conductor, which is measured in SI in m;

2. Resistance is inversely proportional to the cross-sectional area of ​​the conductor, which we will measure in mm 2 due to its smallness;

3. Resistance depends on the specific resistance of the substance (read "ro"), which is a tabular value and is usually measured in.

Rice. 1. Explorer

For example, we give a table of the values ​​of the resistivity of some metals, which are obtained empirically:

Resistivity,

It is worth noting that among good conductors, which are metals, precious metals are the best, while silver is considered the best conductor, since it has the lowest low resistivity. This explains the use of precious metals in the soldering of critical elements in electrical engineering. From the values ​​of the resistivity of substances, one can draw conclusions about their practical application - substances with a high resistivity are suitable for the manufacture of insulating materials, and with a small one - for conductors.

Comment. In many tables, resistivity is measured in, which is associated with the measurement of area in m2 in SI.

The physical meaning of resistivity- resistance of a conductor with a length of 1 m and a cross-sectional area of ​​1 mm 2.

The formula for calculating the electrical resistance of a conductor, based on the above reasoning, is as follows:

If we pay attention to this formula, then we can conclude that the specific resistance of the conductor is expressed from it, that is, by determining the current strength and voltage on the conductor and measuring its length with the cross-sectional area, using Ohm's law and the specified formula, we can calculate resistivity. Then, its value can be checked against the data in the table and determine what substance the conductor is made of.

All parameters that affect the resistance of conductors must be taken into account when designing complex electrical circuits, such as power lines, for example. In such projects, it is important to choose a balanced ratio of the lengths, cross-sections and materials of conductors to effectively compensate for the thermal effect of the current.

The next lesson will consider the device and the principle of operation of a device called a rheostat, the main characteristic of which is resistance.

Bibliography

1. Gendenshtein L.E., Kaidalov A.B., Kozhevnikov V.B. Physics 8 / Ed. Orlova V.A., Roizen I.I. - M .: Mnemosyne.
2. A.V. Peryshkin Physics 8. - M .: Bustard, 2010.
3. Fadeeva A.A., Zasov A.V., Kiselev D.F. Physics 8. - M .: Education.

1. Internet portal Exir.ru ().
2. Cool physics ().

Homework

1. P. 103-106: questions number 1-6. A.V. Peryshkin Physics 8. - M .: Bustard, 2010.
2. The length and cross-sectional area of ​​the aluminum and iron wires are the same. Which conductor has the highest resistance?
3. What is the resistance of a copper wire with a length of 10 m and a cross-sectional area of ​​0.17 mm 2?
4. Which of the solid iron rods of different diameters has the highest electrical resistance? The masses of the rods are the same.