7 electrical resistance. What is electrical resistance? Series and parallel connection of resistors

The concept of electrical resistance and conductivity

Any body through which electricity, offers him some resistance.The property of a conductor material to prevent the passage of electric current through it is called electrical resistance.

Electronic theory explains the essence of the electrical resistance of metal conductors in this way. When moving along a conductor, free electrons encounter atoms and other electrons countless times on their way and, interacting with them, inevitably lose part of their energy. The electrons experience, as it were, resistance to their movement. Different metal conductors having different atomic structure have different resistance to electric current.

Exactly the same explains the resistance of liquid conductors and gases to the passage of electric current. However, one should not forget that in these substances, not electrons, but charged particles of molecules meet resistance during their movement.

Resistance is indicated by Latin letters R or r.

The ohm is taken as the unit of electrical resistance.

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

If, for example, the electrical resistance of the conductor is 4 ohms, then it is written as follows: R \u003d 4 ohms or r \u003d 4 ohms.

To measure the resistance of a large value, a unit called megohm is adopted.

One meg is equal to one million ohms.

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

Therefore, to characterize the conductor (in terms of the passage of electric current through it), one can consider not only its resistance, but also the reciprocal of the resistance and is called conductivity.

electrical conductivity The ability of a material to pass an electric current through itself is called.

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

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 the electrical resistance of various materials, the concept of the so-called resistivity has been introduced.

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

For example, the resistivity of copper is 0.017, that is, a copper conductor 1 m long and 1 mm2 in 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, that is, the longer the conductor, the greater its electrical resistance.

The resistance of a conductor is inversely proportional to its cross-sectional area, that is, 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 transition to another vessel through a thick tube will occur much faster than through a thin one, i.e., a thick tube will offer less resistance to the flow of water. In the same way, it is easier for an electric current to pass through a thick conductor than through a thin one, that is, the first one offers him less resistance than the second.

The electrical resistance of a conductor is equal to the specific resistance of the material from which this 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 - conductor resistance, ohm, l - conductor length in m, S - conductor cross-sectional area, mm 2.

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

S \u003d Pi x d 2 / 4

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

And so 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 ​​\u200b\u200bthe conductor, then the formula is reduced to the following form:

S = pl / 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 has to be used in cases where the resistance and dimensions of the conductor are known, and its material is unknown and, moreover, it is difficult to determine by appearance. To do this, it is necessary 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 decreases with decreasing. 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 coal decreases with increasing temperature.

The electronic theory of the structure of matter gives the following explanation for the increase in the resistance of metallic 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 more resistance to the directed movement of free electrons, which is why the resistance of the conductor increases. With a decrease in temperature, better conditions are created for the directed 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, the metal atoms seem to freeze in place, without impeding the movement of electrons at all.

Electrical resistance- physical quantity that characterizes the properties of the conductor to prevent the passage of electric current and is equal to the ratio of the voltage at the ends of the conductor to the strength of the current flowing through it.

Circuit resistance alternating current and for variable electromagnetic fields is described by the concepts of impedance and wave resistance . Resistance   (resistor) is also called a radio component designed to be introduced into electrical circuits of active resistance.

Resistance (often denoted by the letter R or r) is considered, within certain limits, a constant value for a given conductor; it can be calculated as

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✪ 8 cells - 129. Work and power of electric current

✪ Lesson 358. Active resistance in an alternating current circuit. Effective value of current and voltage

✪ Lesson 305. Electric current in semiconductors. Intrinsic and impurity conductivity.

✪ Lesson 296. Temperature dependence of the resistance of metals. Superconductivity

✪ 8 cells - 110. Electrical circuit and its components

Subtitles

Units and dimensions

• stat (in CGSE and Gaussian system, 1 statΩ = (10 9 −2) / cm \u003d 898 755 178 736.818 Ohm (exactly) ≈ 8.98755 10 11 Ohm, equal to the resistance of the conductor through which a current of 1 statvolt flows under a voltage of 1 statvolt);
• abom (in SGSM, 1 abΩ \u003d 1 10 −9 Ohm \u003d 1 nanoohm, equal to the resistance of the conductor through which a current of 1 abampere flows under a voltage of 1 abvolt).

The dimension of resistance in the CGSE and the Gaussian system is TL−1 (that is, it coincides with the dimension of the reciprocal velocity, s/cm), in CGSM - LT−1 (that is, it coincides with the dimension of speed, cm/s) .

The reciprocal of resistance is electrical conductivity, the unit of measurement of which in the SI system is siemens (1 Sm \u003d 1 Ohm −1), in the CGSE (and Gaussian) statistical siemens and in SGSM - absimens.

Physics of the phenomenon

The high electrical conductivity of metals is due to the fact that they contain a large number of current carriers - conduction electrons formed from valence electrons of metal atoms that do not belong to a specific atom. An electric current in a metal arises under the action of an external electric field, which causes an ordered movement of electrons. Electrons moving under the action of the field are scattered by inhomogeneities of the ionic lattice (on impurities, lattice defects, as well as violations of the periodic structure associated with thermal vibrations of ions). In this case, the electrons lose their momentum, and the energy of their movement is converted into the internal energy of the crystal lattice, which leads to heating of the conductor when an electric current passes through it.

Resistivity is a scalar physical quantity, numerically equal to the resistance of a homogeneous cylindrical conductor of unit length and unit cross-sectional area.

The resistance of metals decreases with decreasing temperature; at temperatures of the order of several kelvins, the resistance of most metals and alloys tends to or becomes equal to zero (the effect of superconductivity). On the contrary, the resistance of semiconductors and insulators increases with decreasing temperature (in a certain range). The resistance also changes as the current/voltage flowing through the conductor/semiconductor increases.

Dependence of resistance on the material, length and cross-sectional area of ​​the conductor

In a metal, free electrons are mobile charge carriers. We can assume that during their chaotic motion they behave like gas molecules. Therefore, in classical physics, free electrons in metals are called an electron gas and, in the first approximation, it is believed that the laws established for an ideal gas are applicable to it.

The density of the electron gas and the structure of the crystal lattice depend on the type of metal. Therefore, the resistance of a conductor must depend on the type of its substance. In addition, it must also depend on the length of the conductor, its cross-sectional area and temperature.

The influence of the conductor cross section on its resistance is explained by the fact that with a decrease in the cross section, the flow of electrons in the conductor at the same current strength becomes denser, therefore, the interaction of electrons with particles of matter in the conductor becomes stronger.

Without a certain initial knowledge of electricity, it’s hard to imagine how electrical appliances work, why they work at all, why you need to plug in the TV to make it work, and a small battery is enough for a flashlight to shine in the dark.

And so we will understand everything in order.

Electricity

Electricity is a natural phenomenon that confirms the existence, interaction and movement of electric charges. Electricity was first discovered as early as the 7th century BC. Greek philosopher Thales. Thales drew attention to the fact that if a piece of amber is rubbed against wool, it begins to attract light objects to itself. Amber in ancient Greek is electron.

This is how I imagine Thales sitting, rubbing a piece of amber on his himation (this is the woolen outerwear of the ancient Greeks), and then, with a puzzled look, looks at how hair, scraps of thread, feathers and scraps of paper are attracted to amber.

This phenomenon is called static electricity. You can repeat this experience. To do this, thoroughly rub a regular plastic ruler with a woolen cloth and bring it to small pieces of paper.

It should be noted that for a long time this phenomenon has not been studied. And only in 1600, in his essay "On the Magnet, Magnetic Bodies, and the Great Magnet - the Earth", the English naturalist William Gilbert introduced the term - electricity. In his work, he described his experiments with electrified objects, and also established that other substances can become electrified.

Then, for three centuries, the most advanced scientists of the world have been exploring electricity, writing treatises, formulating laws, inventing electrical machines, and only in 1897, Joseph Thomson discovers the first material carrier of electricity - an electron, a particle, due to which electrical processes in substances are possible.

Electron is an elementary particle, has a negative charge approximately equal to -1.602 10 -19 Cl (Pendant). Denoted e or e -.

Voltage

To make charged particles move from one pole to another, it is necessary to create between the poles potential difference or - Voltage. Voltage unit - Volt (IN or V). In formulas and calculations, stress is indicated by the letter V . To get a voltage of 1 V, you need to transfer a charge of 1 C between the poles, while doing work of 1 J (Joule).

For clarity, imagine a tank of water located at a certain height. A pipe comes out of the tank. Water under natural pressure leaves the tank through a pipe. Let's agree that water is electric charge, the height of the water column (pressure) is voltage, and the water flow rate is electricity.

Thus, the more water in the tank, the higher the pressure. Similarly, from an electrical point of view, the greater the charge, the higher the voltage.

We begin to drain the water, while the pressure will decrease. Those. the charge level drops - the voltage value decreases. This phenomenon can be observed in a flashlight, the light bulb shines dimmer as the batteries run out. Note that the lower the water pressure (voltage), the lower the water flow (current).

Electricity

Electricity- this is a physical process of directed movement of charged particles under the influence of an electromagnetic field from one pole of a closed electrical circuit to another. Charge-transporting particles can be electrons, protons, ions, and holes. In the absence of a closed circuit, current is not possible. particles that can carry electric charges do not exist in all substances, those in which they exist are called conductors And semiconductors. And substances in which there are no such particles - dielectrics.

Unit of measurement of current strength - Ampere (A). In formulas and calculations, the current strength is indicated by the letter I . A current of 1 Ampere is formed when a charge of 1 Coulomb (6.241 10 18 electrons) passes through a point in the electrical circuit in 1 second.

Let's go back to our water-electricity analogy. Only now let's take two tanks and fill them with an equal amount of water. The difference between the tanks is in the diameter of the outlet pipe.

Let's open the taps and make sure that the flow of water from the left tank is greater (the pipe diameter is larger) than from the right one. This experience is a clear proof of the dependence of the flow rate on the diameter of the pipe. Now let's try to equalize the two streams. To do this, add water to the right tank (charge). This will give more pressure (voltage) and increase the flow rate (current). In an electrical circuit, the pipe diameter is resistance.

The conducted experiments clearly demonstrate the relationship between tension, current And resistance. We'll talk more about resistance a little later, and now a few more words about the properties of electric current.

If the voltage does not change its polarity, plus to minus, and the current flows in one direction, then this is D.C. and correspondingly constant pressure. If the voltage source changes its polarity and the current flows in one direction, then in the other - this is already alternating current And AC voltage . Maximum and minimum values ​​(marked on the graph as io ) - This amplitude or peak currents. In household outlets, the voltage changes its polarity 50 times per second, i.e. the current oscillates back and forth, it turns out that the frequency of these oscillations is 50 Hertz, or 50 Hz for short. In some countries, such as the USA, the frequency is 60 Hz.

Resistance

Electrical resistance- a physical quantity that determines the property of the conductor to prevent (resist) the passage of current. Resistance unit - Ohm(denoted Ohm or the Greek letter omega Ω ). In formulas and calculations, resistance is indicated by the letter R . A conductor has a resistance of 1 ohm, to the poles of which a voltage of 1 V is applied and a current of 1 A flows.

Conductors conduct current differently. Their conductivity depends, first of all, on the material of the conductor, as well as on the cross section and length. The larger the cross section, the higher the conductivity, but the longer the length, the lower the conductivity. Resistance is the inverse of conduction.

On the example of a plumbing model, the resistance can be represented as the diameter of the pipe. The smaller it is, the worse the conductivity and the higher the resistance.

The resistance of the conductor is manifested, for example, in the heating of the conductor when current flows in it. Moreover, the greater the current and the smaller the cross section of the conductor, the stronger the heating.

Power

Electric power is a physical quantity that determines the rate of electricity conversion. For example, you have heard more than once: "a light bulb for so many watts." This is the power consumed by the light bulb per unit of time during operation, i.e. converting one form of energy into another at a certain rate.

Sources of electricity, such as generators, are also characterized by power, but already generated per unit of time.

Power unit - Watt(denoted Tue or W). In formulas and calculations, power is indicated by the letter P . For AC circuits, the term is used Full power, unit - Volt-ampere (V A or VA), denoted by the letter S .

And finally about electrical circuit. This circuit is a set of electrical components capable of conducting electric current and connected to each other in an appropriate way.

What we see in this image is an elementary electrical appliance (flashlight). under tension U(C) a source of electricity (batteries) through conductors and other components with different resistances 4.59 (237 Votes)

To begin with, let's consider the question of how, in due time, researchers came to understand the value, called " current resistance". When considering the basics of electrostatics, the issues of electrical conductivity have already been touched upon, including the fact that different substances have different conductivity (the ability to pass free charged particles). For example, metals are characterized by good conductivity (which is why they are called conductors), while plastic and wood are poor (dielectrics or non-conductors). Such differences are associated with the peculiarities of the molecular structure of different substances.

The most productive work on the study of the conductivity of various substances was the experiments conducted by Georg Ohm (1789-1854) (Fig. 1).

The essence of Ohm's work was as follows. scientist used wiring diagram, consisting of current source, conductor, as well as a special device for tracking current strength. Changing the conductors in the circuit, Ohm traced the following pattern: the current strength in the circuit increased with increasing voltage. Ohm's next discovery was that when the conductors were replaced, the degree of increase in current strength with increasing voltage also changed. An example of such a dependence is shown in Figure 2.

The x-axis shows tension, and the y-axis shows current strength. The graph shows two straight lines, showing different rates of increase in current with increasing voltage, depending on the conductor that is part of the circuit.

The result of Ohm's research was the following conclusion: "Different conductors have different conductivity properties", as a result of which the concept appeared current resistance.

Electrical current resistance.

Electrical resistance is a physical quantity that characterizes the ability of a conductor to influence electricity flowing in the conductor.

• Value designation: R
• Unit: Ohm

As a result of experiments with conductors, it was determined that the relationship between current strength and the voltage in the electrical circuit also depends on the size of the conductor used, and not only on the substance. The influence of conductor dimensions will be discussed in more detail in a separate lesson.

Due to what does it appear current resistance? During the movement of free electrons, there is a constant interaction between the ions that make up the structure of the crystal lattice and the electrons. As a result of this interaction, the movement of electrons slows down (in fact, due to the collision of electrons with atoms - the nodes of the crystal lattice), due to which current resistance is created.

Another physical quantity is also associated with electrical resistance - current conduction, the reciprocal of the resistance.

Current resistance formulas.

Consider the relationship between the values ​​studied in the last lessons. As mentioned, with increasing voltage increases in the circuit and current strength, these quantities are proportional to: I~U

An increase in the resistance of the conductor leads to a decrease in the current strength in the circuit, so these values ​​are inversely proportional to each other: I~1/R

As a result of the research, the following regularity was revealed: R=U/I

We paint the receipt of the unit current resistance: 1Ω=1V/1A

Thus, 1 ohm is such a current resistance at which the current strength in the conductor is 1 A, and the voltage at the ends of the conductor is 1 V.

Actually, current resistance 1 Ohm is too small and in practice conductors are used that are characterized by a higher resistance (1 KΩ, 1 MΩ, etc.).

Current and voltage are interrelated quantities that affect each other. This will be covered in more detail in the next lesson.

Among other indicators characterizing electrical circuit, conductor, it is worth highlighting the electrical resistance. It determines the ability of the atoms of a material to prevent the directed passage of electrons. Assistance in determining this value can be provided both by a specialized device - an ohmmeter, and mathematical calculations based on knowledge of the relationship between quantities and the physical properties of the material. The indicator is measured in Ohms (Ohm), the symbol is R.

Ohm's law - a mathematical approach to determining resistance

The ratio established by Georg Ohm defines the relationship between voltage, current, resistance, based on the mathematical relationship of concepts. The validity of the linear relationship - R \u003d U / I (ratio of voltage to current strength) - is not observed in all cases.
Unit [R] = B/A = Ohm. 1 ohm is the resistance of a material carrying a current of 1 ampere at a voltage of 1 volt.

Empirical formula for calculating resistance

Objective data on the conductivity of a material follow from its physical characteristics, which determine both its own properties and reactions to external influences. Based on this, the conductivity depends on:

• size.
• Geometry.
• Temperatures.

Atoms of a conducting material collide with directed electrons, preventing their further advancement. At a high concentration of the latter, the atoms are not able to resist them and the conductivity is high. Large resistance values ​​are typical for dielectrics, which are characterized by almost zero conductivity.

One of the defining characteristics of each conductor is its resistivity - ρ. It determines the dependence of resistance on the conductor material and external influences. This is a fixed (within one material) value that represents the data of the conductor of the following dimensions - length 1 m (ℓ), cross-sectional area 1 sq.m. Therefore, the relationship between these quantities is expressed by the relation: R = ρ* ℓ/S:

• The conductivity of a material decreases as its length increases.
• An increase in the cross-sectional area of ​​the conductor entails a decrease in its resistance. This pattern is due to a decrease in the density of electrons, and, consequently, the contact of material particles with them becomes more rare.
• An increase in the temperature of the material stimulates an increase in resistance, while a decrease in temperature causes it to decrease.

It is advisable to calculate the cross-sectional area according to the formula S \u003d πd 2 / 4. A tape measure will help in determining the length.

Relationship with power (P)

Based on the formula of Ohm's law, U = I*R and P = I*U. Therefore, P = I 2 *R and P = U 2 /R.
Knowing the magnitude of the current strength and power, the resistance can be determined as: R \u003d P / I 2.
Knowing the magnitude of voltage and power, the resistance is easy to calculate by the formula: R \u003d U 2 /P.

The resistance of the material and the values ​​of other associated characteristics can be obtained using special measuring instruments or based on established mathematical patterns.