Copper resistance in ohms. Calculation of the resistivity of metals, in particular copper

• Constantan (58.8 Cu, 40 Ni, 1.2 Mn)
• Manganin (85 Cu, 12 Mn, 3 Ni)
• Nickel silver (65 Cu, 20 Zn, 15 Ni)
• Nickelin (54 Cu, 20 Zn, 26 Ni)
• Nichrome (67.5 Ni, 15 Cr, 16 Fe, 1.5 Mn)
• Rheonate (84Cu, 12Mn, 4 Zn)
• Fechral (80 Fe, 14 Cr, 6 Al)

Resistivity of nichrome

Each body through which an electric current is passed automatically provides a certain resistance to it. The property of a conductor to resist electric current is called electrical resistance.

Consider the electronic theory of this phenomenon. When moving along a conductor, free electrons constantly meet other electrons and atoms on their way. Interacting with them, a free electron loses part of its charge. Thus, the electrons encounter resistance from the conductor material. Each body has its own atomic structure, which provides different resistance to electric current. The unit of resistance is the ohm. The resistance of materials is indicated - R or r.

The lower the resistance of the conductor, the easier it is for the electric current to pass through this body. And vice versa: the higher the resistance, the worse the body conducts electric current.

The resistance of each individual conductor depends on the properties of the material from which it is made. To accurately characterize the electrical resistance of a particular material, the concept was introduced - specific resistance (nichrome, aluminum, etc.). The specific resistance is considered to be the resistance of a conductor up to 1 m long, the cross section of which is 1 sq. mm. This indicator is denoted by the letter p. Each material used in the manufacture of a conductor has its own resistivity. For example, consider the resistivity of nichrome and fechral (more than 3 mm):

• Х15Н60 — 1.13 Ohm*mm/m
• Kh23Yu5T - 1.39 Ohm * mm / m
• Х20Н80 — 1.12 Ohm*mm/m
• XN70YU - 1.30 Ohm*mm/m
• XN20YUS - 1.02 Ohm*mm/m

The specific resistance of nichrome, fechral indicates the main scope of their application: the manufacture of thermal devices, household appliances and electric heating elements of industrial furnaces.

Since nichrome and fechral are mainly used in the production of heating elements, the most common products are nichrome thread, tape, Kh15N60 and Kh20N80 strip, as well as Kh23Yu5T fechral wire.

One of the physical quantities used in electrical engineering is electrical resistivity. Considering the specific resistance of aluminum, it should be remembered that this value characterizes the ability of a substance to prevent the passage of electric current through it.

Concepts Related to Resistivity

The value opposite to resistivity is called conductivity or electrical conductivity. The usual electrical resistance is characteristic only of a conductor, and the specific electrical resistance is characteristic only of a particular substance.

As a rule, this value is calculated for a conductor having a uniform structure. To determine electrical homogeneous conductors, the formula is used:

The physical meaning of this quantity lies in a certain resistance of a homogeneous conductor with a certain unit length and cross-sectional area. The unit of measurement is the SI unit Ohm.m or the off-system unit Ohm.mm2/m. The last unit means that a conductor of a homogeneous substance, 1 m long, having a cross-sectional area of ​​​​1 mm2, will have a resistance of 1 ohm. Thus, the resistivity of any substance can be calculated using a section of an electrical circuit 1 m long, the cross section of which will be 1 mm2.

Resistivity of different metals

Each metal has its own individual characteristics. If we compare the resistivity of aluminum, for example, with copper, it can be noted that for copper this value is 0.0175 Ohm.mm2 / m, and for aluminum - 0.0271 Ohm.mm2 / m. Thus, the resistivity of aluminum is much higher than that of copper. It follows from this that the electrical conductivity is much higher than that of aluminum.

Certain factors influence the value of the resistivity of metals. For example, during deformations, the structure of the crystal lattice is disturbed. Due to the resulting defects, the resistance to the passage of electrons inside the conductor increases. Therefore, there is an increase in the resistivity of the metal.

Temperature also has an effect. When heated, the nodes of the crystal lattice begin to oscillate more strongly, thereby increasing the resistivity. Currently, due to the high resistivity, aluminum wires are being replaced everywhere with copper wires, which have a higher conductivity.

- an electrical quantity that characterizes the property of a material to prevent the flow of electric current. Depending on the type of material, the resistance can tend to zero - be minimal (miles / micro ohms - conductors, metals), or be very large (giga ohms - insulation, dielectrics). The reciprocal of electrical resistance is .

unit of measurement electrical resistance - Ohm. It is denoted by the letter R. The dependence of resistance on current and in a closed circuit is determined.

Ohmmeter- a device for direct measurement of circuit resistance. Depending on the range of the measured value, they are divided into gigaohmmeters (for large resistance - when measuring insulation), and into micro / milliohmmeters (for small resistances - when measuring transient resistance of contacts, motor windings, etc.).

There is a wide variety of ohmmeters by design from different manufacturers, from electromechanical to microelectronic. It is worth noting that a classic ohmmeter measures the active part of the resistance (the so-called ohms).

Any resistance (metal or semiconductor) in an AC circuit has an active and a reactive component. The sum of active and reactance is AC circuit impedance and is calculated by the formula:

where, Z is the total resistance of the AC circuit;

R is the active resistance of the AC circuit;

Xc is the capacitive reactance of the AC circuit;

(C is the capacitance, w is the angular velocity of the alternating current)

Xl is the inductive reactance of the AC circuit;

(L is the inductance, w is the angular velocity of the alternating current).

Active resistance- this is part of the impedance of the electrical circuit, the energy of which is completely converted into other types of energy (mechanical, chemical, thermal). A distinctive feature of the active component is the complete consumption of all electricity (energy is not returned to the network back to the network), and reactance returns part of the energy back to the network (a negative property of the reactive component).

The physical meaning of active resistance

Each medium where electric charges pass creates obstacles in their path (it is believed that these are the nodes of the crystal lattice), into which they seem to hit and lose their energy, which is released in the form of heat.

Thus, there is a drop (loss of electrical energy), part of which is lost due to the internal resistance of the conductive medium.

The numerical value characterizing the ability of a material to prevent the passage of charges is called resistance. It is measured in Ohms (Ohm) and is inversely proportional to the electrical conductivity.

Different elements of the periodic system of Mendeleev have different specific electrical resistances (p), for example, the smallest sp. silver (0.016 Ohm * mm2 / m), copper (0.0175 Ohm * mm2 / m), gold (0.023) and aluminum (0.029) have resistance. They are used in industry as the main materials on which all electrical engineering and energy are built. Dielectrics, on the other hand, have a high sp. resistance and used for insulation.

The resistance of a conducting medium can vary significantly depending on the cross section, temperature, magnitude and frequency of the current. In addition, different media have different charge carriers (free electrons in metals, ions in electrolytes, "holes" in semiconductors), which are the determining factors of resistance.

The physical meaning of reactance

In coils and capacitors, when applied, energy is accumulated in the form of magnetic and electric fields, which requires some time.

Magnetic fields in alternating current networks change following the changing direction of movement of charges, while providing additional resistance.

In addition, there is a stable phase shift and current strength, and this leads to additional losses of electricity.

Resistivity

How to find out the resistance of a material if it does not flow through it and we do not have an ohmmeter? There is a special value for this - electrical resistivity of the material in

(these are tabular values ​​that are determined empirically for most metals). With this value and the physical quantities of the material, we can calculate the resistance using the formula:

where, p- resistivity (units of measurement ohm * m / mm 2);

l is the length of the conductor (m);

S - cross section (mm 2).

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 taken into account using the resistivity, denoted by the Greek letter? and representing a length of 1 m and a cross-sectional area of ​​1 mm2. The smallest resistivity? \u003d 0.016 Ohm mm2 / m has silver. 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 rheostatic alloys, the resistivity may change somewhat.

The resistance is calculated by the formula:

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

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

It is best to measure the diameter of the wire with a micrometer, but if it is not available, then wrap 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 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 must be taken as some average values. For example, for a nickeline 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 allowable current is 0.075 A.

2. For a different current density value, the data of 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 by 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 \u003d 0.017 30 / 0.0078 \u003d 65.50m.

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 \u003d 0.78 0.52 \u003d 0.195 mm2. And the length of the wire will be l \u003d 0.195 40 / 0.42 \u003d 18.6 m.

Specific electrical resistance, or simply the specific resistance of a substance, is a physical quantity that characterizes the ability of a substance to prevent the passage of an electric current.

Resistivity is denoted by the Greek letter ρ. The reciprocal of resistivity is called specific conductivity (electrical conductivity). Unlike electrical resistance, which is a property of a conductor and depends on its material, shape and size, electrical resistivity is a property of a substance only.

The electrical resistance of a homogeneous conductor with resistivity ρ, length l and cross-sectional area S can be calculated by the formula (it is assumed that neither the area nor the cross-sectional shape changes along the conductor). Accordingly, for ρ,

It follows from the last formula: the physical meaning of the specific resistance of a substance lies in the fact that it is the resistance of a homogeneous conductor made of this substance of unit length and with a unit cross-sectional area.

The unit of resistivity in the International System of Units (SI) is Ohm m.

It follows from the ratio that the unit of measurement of resistivity in the SI system is equal to such a specific resistance of a substance at which a homogeneous conductor 1 m long with a cross-sectional area of ​​​​1 m², made from this substance, has a resistance equal to 1 Ohm. Accordingly, the resistivity of an arbitrary substance, expressed in SI units, is numerically equal to the resistance of an electrical circuit section made of this substance, 1 m long and with a cross-sectional area of ​​1 m².

The technique also uses an outdated off-system unit Ohm mm² / m, equal to 10 −6 of 1 Ohm m. This unit is equal to such a specific resistance of a substance at which a homogeneous conductor 1 m long with a cross-sectional area of ​​​​1 mm², made from this substance, has a resistance equal to 1 ohm. Accordingly, the specific resistance of a substance, expressed in these units, is numerically equal to the resistance of an electrical circuit section made of this substance, 1 m long and with a cross-sectional area of ​​1 mm².

Electromotive force (EMF) is a scalar physical quantity that characterizes the work of external forces, that is, any forces of non-electric origin acting in quasi-stationary DC or AC circuits. In a closed conducting circuit, the EMF is equal to the work of these forces in moving a single positive charge along the entire circuit.

By analogy with the strength of the electric field, the concept of intensity of external forces is introduced, which is understood as a vector physical quantity equal to the ratio of the external force acting on the test electric charge to the magnitude of this charge. Then in a closed loop, the EMF will be equal to:

where is the contour element.

EMF, like voltage, is measured in volts in the International System of Units (SI). We can talk about the electromotive force in any part of the circuit. This is the specific work of external forces not in the entire circuit, but only in this section. The EMF of a galvanic cell is the work of external forces when moving a single positive charge inside the cell from one pole to another. The work of external forces cannot be expressed in terms of the potential difference, since external forces are non-potential and their work depends on the shape of the trajectory. So, for example, the work of external forces when moving a charge between the current terminals is outside of itself? source is zero.