Electricity and magnetism
Electricity and magnetism
The section of physics covering knowledge of static electricity, electrical currents and magnetic phenomena.
ELECTROSTATICS
Electrostatics addresses phenomena associated with resting electrical charges. The presence of forces acting between such charges was noted during the time of Homer. The word "electricity" comes from the Greek Elektron (amber), since the first friction-described friction electrification stories are connected with this material. In 1733 Sh. Dufe (1698-1739) discovered that there are electrical charges of two types. The charges of the same type are formed on the surge, if it rubbed it with a woolen cloth, the charges of another type - on the glass, if they rub it with silk. The same charges are repelled, different - attract. The charges of different types, connecting, neutralize each other. In 1750 B. Franklin (1706-1790) developed the theory of electrical phenomena based on the assumption that all materials contain some kind of "electrical liquid". He believed that with the friction of two materials, a part of this electrical fluid moves from one of them to another (while the total amount of electrical fluid is saved). The excess of electrical fluid in the body informs him the charge of one type, and its disadvantage is manifested as the presence of a charge of another type. Franklin decided that when rubbed Surguche, the wool wool takes some amount of electrical fluid. Therefore, he called the charge of Surguche Negative. The views of Franklin are very close to modern ideas, according to which the electrification by friction is due to the flow of electrons from one of the driving bodies to another. But since in reality, the electrons flow from wool on the surgasch, an excess occurs in the surgium, and not a lack of this electrical fluid, which is now identified with electrons. In Franklin, there was no way to determine in which direction the electrical fluid flows, and we are obliged by its unsuccessful choice by the fact that electron charges turned out to be "negative". Although such a charge sign causes some confusion in the study of the subject, this conventionity is too firmly rooted in the literature in order to talk about changing the charge sign in an electron after its properties have already been well studied. Using the tweeters developed by G. Cavendish (1731-1810), in 1785 sh. Cylon (1736-1806) showed that the force acting between two point electric charges is proportional to the product of the values \u200b\u200bof these charges and is inversely proportional to the square of the distance between them, namely:
Where F is the force with which the charge q repels the charge of the same sign Qў, and R is the distance between them. If the signs of charges are opposite, the force F is negative and the charges are not repelled, but attract each other. The proportionality coefficient K depends on which units are measured F, R, Q and Q. "
Units of charge measurement initially did not exist, but the law of the coulon makes it possible to introduce such a unit. This unit of electrical charge measurement is assigned the name "pendant" and abbreviated designation CL. One pendant (1 CL) is a charge that remains on an initially electrically neutral body after removing 6,242 * 1018 electrons from it. If in the formula (1) of charges q and q "are expressed in the coulons, F - in Newton, and R - in meters, then k" 8,9876 * 10 9 h * m2 / cl2, i.e. Approximately 9 * 10 9N * M2 / CL2. Usually instead of k use the E0 \u003d 1 / 4PK constant. Although the expression for the Culon law is slightly complicated, this allows us to do without a 4P multiplier in other formulas that are used more often than the Culon law.
Electrostatic machines and Leiden Bank. The machine for obtaining a static charge of a large magnitude by friction invented approximately 1660 O. Herica (1602-1686), which described her new experiments on the empty space (De Vacuo Spatio, 1672). Soon other options for such a car appeared. In 1745, E. Kleist from Cammin and regardless of him, P. Muschenbruck from Leiden found that the glass ass, laid out from the inside and outside the conductive material, can be used to accumulate and storing the electrical charge. Glass jars laid out from the inside and outside tin foil are the so-called Leiden banks - were the first electrical capacitors. Franklin showed that when charging Leiden's bank, the outer coating of the tin foil (outdoor) acquires the charge of one sign, and the internal occurrence is equal to the value of the opposite sign. If both charged plates are shown in contact or connected by the conductor, the charges completely disappear, which indicates their mutual neutralization. From here it follows that the charges are freely moved along the metal, but can not move around the glass. Materials type materials for charges are moved freely, were named wires, and glass type materials, through which charges do not pass, are insulators (dielectrics).
Dielectrics. The perfect dielectric is the material, the internal electrical charges of which are associated so firmly that it is not able to carry out an electric current. Therefore, it can serve as a good insulator. Although there are no ideal dielectrics in nature, the conductivity of many insulating materials at room temperature does not exceed 10-23 copper conductivity; In many cases, such conductivity can be considered equal to zero.
Conditions. The crystal structure and distribution of electrons in solid conductors and dielectrics are similar to each other. The main difference lies in the fact that in dielectric all electrons are firmly related to the corresponding nuclei, whereas in the conductor there are electrons that are in the outer shell of atoms that can freely move on the crystal. Such electrons are called free electrons or conduction electrons, as they are power charges. The number of conductivity electrons per mettle atom depends on the electron structure of atoms and the degree of perturbation of the outer electronic shells of the atom of its neighbors along the crystal lattice. At the elements of the first group of the periodic system of elements (lithium, sodium, potassium, copper, rubidium, silver, cesium and gold) Internal electronic shells are filled with entirely, and in the outer shell there is a single electron. The experiment confirmed that these metals have one atom, the number of conductivity electrons approximately equal to one. However, for most metals, other groups are characterized by an average fractional values \u200b\u200bof the number of electrons of conductivity per one atom. For example, transient elements - nickel, cobalt, palladium, rhenium and most of their alloys - the number of conductivity electrons per atom is approximately 0.6. The number of current carriers in semiconductors is much smaller. For example, in Germany at room temperature it is about 10-9. The extremely small number of media in semiconductors leads to the emergence of many interesting properties.
See solid physics;
Semiconductor electronic devices;
Transistor. The thermal fluctuations of the crystal lattice in the metal support the constant movement of the conductivity electrons, the speed of which at room temperature reaches 106 m / s. Since this is chaotically, it does not lead to an electric current. When the electrical field is overlapping, a small common drift appears. This drift of free electrons in the explorer is an electric current. Since electrons are charged negative, the current direction is opposite to the direction of their drift.
Potential difference. To describe the properties of the condenser, it is necessary to introduce the concept of potential difference. If there is a positive charge on one capacitor, and on the other is a negative charge of the same value, then for the transfer of an additional portion of a positive charge with a negative attachment to a positive one, it is necessary to work against the forces of attraction from negative charges and repulsion of positive. The potential difference between the plates is defined as the ratio of work on the transfer of a trial charge to the magnitude of this charge; It is assumed that the trial charge is significantly less than the charge, which was originally on each of the plates. Several modified formulation, it is possible to determine the potential difference between any two points, which can be anywhere: on a wire with a current, on different condenser plates or simply in space. This definition is such: the potential difference between the two points of space is equal to the ratio of operation spent on the movement of a test charge from a point with a lower potential to a point with a higher potential, to the value of the trial charge. It is assumed again that the test charge is sufficiently small and does not violate the distribution of charges, creating a measurable potential difference. The potential difference V is measured in volts (B), provided that W work is expressed in Joules (J), and the test charge Q is in the coulons (CL).
Capacity. The capacitance of the capacitor is equal to the ratio of the absolute value of the charge on any of its two plates (we will remind that their charges differ only to familiar) to the potential difference between the plates:
The C capacitance is measured in the Farades (f) if Q is pronounced in the coulutes (CL), and the potential difference is in Volta (B). Two just mentioned units of measurement, volts and Farad are named so in honor of the scientists A. Volti and M. Faradey. Faraday turned out to be so large that the capacity of most capacitors is expressed in micropraids (10 -6 Φ) or picofarades (10 -12 f).
Electric field. Near electric charges There is an electric field, the value of which at this point is equal to the definition, the ratio of the force acting on the point test charge placed at this point to the value of the test charge, again, provided that the test charge is sufficiently small and not Changes the distribution of charges creating a field. According to this definition, the power f and the electric field strength e are connected by the ratio
Faraday introduced an idea of \u200b\u200bthe power lines of the electric field beginning with positive and ending on negative charges. In this case, the density (density) of the power lines is proportional to the field strength, and the direction direction at this point coincides with the direction of tangent to the power line. Later, K. Gauss (1777-1855) confirmed the validity of this guessed. Based on the reverse squares established by the pendant (1), it mathematically strictly showed that the power lines, if they build them in accordance with the views of Faraday, are continuously everywhere in an empty space, starting on positive charges and ending with negative. This generalization received the name of Theorem Gauss. If the total number of power lines coming from each charge q is Q / E0, then the density of the lines at any point (that is, the ratio of the number of lines crossing the imaginary small-sized pad placed in this point perpendicular to them, to the area of \u200b\u200bthis site) equal to the magnitude of the electric field strength at this point, expressed either in the N / CL, or in per / m. The simplest capacitor is two parallel conductive plates located close to each other. When charging the capacitor, the plates acquire the same, but opposite to the charge sign, uniformly distributed over each of the plates, with the exception of the edges. According to the Gauss Theorem, the field strength between such plates is constant and is equal to E \u003d Q / E0A, where Q is a charge on a positively charged plate, and a - plate area. Due to the determination of the difference in potentials, we have V \u003d ED, where D is the distance between the plates. Thus, V \u003d QD / E0A, and the container of such a plane-parallel capacitor is equal to:
Where C is expressed in the pharands, and a and d, respectively, in m2 and m.
D.C
In 1780 L. Galvani (1737-1798), he noticed that the charge beloved from the electrostatic machine to the paw of a dead frog causes the paw to drag sharply. Moreover, the paws of the frog, fixed above the iron plate on a brass wire introduced into its spinal cord, jerked whenever they touched the plates. Galvani correctly explained this by the fact that electric charges, passing through the nervous fibers, make the muscles of the frog shrink. This movement movement was called electroplated. After the experiments carried out by electroplating, Volta (1745-1827) invented the so-called volts of the pillar - a galvanic battery made of several successively connected electrochemical elements. Its battery consisted of alternating copper and zinc circles separated by wet paper, and allowed to observe the same phenomena as an electrostatic machine. Repeating the experiments of Volta, Nikolson and Karlal in 1800 found that it is possible to apply copper from the copper sulfate solution to the copper conductor. W. Vollarston (1766-1828) received the same results with the help of an electrostatic machine. M. Faraday (1791-1867) showed in 1833 that the mass of the element obtained by electrolysis produced by these amount of charge is proportional to its atomic mass divided by valence. This provision is now called the Faraday law for electrolysis. Since the electric current is the transfer of electrical charges, naturally determine the current force unit as a charge in the coulons, which takes place every second through this site. The strength of the current 1 cell / s was named ampere in honor of A. Ampere (1775-1836), which opened many important effects associated with the effect of electric current. Ohm law, resistance and resistivity. In 1826, OM (1787-1854) announced a new opening: The current in a metal conductor when introduced into the chain of each additional section of the Voltov pillar increased by the same magnitude. It was generalized in the form of the law Ohm. Since the potential difference created by the volt post is proportional to the number of inclusive sections, this law claims that the difference in the potentials V between two points of the conductor, divided by current I in the conductor, is constant and independent of V or I. Attraction
It is called the resistance of the conductor on the plot between the two points. Resistance is measured in Omah (OM), if the potential difference V is expressed in volts, and the current I is in amperes. The resistance of the metal conductor is proportional to its length L and inversely in proportion to the area and its cross section. It remains constant, while its temperature is constant. Usually these provisions are expressed by the formula
Where R is a resistivity (OMHM), depending on the material of the conductor and its temperature. The temperature coefficient of the resistivity is defined as the relative change in R value when the temperature changes by one degree. The table shows the values \u200b\u200bof the resistivity and temperature coefficients of the resistance of some conventional materials, measured at room temperature. The specific impedances of pure metals are usually lower than that of alloys, and temperature coefficients are higher. Resistivity of dielectrics, especially sulfur and mica, much higher than metals; The ratio reaches the value of 1023. Temperature coefficients of dielectrics and semiconductors are negative and have relatively large values.
Thermal effect of electric current. The thermal effect of the electric current was first observed in 1801, when the current was able to melt various metals. The first industrial use of this phenomenon refers to 1808 when electrogenated powder was proposed. The first coal arc, intended for heating and lighting, was exhibited in Paris in 1802. To the poles of the Voltov pillar, which counted 120 elements, connected electrodes from charcoal, and when both coal electrodes were brought into contact, and then divorced, "sparkling discharge exclusive Brightness. " Exploring the thermal effect of electric current, J. Joule (1818-1889) conducted an experiment that failed the solid base under the law of energy conservation. Joule first showed that the chemical energy that is spent on maintaining in the current conductor is approximately equal to the amount of heat that is released in the conductor during current passage. It also found that the heat released in the conductor is proportional to the square for the current force. This observation is consistent with both the Ohm law (V \u003d IR) and the determination of the potential difference (V \u003d W / Q). In the case of a direct current, during T T through the conductor, the charge Q \u003d IT passes. Therefore, electrical energy that turned into a conductor to heat is equal to:
This energy is called Jowle warmth and is expressed in Joules (J), if the current I is expressed in amperes, R - in Omah, and T - in seconds. Electrical sources for DC circuits. When the constant electric current circuit occurs, there is an equally constant transformation of electrical energy to heat. To maintain current, it is necessary that electrical energy is produced in some parts of the chain. Volt pillar and other chemical current sources convert chemical energy into electric. In subsequent sections, other devices producing electrical energy are also discussed. All of them act like the electrical "pumps" moving electrical charges against the action of forces flowing down by a constant electric field. An important parameter of the current source is the electromotive force (EMF). EMF of the current source is defined as the potential difference on its clamps in the absence of current (with an open external chain) and is measured in volts.
Thermoelectricity. In 1822, T. Seebek discovered that in the chain composed of two different metals, the current occurs if one point of their connection is hot. Such a chain is called a thermoelement. In 1834, J. Peltier found that when the current passes through the spin of two metals in one direction, heat is absorbed, and in the other - it is allocated. The magnitude of this reversible effect depends on the materials falling and its temperature. Each spike of the thermoelement possesses EMF EJ \u003d WJ / Q, where WJ is a heat energy that turns into electrical in one direction of the movement of charge Q, or electrical energy that turns into heat when the charge is moving in another direction. These EDC are opposite to the direction, but are usually not equal to one another if the temperature of the dials differ. W. Thomson (1824-1907) found that the complete emf of the thermoelement is not folded from two, but from four EDS. In addition to the EMF, arising in the spa, there are two additional EMFs caused by the temperature drop on the conductor forming the thermoelement. They were given the name of the EDS Thomson.
The effects of Seebek and Peltier. The thermoelement is a "thermal machine", in a certain attitude similar to the current generator, cited steam turbine, but without moving parts. Like a turbogenerator, it turns heat into electricity, selecting it from the "heater" with a higher temperature and giving part of this heat "refrigerator" with a lower temperature. In the thermoelement, acting like a thermal machine, the "heater" is at hot spa, and the "refrigerator" is cold. The fact that heat with a lower temperature is lost, limits the theoretical efficiency of the transformation of thermal energy in the electrical value (T1 - T2) / T1 where T1 and T2 is the absolute temperatures of the "heater" and "refrigerator". Additional decrease in the efficiency of the thermoelement is due to heat loss due to heat transfer from the "heater" to the "refrigerator".
See heat; Thermodynamics. The heat transformation into electrical energy occurring in the thermoelement is usually called the Seebeck effect. Thermal elements, called thermocouples, are used to measure temperature, especially in hard-to-reach places. If one paw is in a controlled point, and the other at room temperature, which is known, the thermo-emf serves as a measure of temperature at a controlled point. Big successes are achieved in the field of thermoelements to direct heat transformation into electricity on an industrial scale. If through the thermoelement to skip the current from the external source, then the cold spay will absorb heat, and hot - allocate it. Such a phenomenon is called Peltier Effect. This effect can be used either for cooling with cold spa, or for heating with hot spay. The thermal energy, highlighted by hot spawning, is more than the total amount of heat supplied to the cold spa, by the value corresponding to the electrical energy. Thus, hot spay highlights more heat than it would correspond to the total amount of electrical energy supplied to the device. In principle, a large number of successively connected thermoelements, the cold spahs of which are derived outward, and the hot rooms are inside the room, can be used as a heat pump pumping heat from a lower temperature region to a higher temperature area. Theoretically, the gains in thermal energy compared to the cost of electrical energy can be T1 / (T1 - T2). Unfortunately, for most materials, the effect is so small that there would be too many thermoelements in practice. In addition, the applicability of the Peltier effect somewhat limits the heat transfer from the hot spa to the cold due to thermal conductivity in the case of metal materials. Studies of semiconductors led to the creation of materials with sufficiently large Peltier effects for a number of practical applications. The Peltier effect turns out to be particularly valuable if necessary, cooling hard-to-reach areas, where ordinary cooling methods are not suitable. With the help of such devices, the devices are cooled, for example, instruments in spacecraft.
Electrochemical effects. In 1842, Helmholtz demonstrated that in the source of the type of Voltov pillar, the chemical energy turns into electrical, and in the process of electrolysis, electrical energy turns into a chemical. Chemical sources of current type of dry elements (ordinary batteries) and batteries were extremely practical. When charging the battery with an electric current of optimal value, most of the electrical energy reported to it turns into chemical energy that can be used when the battery is discharged. And when charging, and when the battery is discharged, part of the energy is lost in the form of heat; These thermal losses are due to the internal resistance of the battery. EMF of such a current source is equal to the potential difference on its clamps under an open circuit, when there is no IR voltage drop on the inner resistance.
DC circuits. To calculate the DC power in a simple chain, you can use the law open by Ohom when the Voltov column is studied:
Where R is the chain resistance and V - EDC source. If several resistors with resistances R1, R2, etc. Connected consistently, then in each of them the current I of the same and the total potential difference is equal to the sum of individual potential differences (Fig. 1, a). Common resistance can be defined as the resistance of the RS serial connection of the resistor group. The difference of potentials on this group is equal
Hence,
If the resistors are connected in parallel, the potential difference on the group coincides with the difference in potentials on each single resistor (Fig. 1, b). Full current through a group of resistors is equal to the sum of currents through individual resistors, i.e.
Since I1 \u003d V / R1, I2 \u003d V / R2, I3 \u003d V / R3, etc., the resistance of the parallel connection of the RP group is determined by the ratio
Where follows
When solving problems with DC circuits of any type, you must first simplify the task, using relations (9) and (10).
The laws of Kirchhoff. Kirchhof (1824-1887) investigated in detail Ohm's law and developed a general method for calculating constant currents in electrical circuits, including containing several sources of EDC. This method is based on two rules called Kirchhoff's laws: 1. The algebraic sum of all currents in any circuit node is zero. 2. The algebraic sum of all IR potential differences in any closed loop is equal to the algebraic amount of all EDS in this closed circuit. These two laws are enough to solve any problem associated with DC chains.
see also
Power Battery;
Electrical chains.
Magnetostatics
The magnetostatics dealt with the forces arising between bodies with constant magnetization. The properties of natural magnets are reported in the writings of Falez Miletsky (approx. 600 BC) and Plato (427-347 BC). The word "magnet" arose due to the fact that natural magnets were discovered by the Greeks in Magnesia (Fessels). To 11 c. The message of the Chinese Shen Qua and Chu Yu on the manufacture of compasses from natural magnets and using them in navigation. If a long needle of a natural magnet is balanced on the axis, allowing it to be freely rotated in the horizontal plane, then it is always facing one end to the north, and the other is to the south. Placing an end pointing to the north, you can use such a compass to determine the directions. Magnetic effects were concentrated in such a needle, and therefore they were called poles (respectively by the Northern and South). Writing W. Hilbert about magnet (De Magnee, 1600) was the first attempt to study magnetic phenomena from the standpoint of science. In this work, the information about electricity and magnetism, as well as the results of the author's own experiments, were collected. Rods made of iron, steel and some other materials are magnetized when contacting natural magnets, and their ability to attract small pieces of iron, as in natural magnets, usually manifests itself near the poles located in the ends of the rods. Like electrical charges, the poles are two types. The same poles are mutually repelled, and the opposites are attracted. Each magnet has two identical poles of the opposite sign. Unlike electrical charges, which can be separated from each other, the pairs of poles were inseparable. If the magnetized rod is neatly cutting in the middle between the poles, then two new poles of the same strength appear. Since electrical charges do not affect magnetic poles and, on the contrary, electric and magnetic phenomena for a long time were considered completely different in nature. The pendant set the law for the forces of attraction and repulsion of the poles, taking advantage of the weights similar to those that he applied, finding out the law for the forces acting between two point charges. It turned out that the force acting between the point poles is proportional to their "magnitude" and inversely proportional to the square of the distance between them. This law is recorded in the form of
Where P and P "- the" values \u200b\u200b"of the poles, R is the distance between them, and Km is a proportionality coefficient, which depends on the units used. In modern physics, refused to consider the magnetic poles (for reasons that are explained in the next section), So this law is mainly historical interest.
Magnetic Effects of Electric Current
In 1820, Ersted (1777-1851) found that the conductor with current acts on a magnetic arrow, turning it. Literally a week later, the ampere showed that two parallel conductor with a current of one direction attracted each other. Later, he suggested that all magnetic phenomena were due to currents, and the magnetic properties of permanent magnets are associated with currents constantly circulating inside these magnets. This assumption is fully consistent with modern ideas.
See magnets and magnetic properties of a substance. Electric fields created by electric charges in the surrounding space are characterized by force acting on a single trial charge. Around the magnetized materials and electrical conductors, magnetic fields arise, which were originally characterized by force acting on the "single" trial pole. Although this method of determining the magnetic field strength is no longer applied, this approach has been preserved when determining the direction of the magnetic field. If a small magnetic arrow is suspended in its center of mass and can rotate freely in any direction, then its orientation and will indicate the direction of the magnetic field. From the use of magnetic poles to determine the characteristics of magnetic fields, it was necessary to refuse for a number of reasons: first, it is impossible to isolate a separate pole; Secondly, no position nor the amount of the pole cannot be accurately determined; Thirdly, magnetic poles are essentially fictitious concepts, since in fact magnetic effects are due to the movement of electrical charges. Accordingly, this magnetic fields are now characterized by the force with which they act on conductors with a current. In fig. 2 shows a conductor with a current I lying in the plane of the pattern; The current direction is indicated by the arrow. The conductor is located in a homogeneous magnetic field, the direction of which is parallel to the plane of the pattern and is an angle F with the direction of the conductor with the current. The magnitude of the induction of the magnetic field B is given by the expression
where F is the force with which the field B acts on the conductor element L with a current I. The direction of force F is perpendicular to both the direction of the magnetic field and the current direction. In fig. 2 This force is perpendicular to the plane of the pattern and is directed from the reader. The value B in principle can be determined by turning the conductor until f reaches the maximum value at which B \u003d Fmax / IL. The direction of the magnetic field can also be installed, turning the conductor, until the force f turns into zero, i.e. The conductor will be parallel to B. Although these rules are difficult to apply in practice, experimental methods for determining the magnitude and direction of magnetic fields are based on them. The force acting on the conductor with current is usually written in the form of
J. Bio (1774-1862) and F. Savar (1791-1841) brought the law to calculate the magnetic field created by the known distribution of electrical currents, namely
Where b is a magnetic induction, created by an element of a low-length conductor L with a current I. The direction of the magnetic field created by this element of the current is shown in Fig. 3, which also explains the values \u200b\u200bof R and F. The proportionality coefficient K depends on the choice of measurement units. If i is expressed in amperes, l and r - in meters, and b - in Teslas (TL), then k \u003d m0 / 4p \u003d 10-7 pm / m. To determine the value and direction B at any point of the space that creates a high-length conductor and an arbitrary shape, it is necessary to mentally smash the conductor to short segments, calculate the values \u200b\u200bB and determine the direction of fields created by individual segments, and then fold these individual fields. For example, if the current I in the conductor forming the circle with a radius A is directed clockwise, the field in the center of the circle is easily calculated. In formula (13), the distance R from each element of the conductor to the center of the circle is equal to A and F \u003d 90 °. In addition, the field created by each element perpendicular to the circumference plane and directed from the reader. Folding all the fields, we get magnetic induction in the center:
To find the field near the conductor created by a very long straight conductor with a current I, to summarize fields it will be necessary to resort to integration. Found in this way the field is equal:
Where R is the distance to perpendicular from the conductor. This expression is used in the currently definition of the ampere.
Galvanometers. The ratio (12) allows you to compare the forces of electrical currents. The device created for this purpose is called a galvanometer. The first such device was built by I. Shuger in 1820. He was a coil of the wire, inside which the magnetic arrow is suspended. The measured current was skipped through the coil and created a magnetic field around the arrow. The arrow acted a torque, proportional strength of the current, which was balanced due to the elasticity of the suspension yarn. The magnetic field of the Earth makes distortion, but its influence can be excluded, surrounding the arrow with permanent magnets. In 1858, U.Tomson, more famous as Lord Kelvin, attached the mirror to the arrow and introduced a number of other improvements, significantly improving the sensitivity of the galvanometer. Such galvanometers belong to the class of instruments with a moving arrow. Although the galvanometer with a moving arrow can be made extremely sensitive, it almost completely suppressed the device with a movable coil or frame placed between the poles of a permanent magnet. The magnetic field of a large horseshoe magnet in the galvanometer is so strong compared to the magnetic field of the Earth, that the influence of the latter can be neglected (Fig. 4). The galvanometer with a mobile frame was proposed in 1836 W. Sternzhen (1783-1850), but did not receive due recognition, while in 1882 J.D. "Arsonval did not create a modern version of this device.
Fig. 4. Galvanometer D Arsonval for measuring the power of the electric current. The arrow is connected to a movable frame suspended between the poles of the horseshoe magnet.
Electromagnetic induction. After Ersted found that the constant current creates a torque acting on a magnet, many attempts were made to detect a current caused by the presence of magnets. However, the magnets were too weak, and the current measurement methods are too rude to detect any effect. Finally, two researchers - J. Henry (1797-1878) in America and M. Faraday (1791-1867) in England - in 1831, independently of each other found that when changing the magnetic field, short-term currents appear in the number of conductive circuits, but short-term currents arise, but The effect is absent if the magnetic field remains constant. Faraday believed that not only electrical, but also magnetic fields are power lines that fill the space. The number of power lines of the magnetic field crossing the arbitrary surface S corresponds to the value F, which is called the magnetic flow:
Where BN is the projection of the magnetic field B to the normal to the DS area element. The unit of measurement of the magnetic flux is called Weber (WB); 1 WB \u003d 1 Tl * m2. Faraday was formulated by a law on EMF, inscribed in a closed twist of the wire with a changing magnetic field (the law of magnetic induction). According to this law, such an emf is proportional to the rate of changes in the total magnetic flux through the turn. In the system, the system of the coefficient of proportionality is 1 and, thus, the EMF (VOLT) is equal to the rate of change of magnetic flux (in WB / s). Mathematically, this is expressed by the formula
Where the minus sign shows that the magnetic fields of the currents created by this EDC are directed so that the change in the magnetic flux decreases. This rule for determining the direction of the EMF is consistent with the more general rule formulated in 1833 E.Lenz (1804-1865): the induced EMF is directed so that he opposes its emergence. In the case of a closed circuit in which the current occurs, this rule can be derived directly from the law of energy conservation; This rule is determined by the direction of the EMF induce and in the case of an open circuit when the induction current does not occur. If the coil consists of n turns of the wire, each of which is penetrated by the magnetic flow F, then
This ratio is fair regardless of which reason the magnetic flow chain changes.
Generators. The principle of operation of the electromashic generator is shown in Fig. 5. The rectangular coil of the wire rotates counterclockwise in a magnetic field between the poles of the magnet. The ends of the turn are removed to the contact rings and are connected to the external chain through the contact brushes. When the plane of the turn is perpendicular to the field, piercing the magnetic flow of the magnetic flux. If the plane of the turn is parallel to the field, then the magnetic flux is zero. When the cooler plane turns out to be perpendicular to the field, turning 180 °, the magnetic flux through the current maximum in the opposite direction. Thus, when the turn is rotated, the magnetic flow changes continuously and in accordance with the law of Faraday, the voltage on the clips changes.
To analyze what happens in a simple alternator of alternating current, we will consider the magnetic flow positive when the angle Q is in the range from 0 ° to 180 °, and negative when Q is from 180 ° to 360 °. If b is the induction of the magnetic field and A - the area of \u200b\u200bthe turn, then the magnetic flow through the round will be equal to:
If the coil rotates with the frequency F about. / S (i.e. 2pf rad / s), then after time t from the start of rotation, when q was equal to 0, we get Q \u003d 2PFT. Thus, the expression for flow through the round is acquired
According to the Faraday law, the inspected voltage is obtained by the flow differentiation:
Signs in the brushes in the figure show the polarity of the inspection voltage at the appropriate moment. Cosine varies from +1 to -1, so the value of 2pfab is simply voltage amplitude; You can designate it through
(At the same time, we lowered the "minus" sign, replacing it with an appropriate choice of polarity of the generator conclusions in Fig. 5.) In Fig. 6 shows a timetage change in time.
The voltage produced by the above-described generator periodically changes its direction to the opposite; The same refers to currents created in electrical circuits by this voltage. Such a generator is called alternator. The current, always preserving the same direction, is called constant. In some cases, such as charging batteries, such a current is necessary. You can two ways to receive a constant current from the variable. One is that the external circuit includes a rectifier, transmitting a current only in one direction. This allows you to turn off the generator for one half-period and include it only in that half-period when the voltage has the necessary polarity. Another method is to switch contacts connecting the coil with an external chain through each half-period when the voltage changes the polarity. Then the current in the outer chain will always be directed in one direction, although the voltage inspected in the twist changes its polarity. The switching of contacts is carried out using the collector semi-colts installed instead of the current collecting rings, as shown in Fig. 7, a. When the plane is vertical, the rate of change of magnetic flux and, therefore, the inspected voltage is dropped to zero. It is at this moment that the brushes slip over the gap separating two semirings, and the external circuit switching. The voltage arising in the outer chain varies as shown in Fig. 7, b.
see also Electromachine generators and electric motors.
Mutual induction. If two closed wire coils are located nearby, but electrically not connected with each other, then when changing the current in one of them, the EMF is revealed. Since the magnetic flux through the second coil is proportional to the current in the first coil, the change in this current entails the change in the magnetic flux with the guidance of the corresponding EMF. Coils can be changed roles, and then when changing the current in the second coil, EDC will be guided in the first. EMF, inserted in one coil, is determined by the speed of current change in the other and depends on the size and number of turns of each coil, as well as from the distance between the coils and their orientation, one relative to the other. These dependencies are relatively simple, if there are no magnetic materials nearby. The attitude of the EMC, induced in one coil, to the rate of change of current in the other is called the coefficient of mutually induction of two coils corresponding to these location. If the induced EMF is expressed in volts, and the speed of current change is in amperes per second (A / C), then the mutually induction will be expressed in Henry (GG). EMF, inspected in coils, are given in the following formulas:
Where M is the intention coefficient of two coils. The coil connected to the current source is called a primary coil or winding, and the other is secondary. A permanent current in the primary winding does not create voltages in secondary, although at the time of turning on and off the current in the secondary winding it is briefly arising with EMU. But if the EMF is connected to the primary winding, creating an alternating current in this winding, the EDC variable is indoable and in the secondary winding. Thus, the secondary winding can be used by alternating current active load or other circuits without directly connecting them to the EDC source.
Transformers. The intention of two windings can be significantly increased by winding them on a common core of ferromagnetic material, such as iron. A similar device is called a transformer. In modern transformers, the ferromagnetic core forms a closed magnetic chain, so that almost the entire magnetic stream passes inside the core and, therefore, through both windings. The source of the EDC variable connected to the primary winding creates an alternating magnetic flux in the iron core. This flow reserves variables of the EMF and in the primary, and in secondary windings, and the maximum values \u200b\u200bof each EDC are proportional to the number of turns in the appropriate winding. In good transformers, the windings resistance is so small that the EMF, induced in the primary winding, almost coincides with the applied voltage, and the potential difference at the secondary winding conclusions almost coincides with the EMF induced in it. Thus, the ratio of the voltage drop at the load of the secondary winding to the voltage applied to the primary winding is equal to the ratio of the number of turns in the secondary and primary windings, which is usually written in the form of equality
Where V1 is the voltage drop on the N1 turns of the primary winding, and V2 is the voltage drop on the N2 turns of the secondary winding. Depending on the ratio of the number of turns in the primary and secondary windings, the increase and lower transformers differ. The ratio N2 / N1 is greater than the units in the increasing transformers and less than the unit in lowering. Thanks to transformers, an economical transmission of electrical energy over long distances is possible.
see also Electric transformer. Self-induction. The electric current in a separate coil also creates a magnetic stream that permeates this coil itself. If the current in the coil changes over time, the magnetic flux through the coil will be changed, tiping it in it in the same way as this happens when the transformer is working. The emergence of EMF in the coil when changing the current is called self-induction. Improption affects the current in the coil. Similarly, the inertia is influenced by the movement of bodies in the mechanics: it slows down the setting of the DC in the chain when it is turned on and prevents it from an instantaneous stop when it is turned off. It also serves as a sparks occurring between the circuit breaker contacts when the circuit is blurred. In the AC circuit, self-induction creates a reactive resistance that limits the amplitude of the current. In the absence of magnetic materials near a fixed coil, a magnetic flow that permeates it is proportional to the current in the chain. According to the law of Faraday (16), EMF of self-induction should in this case be proportional to the current change rate, i.e.
Where L is the proportionality coefficient, called self-induction or inductance of the chain. Formula (18) can be considered as determining the value of L. If the factory index is expressed in volts, current I - in amperes and time T - in seconds, then L will be measured in Henry (GG). The minus sign indicates that the EMF is opposed to an increase in current I, as follows from the Lenza law. External EMF, overcoming self-induction EMF, should have a plus sign. Therefore, in alternating current circuits, the voltage drop in inductance is L di / dt.
Variables Toki.
As already mentioned, variable currents are currents whose direction periodically changes. The number of periods of cyclic changes of the current per second is called the frequency of AC and is measured in Hertz (Hz). Electricity is usually supplied to the consumer as an AC with a frequency of 50 Hz (in Russia and in European countries) or 60 Hz (in the USA). Since alternating current changes over time, simple ways to solve problems suitable for DC circuits here are directly not applicable. At very high frequencies, the charges can perform a oscillatory movement - to flow from one chain to others and back. At the same time, in contrast to the DC circuits, the currents in sequentially connected conductors may be unequal. Capacities present in alternating current circuits enhance this effect. In addition, when changing the current, self-induction effects are affected, which become essential even at low frequencies, if coils are used with high inductance. At relatively low frequencies of the AC circuit, it is still possible to calculate using the Kirchhoff rules, which, however, must be modified accordingly. The chain, which includes different resistors, inductors and condense coils, can be considered as if it consisted of a generalized resistor, capacitor and inductors connected sequentially. Consider the properties of such a circuit connected to the sinusoidal alternating current generator (Fig. 8). To formulate rules to calculate the AC circuit, you need to find a ratio between the voltage drop and the current for each of the components of such a chain.
The capacitor plays completely different roles in the chains of variable and constant currents. If, for example, to the chain in Fig. 8 Connect the electrochemical element, the condenser will start charge until it becomes equal to the EDC element. Then the charging stops and the current will fall to zero. If the circuit is connected to an AC generator, then in one half-period electrons will flow out of the left edge of the condenser and accumulate on the right, and in the other - on the contrary. These moving electrons are alternating current, the strength of which is the same on both sides of the condenser. While the variable current frequency is not very large, the current through the resistor and the inductor coil is also the same.
Reactive and full resistance. To analyze the ratio between the current and the voltage for the contour shown in Fig. 8, assume that the charge on the left plate of the capacitor is given by the expression
And the charge on the right plate is q. Here q is the maximum charge (CL), T - time (C), and w \u003d 2pf, where F is the frequency of the AC (Hz). Current via each chain element is:
Where the maximum current of Imasa is equal to W Q. A variable voltage drop on the condenser is:
According to the Ohm law, the voltage drop on the resistor is given by expression
The voltage drop of the entire chain from A to B is:
or
Where
Moreover
The value of XL is called inductive resistance and is expressed in Omah if L - in Henry; The value of XC is called capacitive resistance and is expressed in Omah, if C is in the Farades. The total reactive resistance of the chain X is also expressed in Oma. Formula (19) can be brought to a simple and clearer, using the trigonometric identity of COS (A + B) \u003d COS A COS B - SIN A SIN B. Since R and X are expressed in ohms, they can be considered as the cathets of a rectangular triangle to determine the angle Q (Fig. 9). Hypotenuse
It is called the full resistance (impedance) of the serial connection. In fig. 9 shows a complete resistance triangle, from which it appears that R \u003d z cos q, x \u003d z sin Q and Tg Q \u003d X / R. Expression (19) can be rewritten in the form V \u003d iMAXZ (COS Q COS W T - SIN Q SIN W T), which reduces to expression
If you use the above trigonometric identity; Expression (21) can be rewritten in the form
Where
From formula (21) it follows that voltage V on the clips of the chain is maximal as possible at t \u003d -q / w, while the current I is maximum at t \u003d 0, i.e. The current is lagging behind the phase from the voltage to the angle q. Thus, the current lags behind the phase from the voltage if inductive resistance prevails, i.e. If XL is greater than XC. The current is ahead of the voltage if capacitive resistance dominates, i.e. XC More XL. It should be noted that the relation (22) differs from the OL law only by the fact that in it the active resistance R is replaced by the full resistance of Z. If the resistance R and the maximum voltage drop on the chain clamps are supported by constant, then the highest value of the maximum current IMAX meets the equality of two reactive resistance. If inductance and capacity are also constant, then the equality of their reactive resistance can be achieved, changing the frequency of alternating current. This is achieved with a circular frequency
In this case, they talk about the resonant setting of the chain.
Above it was assumed that the alternating current in the chain was established. In fact, when connecting the circuit to the source of alternating voltage, transient processes occur in it. If the chain resistance is not negligible, the transitional currents select their energy in the form of heat in the resistor and quickly fade, after which the stationary alternating current mode is set, which was supposed to be higher. In many cases, transient processes in alternating circuits can be neglected. If they need to be considered, then it is necessary to investigate the differential equation describing the current dependence on time.
Effective values. The main task of the first district power plants was to ensure the desired heat of the threads of lighting lamps. Therefore, the question of the efficiency of use for these chains of constant and alternating currents. According to formula (7), for electrical energy transforming into heat in a resistor, the heat dissipation is proportional to the square of the current force. In the case of AC, the heat dissipation continuously fluctuates together with the instantaneous value of the current for the current of the current force. If the current varies according to the sinusoidal law, then the time-averaged value of the instantaneous current equal to half the square of the maximum current, i.e.
The square root from this value is called an effective variable value. Consequently, the effective value of the forces of the AC is equal to:
This should be a permanent current to ensure the same heating of the filament as an alternating current with the amplitude of IMAX. Obviously, the amplitude of alternating voltage on the incandescent lamp must be more than the corresponding constant voltage. Thus, the effective value of the voltage of alternating current is defined as
According to the formula (22), the impedance of the AC circuit is equal to:
In the absence of the jet elements in the chain, we have Z \u003d R and R \u003d V / I, it seems that the ratio between the effective voltage and current values \u200b\u200bin the AC circuit turns out to be the same as in the DC circuit. The power coming into a serial circuit, expressed through the effective values \u200b\u200bof current and voltage, is equal to:
Since the power released in the DC circuit is p \u003d vi, the value of Cos Q is called the power factor. But v \u003d iz, and r \u003d z cos q (Fig. 9). Thus, the power secreted by alternating current in the serial circuit is equal to:
Where it can be seen that all the power is spent on the heating of the resistor, while in the capacitor and inductance, the power is not absorbed. True, real inductance coils still absorb some power, especially if they have an iron core. With continuous reclamation, the iron core is heated - partially injected in the iron currents, and partly due to internal friction (hysteresis), which prevents reclamation. In addition, inductance can cause currents in the schemes located nearby. When measuring in alternating circuits, all these losses look like power loss in resistance. Therefore, the resistance of the same chain for AC is usually somewhat larger than for constant, and it is determined through power loss:
In order for the power station to work economically, thermal losses in the power line (LEP) should be low enough. If the PC is the power supplied to the consumer, then Pc \u003d VCI for both the permanent and alternating current, since with the proper calculation, the COS Q value can be made equal to one. Power losses will be PL \u003d RLi2 \u003d RLPC2 / VC2. Since at least two conductor l lengths are required for LAP, its resistance is RL \u003d R 2L / a. In this case, loss losses
If the conductors are made of copper, the specific resistance of the r which is minimally, then the numeric does not remain values \u200b\u200bthat could be significantly reduced. The only practical way to reduce losses is to increase VC2, since the use of conductors with a large cross-sectional area A is unprofitable. This means that the power should be transmitted using as high voltage as possible. Conventional electromashic current generators acting by turbines cannot produce a very high voltage that is not withstanding their insulation. In addition, ultra-high voltage is dangerous for service personnel. However, the voltage of the alternating current generated by the power plant is possible for transmissions on the LAM to increase using transformers. At the other end of the power passer, the consumer uses downstream transformers, which give the output more secure and practical low voltage. Currently, the voltage in the LAP reaches 750,000 V.
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