Electrical resistance is determined by the formula. Resistance. Examples of problems with solutions

29.08.2018 Education

Many have heard of such a concept, found and widely used in the field of electricity, as electrical resistance. But not everyone knows what its nature is. What is the essence, and what does it represent in general, what does it depend on. I propose in this article to understand what current resistance is. So, by electrical resistance we mean two things. In one sense this is physical quantity, in another, it is an electrical component, part, element.

A narrow or obstructed area, such as a highway or pipeline. A point or area of ​​traffic jams. The narrow part of the bottle is at the top. A group of American scientists indirectly confirmed that the electrical resistance of a two-dimensional electron gas can have negative values. For this purpose, electron microwave rays must be exposed to a certain frequency range. However, this new electrical state is unstable and therefore not constant across the area of ​​the gas, so that the resistance of the entire gas is zero on the outside.

When two semiconductors with different electron densities are brought into contact with each other, a layer of increased electron density can form at the interface surface, allowing electrons to move almost freely. To this end, the researchers first applied an electrical voltage to the gas to cause electrons to move along the separation layer. In addition, they were exposed to a weak magnetic field perpendicular to the layer. When the researchers irradiated the layer with microwaves, the electrical resistance of the electron gas dropped to zero for certain frequencies.

Now about what exactly the essence of current resistance is. Let's start with the basics, the structure of the atom, its crystal lattice, and the movement of electricity inside an electrical conductor. Let me remind you that an atom is the smallest particle of matter. It is structured as follows: in the center there is a so-called nucleus, consisting of smaller particles, protons and neutrons. Another particles called electrons (they are much smaller in size than the nucleus) rotate around this atomic nucleus at tremendous speed.

This effect was observed for the first time several years ago, and theorists have since proposed that even in some areas of the gas negative resistance is formed? the electrons then move in the wrong direction against the external voltage. However, since this state is unstable, the resistance fluctuates widely. Thus, regions with negative resistance cannot be examined directly, and the average resistance over the entire gas is zero.

So Zudov and his colleagues adopted a trick: they used their gas to combine a combination of two microwave beams with different frequencies. If both frequencies were outside the range at which the gas resistance decreased to zero, its resistance was simply adjusted to the average value of the two resistors, which occurred when only one of the two frequency components was irradiated.

The nucleus of an atom has a positive electrical charge (plus), and the electrons, accordingly, have a negative charge (minus). Any substance is represented by a multitude of atoms that have their own specific structure, called a crystal lattice (if we talk about the solid state of matter). But before moving on to the essence of current resistance, it is worth adding that the space through which electrons rush is called the electron’s orbit (orbitals). The number of orbits may be different for different substances, and they are located one above the other (like an onion).

In the most distant electron orbit, the force of attraction of an electron to the nucleus of an atom is minimal, which facilitates the easy separation of an electron from it and its transfer to a neighboring atom. This is the essence of the movement of electric charges inside a substance (current conductor). When we connect a current source to a conductor by applying a certain potential difference (electrical voltage) to its ends, we force electrons to move in an orderly manner from one pole of the energy source to the other. An electric current of charges arises inside the conductor, its crystal lattice.

And now we can move on to the question of electrical resistance of current, its essence. And so, when electric charges pass inside a conductor, the electron does not have to move along a straight path; their movements are more like jumping from one atom to another. Naturally, with such a movement some energy will be expended (to overcome obstacles). In addition, it is worth considering that atoms do not stand still, they have their own internal chaotic movement inside the crystal lattice of the substance. And the greater this movement (which also depends on the temperature, the higher it is, the more intense the movement of atoms), the greater the obstacle that arises before the movement of charges. It is this obstacle to the movement of current that is called electrical resistance.

There is also such a thing as superconductivity. This is when the electrical resistance of the current is equal to zero. Electric current runs through the conductor without loss. So to speak, the ideal guide. This effect can be achieved if certain substances are brought to a temperature absolute zero(273 degrees Celsius). And as is known from physics, at ultralow temperatures the movement of an atom inside the crystal lattice of a substance practically stops. On the path of electrons, electric current There are no obstacles for charged particles, which gives the effect of superconductivity.

Electrical resistance depends on such fundamental electrical quantities as current and voltage. All these three electrical characteristics merged common law which is called Ohm's law (current equals voltage divided by resistance). The dependence of this trinity is as follows: the greater the resistance of the electrical circuit, the less the current will be, at the same supply voltage. The more voltage we apply to the circuit, the greater the current will flow, with equal circuit resistance. That is, the greater the resistance, the less the current, and vice versa. Current resistance has its own unit of measurement, it is Ohm (1 kiloohm is equal to 1000 ohms). 1 Ohm equals 1 Volt divided by 1 Ampere.


We have analyzed the essence of electrical resistance of current as a physical quantity. But very often when talking about resistance, it means a specific material thing, part, functional element. That is, an ordinary electrical resistor is called resistance, since the direct purpose of this part is precisely to form electrical resistance in a certain part of the circuit. Electrical resistance of current can also be active and reactive. Active resistance exists in all resistive elements (conductors with heating capacity). Various coils and capacitances have reactance. But about this in another topic.

P.S. A beginner may have such a natural question. Why do you need to specifically install a resistance in an electrical circuit, since its essence is to prevent the flow of current? It is necessary, even necessary, just like having brakes on a car. When it becomes necessary to slow down or stop, you simply cannot do without brakes. It’s about the same in the field of electrical and electronics. In some places in the electrical circuit, it is necessary to have less voltage and current than at the input of the power source, which is what a resistor (resistance) does.

The term resistance is in some respects luckier than other physical terms: from early childhood we become familiar with this property of the world around us, mastering our environment, especially when we reach for a toy that we like in the hands of another child, and he resists it. This term is intuitively clear to us, therefore, during school years during physics lessons, getting acquainted with the properties of electricity, the term electrical resistance does not cause us any confusion and its idea is perceived quite easily.

The number of technical implementations of electrical resistance - resistors - produced in the world is incalculable. Suffice it to say that in the most common modern electronic devices - mobile phones, smartphones, tablets and computers - the number of elements can reach hundreds of thousands. According to statistics, resistors make up over 35% of the elements of electronic circuits, and given the scale of production of such devices in the world, we get a mind-boggling figure of tens of trillions of units. Along with other passive radioelements - capacitors and inductors, resistors form the basis of modern civilization, being one of the pillars on which our familiar world rests.

Definition

Electrical resistance is a physical quantity that characterizes certain electrical properties of matter that prevent the free passage of electric current through it without loss. In terms of electrical engineering, electrical resistance is the characteristic of an electrical circuit as a whole or a section of it to prevent the flow of current and is equal, at constant current, to the ratio of the voltage at the ends of the circuit to the current flowing through it.

Electrical resistance is concerned with the transfer or conversion of electrical energy into other forms of energy. When electrical energy is irreversibly converted into heat, we talk about active resistance. With the reversible conversion of electrical energy into the energy of a magnetic or electric field, if alternating current flows in the circuit, we speak of reactance. If inductance predominates in the circuit, we talk about inductive reactance, if capacitance, we talk about capacitive reactance.

The total resistance (active and reactive) for alternating current circuits is described in terms of impedance, and for alternating electromagnetic fields - by characteristic impedance. Resistance is sometimes not entirely correctly called its technical implementation - a resistor, that is, a radio component designed to introduce active resistance into electrical circuits.

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

R - resistance, Ohm;

U is the difference in electrical potential (voltage) at the ends of the conductor, V;

I is the current strength flowing between the ends of the conductor under the influence of a potential difference, A.

This formula is called Ohm's law, named after the German physicist who discovered this law. An important role in the calculation thermal effect active resistance is played by the law of heat released when an electric current passes through resistance - the Joule-Lenz law:

Q = I 2 ∙ R ∙ t

Q is the amount of heat released over a period of time t, J;

I - current strength, A;

R - resistance, Ohm;

t - current flow time, sec.

Units

The basic unit of measurement of electrical resistance in the SI system is the Ohm and its derivatives: kiloohm (kOhm), megaohm (MOhm). You can find the ratio of SI units of resistance to units of other systems in our unit converter.

Historical reference

The first researcher of the phenomenon of electrical resistance, and, subsequently, the author of the famous law of the electrical circuit, later named after him, was the outstanding German physicist Georg Simon Ohm. Published in 1827 in one of his papers, Ohm's law played a decisive role in the further study of electrical phenomena. Unfortunately, his contemporaries did not appreciate his research, like many of his other works in the field of physics, and, by order of the Minister of Education, he was even fired from his post as a mathematics teacher in Cologne for publishing the results of his research in newspapers. And only in 1841, after the Royal Society of London awarded him the Copley Medal at a meeting on November 30, 1841, recognition finally came to him. Taking into account the merits of Georg Ohm, in 1881, at the international congress of electricians in Paris, it was decided to name the now generally accepted unit of electrical resistance (“one ohm”) after him.

Physics of phenomena in metals and its application

According to their properties and relative resistance values, all materials are divided into conductors, semiconductors and insulators. A separate class are materials that have zero or close to zero resistance, the so-called superconductors. The most typical representatives of conductors are metals, although their resistance can vary widely, depending on the properties of the crystal lattice.

According to modern concepts, metal atoms combine into a crystal lattice, and the so-called “electron gas” is formed from the valence electrons of the metal atoms.

The relatively low resistance of metals is due precisely to the fact that they contain a large number of current carriers - conduction electrons - belonging to the entire ensemble of atoms of a given metal sample. Arising from the application of an external electric field, the current in the metal represents the ordered movement of electrons. Under the influence of the field, electrons are accelerated and acquire a certain momentum, and then collide with lattice ions. During such collisions, electrons change momentum, partially losing the energy of their movement, which is converted into the internal energy of the crystal lattice, which leads to heating of the conductor when an electric current passes through it. It should be noted that the resistance of a sample of metal or metal alloys of a given composition depends on its geometry, and does not depend on the direction of the applied external electric field.

Further application of an increasingly stronger external electric field leads to an increase in current through the metal and the release of more and more heat, which can ultimately lead to melting of the sample. This property is used in wire fuses for electrical circuits. If the temperature exceeds a certain norm, the wire melts and interrupts the electrical circuit - current can no longer flow through it. The temperature standard is ensured by choosing the material for the wire according to its melting point. An excellent example of what happens to fuses comes from filming a filament burning out in an ordinary incandescent lamp.

The most typical application of electrical resistance is as a fuel element. We use this property when cooking and heating food on electric stoves, baking bread and cakes in electric ovens, as well as when working with electric kettles, coffee makers, washing machines and electric irons. And we don’t think at all that our comfort in Everyday life again, we should be grateful to electrical resistance: whether we turn on a boiler for a shower, or an electric fireplace, or an air conditioner in the mode of heating the air in the room - in all these devices there is always a heating element based on electrical resistance.

In industrial applications, electrical resistance ensures the preparation of semi-finished food products (drying), chemical reactions during optimal temperature for obtaining dosage forms and even in the manufacture of completely prosaic things, such as plastic bags for various purposes, as well as in the production of plastic products (extrusion process).

Physics of phenomena in semiconductors and its application

In semiconductors, unlike metals, the crystal structure is formed due to covalent bonds between the atoms of the semiconductor and therefore, unlike metals, in their pure form they have a significantly higher electrical resistance. Moreover, if they talk about semiconductors, they usually mention not resistance, but their own conductivity.

The introduction of impurities of atoms with a large number of electrons on the outer shell into a semiconductor creates n-type donor conductivity. In this case, the “extra” electrons become the property of the entire ensemble of atoms in a given semiconductor sample and its resistance decreases. Similarly, introducing into a semiconductor impurities of atoms with a smaller number of electrons on the outer shell creates p-type acceptor conductivity. In this case, the “missing” electrons, called “holes,” become the property of the entire ensemble of atoms in a given semiconductor sample and its resistance also decreases.

The most interesting case is the connection of semiconductor regions with various types conductivity, the so-called p-n junction. This transition has the unique property of anisotropy - its resistance depends on the direction of the applied external electric field. When the “blocking” voltage is turned on, the border p-n layer The junction is depleted of conduction carriers and its resistance increases sharply. When an “opening” voltage is applied in the boundary layer, conduction carriers recombine in the boundary layer and the resistance of the pn junction sharply decreases.

The most important elements of electronic equipment - rectifier diodes - are built on this principle. Unfortunately, when a certain current through the pn junction is exceeded, a so-called thermal breakdown occurs, in which both donor and acceptor impurities move through the pn junction, thereby destroying it, and the device fails.

The main conclusion about resistance p-n junctions is that their resistance depends on the direction of the applied electric field and is nonlinear, that is, it does not obey Ohm’s law.

The processes occurring in MOS transistors (Metal-Oxide-Semiconductor) are of a slightly different nature. In them, the source-drain channel resistance is controlled by electric field corresponding polarity for p- and n-type channels created by the gate. MOSFETs are used almost exclusively in the on-off switch mode and make up the vast majority of electronic components in modern digital technology.

Regardless of their design, all transistors in their physical essence are, within certain limits, inertia-free controlled electrical resistances.

Physics of phenomena in gases and its application

In their normal state, gases are excellent dielectrics because they have a very small number of charge carriers - positive ions and electrons. This property of gases is used in contact switches, overhead power lines and air capacitors, since air is a mixture of gases and its electrical resistance is very high.

Since the gas has ionic-electronic conductivity, when an external electric field is applied, the resistance of the gases initially slowly drops due to ionization of everything more molecules. With a further increase in the external field voltage, a glow discharge occurs and the resistance changes to a steeper voltage dependence. This property of gases was previously used in gas-filled lamps - stabistors - to stabilize direct voltage over a wide range of currents. With a further increase in the applied voltage, the discharge in the gas turns into a corona discharge with a further decrease in resistance, and then in the spark discharge - a small lightning appears, and the gas resistance in the lightning channel drops to a minimum.

The main component of the Terra-P radiometer-dosimeter is a Geiger-Muller counter. Its operation is based on the impact ionization of the gas contained in it when hit by a gamma quantum, as a result of which its resistance sharply decreases, which is recorded.

The property of gases to glow when current flows through them in a glow discharge mode is used for the design of neon advertisements, alternating field indications and in sodium lamps. The same property, only when mercury vapor glows in the ultraviolet part of the spectrum, ensures the operation of energy-saving lamps. In them, the luminous flux of the visible spectrum is obtained as a result of the conversion of ultraviolet radiation by a fluorescent phosphor with which the lamp bulbs are coated. The resistance of gases, just like in semiconductors, has a nonlinear dependence on the applied external field and also does not obey Ohm’s law.

Physics of phenomena in electrolytes and its application

The resistance of conducting liquids - electrolytes - is determined by the presence and concentration of ions of different signs - atoms or molecules that have lost or gained electrons. Such ions, when there is a lack of electrons, are called cations; when there is an excess of electrons, they are called anions. When an external electric field is applied (electrodes with a potential difference are placed in the electrolyte), cations and anions begin to move; the physics of the process consists of discharging or charging ions at the appropriate electrode. In this case, at the anode, the anions give up excess electrons, and at the cathode, the cations receive the missing ones.

A significant difference between electrolytes and metals, semiconductors and gases is the movement of substances in electrolytes. This property is widely used in modern technology and medicine - from purifying metals from impurities (refining) to introducing medicines into a diseased area (electrophoresis). The sparkling plumbing of our baths and kitchens comes from electroplating processes such as nickel and chrome plating. It is unnecessary to remember that the quality of the coating is achieved precisely by controlling the resistance of the solution and its temperature, as well as many other parameters of the metal deposition process.

Since the human body, from a physical point of view, is an electrolyte, knowledge of the human body’s resistance to the flow of electric current plays an essential role in relation to safety issues. Although the typical value of skin resistance is about 50 kOhm (weak electrolyte), it can vary depending on the individual's psycho-emotional state and conditions environment, as well as the area of ​​skin contact with the electrical conductor. Under stress and anxiety or when in uncomfortable conditions, it can decrease significantly, so for safety calculations of human resistance, a value of 1 kOhm is adopted.

It is curious that based on measuring the resistance of various areas of human skin, the method of operation of the polygraph is based - a “lie detector”, which, along with the assessment of many physiological parameters, determines, in particular, the deviation of resistance from current values ​​when asking the subject “uncomfortable” questions. True, this method is of limited applicability: it gives inadequate results when applied to people with unstable psyches, to specially trained agents, or to people with abnormally high skin resistance.

Within certain limits, Ohm's law is applicable to the current in electrolytes; however, when the external applied electric field exceeds certain values ​​characteristic of a given electrolyte, its resistance is also nonlinear.

Physics of phenomena in dielectrics and its application

The resistance of dielectrics is very high, and this quality is widely used in physics and technology when used as insulators. An ideal dielectric is a vacuum and, it would seem, what kind of resistance in a vacuum can we talk about? However, thanks to one of Albert Einstein’s works on the work function of electrons from metals, which was undeservedly ignored by journalists, in contrast to his articles on the theory of relativity, humanity gained access to the technical implementation of a huge class of electronic devices that marked the dawn of radio electronics, and to this day they work properly serving people.

According to Einstein, any conducting material is surrounded by a cloud of electrons, and these electrons, when an external electric field is applied, form an electron beam. Vacuum two-electrode devices have different resistance when changing the polarity of the applied voltage. Previously, they were used to rectify alternating current. Three or more electrode tubes were used to amplify the signals. Now they are being replaced by more energy-efficient transistors.

However, there remains an area of ​​application where devices based on an electron beam are absolutely irreplaceable - these are X-ray tubes, magnetrons used in radar stations and other electric vacuum devices. Engineers to this day peer into the screens of oscilloscopes with cathode ray tubes, determining the nature of the physical processes taking place, doctors cannot do without X-rays, and we all use microwave ovens every day, which contain microwave emitters - magnetrons.

Since the nature of conductivity in a vacuum is only electronic in nature, the resistance of most electric vacuum devices obeys Ohm's law.

Resistors: their purpose, application and measurement

A resistor is an electronic device needed in all electronic circuits. According to statistics, 35% of any radio circuit consists of resistors. Of course, you can try to come up with a circuit without resistors, but these will only be mind games. Practical electrical and electronic circuits without resistors are unthinkable. From the point of view of an electrical engineer, any device that has resistance can be called a resistor, regardless of its internal structure and method of manufacture. A striking example of this is the story of the crash of the airship “Italy” of the polar explorer Nobile. The expedition's radio operator managed to repair the radio station and send a distress signal, replacing the broken resistor with a pencil lead, which ultimately saved the expedition.

Resistors are elements of electronic equipment and can be used as discrete components or components integrated circuits. Discrete resistors are classified by purpose, type of current-voltage characteristic, method of protection and installation method, nature of resistance change, manufacturing technology and dissipated thermal energy. The resistor designation in the circuits is shown in the figure below:

Resistors can be connected in series or in parallel. When resistors are connected in series, the total resistance of the circuit is equal to the sum of the resistances of all resistors:

R = R 1 + R 2 + … + R n

When resistors are connected in parallel, their total circuit resistance is equal to

R = R 1 ∙ R 2 ∙ … ∙ R n /(R 1 + R 2 + … + R n)

According to their purpose, resistors are divided into:

  • general purpose resistors;
  • resistors for special purposes.

According to the nature of the change in resistance, resistors are divided into:

By installation method:

  • for printed circuit installation;
  • for wall-mounted installation;
  • for microcircuits and micromodules.

According to the type of current-voltage characteristic:

Color coding of resistors

Depending on the dimensions and purpose of the resistors, digital symbolic markings or markings with colored stripes for surface-mounted or printed-circuit mounted resistors are used to indicate their ratings. The symbol in the marking can play the role of a comma in the denomination designation: the symbols R and E are used to denote Ohm, the symbol K is used for kiloohms, and the symbol M is used for megaohms. For example: 3R3 means a nominal value of 3.3 Ohms, 33E = 33 Ohms, 4K7 = 4.7 kOhm, M56 = 560 kOhm, 1M0 = 1.0 Mohm.

The most universal and practical method for determining the value of a resistor and its serviceability is to directly measure its resistance with a measuring device. However, when measuring directly into a circuit, be aware that the circuit's power must be turned off and that the measurement will not be accurate.