Copper wire resistance table. Electrical resistance of the conductor

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 represents conductor resistance with a cross section of 1 mm 2 and a length of 1 m. Silver has the lowest resistivity ρ = 0.016 Ohm.mm 2 /m. Below are the values resistivity for multiple conductors:

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

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

Wire resistance calculated using the formula below:

R=(ρ?l)/S

• R - resistance,
• Ohm; ρ - resistivity, (Ohm.mm 2)/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 length of wire 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 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. Cross-sectional area of ​​the wire s = 0.78.0.52 = 0.195 mm 2. Wire length l = 0.195.40/0.42 = 18.6 m.

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 representing a length of 1 m and an area cross section 1 mm2. Lowest resistivity? = 0.016 Ohm mm2/m has silver. Let us give the average value of the resistivity of some conductors:

Silver - 0.016 , Lead - 0.21, Copper - 0.017, Nickelin - 0.42, Aluminum - 0.026, Manganin - 0.42, Tungsten - 0.055, Constantan - 0.5, Zinc - 0.06, Mercury - 0.96, Brass - 0.07, Nichrome - 1.05, Steel - 0.1, Fechral - 1.2, Phosphor bronze - 0.11, Chromal - 1.45.

With different amounts of impurities and with different ratios of components included in the composition of 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 known diameter from of this 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 of 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.

The current flowing in a conductive material is proportional to the voltage across it. Those. As the potential increases, the volume of flowing electrons also increases. True, when using different elements, an equivalent voltage gives a different current value. Thus, the rule is obtained: as the voltage increases, the electric current passing through the conductor will also increase, but not equally, but depending on the characteristics of the element.

Determination of the resistive component

The electrical resistance of a material is the ratio of the magnitude of the current flowing and the voltage applied to it. For each specific element this ratio is different. To indicate this physical quantity use the letter R. When determining it, use the formula of Ohm's law for a section of the chain:

From the presented expression it is clear that the resistive component is the ratio of the potential on the conductor to the current strength on it. Thus, the higher the current value, the weaker the resistive component of the conductor; at higher voltages, the larger it is.

Additional Information. It is often said in common parlance that a resistive value “prevents” the voltage from endlessly increasing the current strength.

For any resistor produced in an industrial environment, there are about ten parameters that you need to pay attention to when choosing it. Its main parameter is resistance. This is a static characteristic for any conductor, specified during its production. Those. By applying more potential to a conducting element, only the current passing through it will change, but not its resistive component. Those. the U/I ratio remains unchanged.

What does resistance depend on?

It is necessary to consider on what factors the electrical resistance of the conductor depends. There are four main parameters:

• Cable length – l;
• Cross-sectional area of ​​the conductive element – ​​S;
• Metal used in cable production;
• Temperature environment– t.

Important! The resistivity of a part is a concept used in physics that shows the ability of an element to retard the conduction of electricity.

To connect a part and its resistive component, the concept of resistivity has been introduced in physical science. This indicator characterizes the value of the resistive component of the cable with a unit length of 1 meter and a unit area of ​​1 m². Parts of the specified length and thickness, produced from different raw materials, will show different meanings resistive value. It's connected with physical properties metals It is from them that wires and cables are mainly made. Each metal material has its own size of elements in the crystal lattice.

The most flawlessly conductive parts are those with the lowest resistive component. Examples of metals with a small specified value are aluminum and copper. The vast majority of transmission wires and cables electrical energy are made from them. They are also used to make buses in transformer substations and main distribution boards of any buildings. Examples of metals with high resistivity include iron and various alloys. Often the resistive component of an element is indicated by a resistor.

As the length of the conductive material increases, the resistance of the metal conductor also increases. This is due to the physical processes occurring in it during the passage electric current. Their essence is this: electrons move along a conducting layer, which contains ions that make up the crystal lattice of any metal. The longer the conductor, the large quantity There are ions present that interfere with the movement of electrons crystal lattice. The more they create obstacles to the conduction of electricity.

To be able to increase the length of the conductor, manufacturers increase the area of ​​materials. This makes it possible to expand the “freeway” for electric current. Those. electrons intersect less with metal lattice details. It follows that a thicker cable has less resistance.

From all of the above, a formula follows for determining the resistance of a conductor, expressed through its length (l), cross-sectional area (S) and metal resistivity (ρ):

The presented expression for determining this parameter does not contain ambient temperature. However, the resistive value of the element changes when a certain temperature is reached. Typically this temperature is 20-25 °C. Therefore, it is impossible not to take into account the ambient temperature when choosing a part. This may cause the conductor to overheat and ignite. For selection, specialized tables are used, the values ​​of which are used in calculations.

Typically, an increase in temperature leads to an increase in the resistive component of the metal element. From a physical point of view, this is due to the fact that as the temperature of the crystal lattice increases, the ions in it leave the state of rest and begin to produce oscillatory movements. This process slows down the electrons because clashes between them occur more often.

Choosing a conductor is enough difficult process, which is best left to professionals. If all factors of a part’s operation are incorrectly assessed, many negative consequences can result, including fire. Therefore, there must be an understanding of what the conductor resistance may depend on.

Video

Concept of electrical resistance and conductivity

Any body through which electric current flows exhibits a certain resistance to it.The property of a conductor material to prevent electric current from passing through it is called electrical resistance.

The electronic theory explains the essence of the electrical resistance of metal conductors. Free electrons, when moving along a conductor, encounter atoms and other electrons on their way countless times and, interacting with them, inevitably lose part of their energy. Electrons experience a kind of resistance to their movement. Different metal conductors, having different atomic structures, offer different resistance to electric current.

The same thing explains the resistance of liquid conductors and gases to the passage of electric current. However, we should not forget that in these substances it is not electrons, but charged particles of molecules that encounter resistance during their movement.

Resistance is denoted by the Latin letters R or r.

The unit of electrical resistance is the ohm.

Ohm is the resistance of a column of mercury 106.3 cm high with a cross section of 1 mm2 at a temperature of 0° C.

If, for example, the electrical resistance of a conductor is 4 ohms, then it is written like this: R = 4 ohms or r = 4 ohms.

To measure large resistances, a unit called megohm is used.

One megohm is equal to one million ohms.

The greater the resistance of a conductor, the worse it conducts electric current, and, conversely, the lower the resistance of the conductor, the easier it is for electric current to pass through this conductor.

Consequently, to characterize a conductor (from the point of view of the passage of electric current through it), one can consider not only its resistance, but also the reciprocal of the resistance and called conductivity.

Electrical conductivity is the ability of a material to pass electric current through itself.

Since conductivity is the reciprocal of resistance, it is expressed as 1/R, and conductivity is denoted by the Latin letter g.

The influence of conductor material, its dimensions and ambient temperature on the value of electrical resistance

The resistance of various conductors depends on the material from which they are made. To characterize electrical resistance various materials the concept of so-called resistivity was introduced.

Resistivity is the resistance of a conductor with a length of 1 m and a cross-sectional area of ​​1 mm2. Resistivity is denoted by the letter p of the Greek alphabet. Each material from which a conductor is made has its own resistivity.

For example, the resistivity of copper is 0.017, i.e. a copper conductor 1 m long and 1 mm2 cross-section has a resistance of 0.017 ohms. The resistivity of aluminum is 0.03, the resistivity of iron is 0.12, the resistivity of constantan is 0.48, the resistivity of nichrome is 1-1.1.

The resistance of a conductor is directly proportional to its length, i.e. the longer the conductor, the greater its electrical resistance.

The resistance of a conductor is inversely proportional to its cross-sectional area, i.e. the thicker the conductor, the lower its resistance, and, conversely, the thinner the conductor, the greater its resistance.

To better understand this relationship, imagine two pairs of communicating vessels, with one pair of vessels having a thin connecting tube, and the other having a thick one. It is clear that when one of the vessels (each pair) is filled with water, its transfer to the other vessel through a thick tube will occur much faster than through a thin tube, i.e., a thick tube will have less resistance to the flow of water. In the same way, it is easier for electric current to pass through a thick conductor than through a thin one, i.e., the first offers it less resistance than the second.

Electrical resistance of a conductor is equal to the resistivity of the material from which the conductor is made, multiplied by the length of the conductor and divided by the area of ​​the cross-sectional area of ​​the conductor:

R = pl/S,

Where - R is the resistance of the conductor, ohm, l is the length of the conductor in m, S is the cross-sectional area of ​​the conductor, mm 2.

Cross-sectional area of ​​a round conductor calculated by the formula:

S = Pi x d 2 / 4

Where is Pi - constant value equal to 3.14; d is the diameter of the conductor.

And this is how the length of the conductor is determined:

l = S R / p,

This formula makes it possible to determine the length of the conductor, its cross-section and resistivity, if the other quantities included in the formula are known.

If it is necessary to determine the cross-sectional area of ​​the conductor, then the formula takes the following form:

S = p l / R

Transforming the same formula and solving the equality with respect to p, we find the resistivity of the conductor:

R = R S / l

The last formula must be used in cases where the resistance and dimensions of the conductor are known, but its material is unknown and, moreover, difficult to determine by appearance. To do this, you need to determine the resistivity of the conductor and, using the table, find a material that has such a resistivity.

Another reason that affects the resistance of conductors is temperature.

It has been established that with increasing temperature the resistance of metal conductors increases, and with decreasing temperature it decreases. This increase or decrease in resistance for pure metal conductors is almost the same and averages 0.4% per 1°C. The resistance of liquid conductors and carbon decreases with increasing temperature.

The electronic theory of the structure of matter provides the following explanation for the increase in resistance of metal conductors with increasing temperature. When heated, the conductor receives thermal energy, which is inevitably transferred to all atoms of the substance, as a result of which the intensity of their movement increases. The increased movement of atoms creates greater resistance to the directional movement of free electrons, which is why the resistance of the conductor increases. As the temperature decreases, better conditions are created for the directional movement of electrons, and the resistance of the conductor decreases. This explains an interesting phenomenon - superconductivity of metals.

Superconductivity, i.e., a decrease in the resistance of metals to zero, occurs at a huge negative temperature - 273 ° C, called absolute zero. At a temperature of absolute zero, metal atoms seem to freeze in place, without at all interfering with the movement of electrons.

When an electrical circuit is closed, at the terminals of which there is a potential difference, an electric current occurs. Free electrons under the influence electrical forces fields move along the conductor. In their movement, free electrons collide with the atoms of the conductor and give them a supply of their kinetic energy.

Thus, electrons passing through a conductor encounter resistance to their movement. When electric current passes through a conductor, the latter heats up.

The electrical resistance of a conductor (denoted by the Latin letter r) is responsible for the phenomenon of converting electrical energy into heat when an electric current passes through the conductor. In the diagrams, electrical resistance is indicated as shown in Fig. 18.

The unit of resistance is taken to be 1 ohm. Om is often represented by the Greek capital letter Ω (omega). Therefore, instead of writing: “The resistance of the conductor is 15 ohms,” you can simply write: r = 15 Ω.

1000 ohms is called 1 kiloohm (1 kohm, or 1 kΩ).

1,000,000 ohms is called 1 megohm (1 mg ohm, or 1 MΩ).

device, having variable electrical resistance and serving to change the current in the circuit is called a rheostat. In the diagrams, rheostats are designated as shown in Fig. 18. As a rule, a rheostat is made of a wire of one or another resistance, 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 you 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, etc.) almost do not change their resistance with increasing temperature.

So, we see that the electrical resistance of a conductor depends on the length of the conductor, the cross-section of the conductor, the material of the conductor, and the temperature of the conductor.

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.

The resistance (in ohms) of a conductor 1 m long, with a cross section of 1 mm 2 is called resistivity and is denoted by the Greek letter ρ (rho).

The conductor resistance can be determined by the formula

where r is the conductor resistance, ohm;

ρ - conductor resistivity;

l- conductor length, m;

S - conductor cross-section, mm2.

From this formula we obtain the dimension for resistivity

In table 1 shows the resistivity of some 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 if you take 62.5 m of silver wire with a cross section of 1 mm 2. Silver is the best conductor, but the high 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 mm 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 copper obtained by refining has found widespread use in electrical engineering for the manufacture of wires, cables, and windings. electric machines and devices. Aluminum and iron are also widely used as conductors.

Detailed characteristics of metals and alloys are given in table. 2.

Example 1. Determine the resistance of 200 m of iron wire with a cross section of 5 mm 2:

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 resistor from nickel wire with a cross section of 0.21 mm2. Determine the required wire length:

Example 4. Determine the cross-section of a nichrome wire with a length of 20 F, 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

Based on the resistivity table, we find that lead has this resistance.

It was previously stated 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, an ammeter is included in 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, while 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 the resistance of a conductor when it is heated, per 1 ohm of initial resistance and per 1 0 temperature, is called temperature coefficient of resistance and is denoted by the letter α (alpha).

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