The reactive tension of the sinusoidal struma is active. Reactive pressure

⁰

Understanding the potential of the retail potential

uallows the robot to designate what is generated by the electric field when moving an elementary electric chargedq, yak dA= udq. At the same hour electric strum dorivnyuєi= dq/dt. Zvіdsi dA= ui dt, otzhe, shvidk_st vikonannya roboti, tobto. fatigue at a given moment, or mitteva tightness dorivnyuє u=U m sinw tі I m sin(w t-j ), even the average tension is more expensive

because the integral of another addendum is equal to zero. Value

cosj called the coefficient of tension .

Why is it so obvious that the average tightness of the lanceug snake struma to deposit not only in the form of the developing value of the struma

I that voltage U, Ale and different phases j between them. The maximum tension in the presence of zero phase zsuvu and more oil recoveryUI. When the phases are destroyed between the strum and the spring± 90° the average tension is close to zero. The maximum value of the voltage of that stream, whether it be an electric machine, is determined by its design, and the maximum tension, as stench can develop, is a supplement to these values. Yakshcho elektrichna lansyug irrationally induced, tobto. phase failure j If there is a significant value, then the electric energy and energy cannot be applied to the full intensity. Therefore, whether the system is dzherelo-navantazhennya іsnuє t.zv. " problem cosj ", as a rule, at the best possible proximity cos j to one.

Viraz (3) you can also pay for help to understand

active warehouse struma I a i voltage U and look

Middle tightness

Pcall it active sweating and win at vatah [W].

We can see the integrand function of virase (3)

Timchasovі diagrams, scho vіdpovіdat tsomu vipadku, induced in fig. 1 a).

The positive values of the mitt's tension indicate the need for energy from the dzherel to the electric station
. Otzhe, with resistive input, all the energy that comes out of the dzherel turns into it into heat . j = 0 (j = ± p /2), then. for a purely reactive Lancug

Timing diagrams that show the daily inductive and daily eminent tension are shown in fig. 1 b) and d). Z virazіv (8) and hourly charts show that the tension is pulsing along the abscissa axis with a subvariant frequency, changing its sign of the skin quarter of the period. Tse means that for the fourth period (

p > 0) energy enters the electric socket from the dzherel and is stored in the magnetic box electric field, and with a stretch of the offensive quarter (p < 0) она целиком возвращается из цепи в источник. Так как площади, ограниченные участками с положительной мощностью и с отрицательной одинаковы, то средняя мощность отдаваемая источником нагрузке равна нулю и there is no transformation of energy in lancius.

I have a good deal of interest 1 > cos

j > 0 (1< |j | < p /2) и

How to see from the timchas diagrams in fig. 1 c), for most of the period, the tension decreases to the pressures (

p> 0), but also use the same time intervals, if the energy is stored in magnetic and electric fields, the energy is turned into a dzherelo. Businesses with positive valuespregardless of the nature of the reactive warehouse demand for more workers with negative values, this is an average pressurePpositive. Tse means what in the electric language transferring the process of converting electrical energy into heat or mechanical work .

Let's take a look at the energy processes in last day

rLC(Fig. 2). The voltage drop at the input of the lancet is vrivnovazhuetsya by the sum of the voltage drop on the elementsu=u r +u L +u C . Mitteva tightness at lanceuzi is more expensive

ui=u r i+u L i+u C i

Bring on the voltage that strum at the entrance of the river

u=U m sinw tі I m sin(w t-j ). There will be a drop in voltage on the elementsu r = rI m sin(w t-j), u L= w LI m sin(w t-j + p /2) = x L I m sin(w t-j+p/2), u C = I m sin(w t-j -p /2)/(w C) = x C I m sin(w t-j -p /2). Submitting qi virazi (9), we take it

P = UI cosj . The third addition to the right part is also the changeable warehouse tension, and the warehouse is located near the quadrature of the changeable warehouse active tension and may amplitudeQ = UI sinj . Qiu name the value reactive sweating . There is more than the average for the quarter of the period of energy, which is exchanged with magnetic and electric fields of interest. Re active tension do not transform into heat, other energy is seen , because її average value for the period to zero.

Reactive tension can also be detected through

reactive warehouses strumu chi voltage

Value

Scalled again . Z virazu (12) shows that even tightness can be revealed by the hypotenuse of a straight-cut tricutnik with a kut j , the legs of which are active and reactive straining.

in such a manner, tension is the most active tension possible, tobto. tightness, which is seen in a purely resistive field

(cosj = 0). The very tightness is indicated by the passport data electrical machines and devices.

Reactive storage strums and stress can be detected through active and reactive storage complex support, the same for storage pressure

P= UI a = U and the tricot of tensions should change the scale of the tricot of the tension (Fig. 3 a)). At another vipadka (Fig. 3 b)), pobudova vikonan for additional active and reactive storage strumaI .

It is obvious that all kinds of tension may have the same variability, so for the specific tension in the form of active tension, which is observed in watts [W], for total tension, a unit is introduced, called volt-ampere [VA], and for reactive tension - volt-ampere reactive [ var]

Viraz for active tension

P= UI cosj allows you to determine the pressure coefficient for the help of a wattmeter, a voltmeter and an ammeter.

For this, at the input of the lancet, turn on the fitting for the diagram of fig. 4 and for їх indications, the coefficient of tension in the visual

W, V and A - indication of the wattmeter, voltmeter and ammeter exploding values.From this point of view, it is also possible to designate the sum of the phases j between the strum and the voltage at the entrance of the two-terminal network.

Unity vimіru - reactive volt-ampere (var, var)

Reactive tension - a value that characterizes the tension that occurs in electrical outbuildings by coliving the energy of an electromagnetic field in the lances of a sinusoidal snake stream, which contributes to the increase in the mean-square value of the voltage U and struma I, multiplied by the sine of the kuta zsuv of the phases between them: (for example, the strum is different from the voltage, the zvd of the phases is considered positive, as it is viperedzha - negative). Reactive pressure tied up with total tension S and active straining R spіvvіdnostnyam: .

Povna tightness

Total electrical pressure unit - volt-ampere (V A, V A)

Povna potuzhnіst - the value, scho dobrivnyuє dobukku dіyuchih value of the periodic electric jet I in lanceugs and tensions U on її grips: S = U I; connected with active and reactive tensions de R- Active tension, Q- reactive tension (with inductive tension Q> 0, and when Q < 0).

Comprehensive

Complex tension

Potency, similarly to impedance, can be written in a complex view:

de - Complex voltage, - Complex strum, - Impedance, * - Complex coincidence operator.

Complex pressure module S. Distracted part of the pre-existing tension R and obvious - reactive tightness Q from the correct sign of the fallow due to the nature of the venture.

Siemens(Russian designation: Div; internationally recognized: S) is the unit of electrical conductivity in the International System of Units (SI), the value is wrapped in ohm.

Through іnshі odinі vіmіru СІ sіmens vrazhaєєєєєєєєє such order:

1 Sm \u003d 1 / Ohm \u003d A / B \u003d kg −1 m −2 s³A².

17) pressure coefficient- a bezrozmіrna physical quantity that characterizes the slowness of a changeable electric stream at a glance of the presence of a reactive warehouse. The tension coefficient shows how much the voltage is applied in phase, which flows through the tension.

Typical assessments of the capacity of the electric supply

With one and the same active tension, the tension tension, as it appears on the wires, is wrapped in proportion to the square of the tension coefficient. In this rank, the smaller the coefficient of tension, the lower the efficiency of the reduction of electricity. To improve the power of the electric shock, there are different ways to correct the coefficient of tension, so that it can be advanced to a value close to one.

For example, the majority of compact fluorescent (energy-saving) lamps that can be used with ballasts are characterized by high values.

18) Z'ednannya at the mirror. Scheme, by design

Like the ends of all the phases of the generator, they are connected to the deep vuzol, and the cob of phases is connected to the heads, which makes the three-promenu star of the supports, the three-phase lansyug, the star of the star. With this, three darts turn into one, the ranks are zero or neutral. Triphasic lance, with a star, is shown in fig. 7.1.

Rice. 7.1

Conductor, scho to go to the dzherel to navantage is called linear droti, provid, scho neutral points of dzherel N and receiver N "is called neutral (zero) wire. phases or between line and neutral wires are called phase voltages. phase struma, streams in linear drots - linear streams. So, as linear darts are connected sequentially with the phases of the dzherel and primach, linear streams when hit by a star, one-hour phasic streams.

Understanding the potential of the retail potential u allows the robot to designate what is generated by the electric field when moving an elementary electric charge dq, yak dA= udq. At the same time, the electric strum is good i= dq/dt. Zvіdsi dA= ui dt, otzhe, shvidk_st vikonannya roboti, tobto. fatigue at a given moment, or mitteva tightness dorivnyuє

de uі i- mittєvі the value of the voltage and struma.

The magnitude of the struma and the tension that enters the viraz (1), є sinusoidal functions of the hour, that mitteva tension є zminnoy value і for її assessment vikoristovuetsya understand average pressure for the period. Її can be taken, integrating over the period T robot, which is generated by an electric field, that buv spіvvіdnosyachi її s the magnitude of the period, tobto.

Come on u=U m sinw tі I m sin(w t-j), then the average tension is more expensive

because the integral of another addendum is equal to zero. Value cosj called the coefficient of tension .

Because of this, it is clear that the average tightness of the lancet of the serpentine struma is not only due to the fluctuating values of the struma I that voltage U, A and vіd raznitsi phases j between them. The maximum tension in the presence of zero phase zsuvu and more oil recovery UI. With the destruction of the phases between the strum and the tension ± 90 °, the average tension reaches zero. The maximum value of the voltage of that stream, whether it be an electric machine, is determined by its design, and the maximum tension, as stench can develop, is a supplement to these values. Yakshcho elektrichna lansyug irrationally induced, tobto. zvv phases jmaє znachnuyu value, then dzherelo elektrichnії energії i navantazhennya can't work on the total pressure. Therefore, whether the system is dzherelo-navantazhennya іsnuє t.zv.

"problem cosj", which means that the possible proximity cos j to one.

Viraz (3) you can also apply for help to understand the active warehouse strum I a i voltage U and look

Vrahovyuchi, scho active warehouse strumu and voltage can be overcome through the resistive warehouse complex support of the lancet yak I a = U/R or U a = IR, viraz (4) can also be written in the form

Middle tightness P call it active sweating and win at vatah [W].

We can see the integrand function of virase (3)

It sounds like the mitt's tension is changing with the constant frequency of the measure, like a constant warehouse UI cosj equal mean active tension.

For cosj = 1 (j = 0), then for the lancer, what can be a purely resistive opir

Timchasovі diagrams, scho vіdpovіdat tsomu vipadku, induced in fig. 1 a).

The positive values of the mitt's tension indicate the need for energy from the dzherel to the electric station. Otzhe, with resistive input, all the energy that comes out of the dzherel turns into it into heat .

For cosj = 0 (j = ± p /2), then for a purely reactive Lancug

Timing diagrams that show the daily inductive and daily eminent tension are shown in fig. 1 b) and d). Z virazіv (8) and hourly charts show that the tension tingles along the abscissa axis with a subwave frequency, changing its sign of the skin quarter of the period. Tse means that for the fourth period ( p> 0) the energy goes into the electric lance from the dzherel and is stored in the magnetic or electric field, and by the extension of the forward quarter ( p < 0) она целиком возвращается из цепи в источник. Так как площади, ограниченные участками с положительной мощностью и с отрицательной одинаковы, то средняя мощность отдаваемая источником нагрузке равна нулю и there is no transformation of energy in lancius.

In the case of a fair amount of interest 1 > cosj > 0 (1< |j | < p /2) и

How to see from the timchas diagrams in fig. 1 c), for most of the period, the tension decreases to the pressures ( p> 0), but also use the same time intervals, if the energy is stored in magnetic and electric fields, the energy is turned into a dzherelo. Businesses with positive values p regardless of the nature of the reactive warehouse demand for more workers with negative values, this is an average pressure P positive. Tse means what in the electric language transferring the process of converting electrical energy into heat or mechanical work .

Let's take a look at the energy processes of the last plant rLC(Fig. 2). The voltage drop at the input of the lancet is vrivnovazhuetsya by the sum of the voltage drop on the elements u=u r+u L+u C. Mitteva tightness at lanceuzi is more expensive

Bring on the voltage that strum at the entrance of the river u=U m sinw tі I m sin(w t-j). There will be a drop in voltage on the elements u r= rI m sin(w t-j), u L= w LI m sin(w t-j + p /2) = x L I m sin(w t-j+p/2), u C= I m sin(w t-j -p /2)/(w C) = x C I m sin(w t-j-p/2). Submitting qi virazi (9), we take it

Rivnyannya (10) in the left and right parts may be permanent and change warehouses. Postiyna warehouse є active or medium tightness. Another addition at the right side of the tse is a change in the warehouse of active tension with a equal amplitude P = UI cosj. The third addition to the right part is also the changeable warehouse tension, and the warehouse is located near the quadrature of the changeable warehouse active tension and may amplitude Q = UI sinj. Qiu name the value reactive sweating . There is more than the average for the quarter of the period of energy, which is exchanged with magnetic and electric fields of interest. Reactive sweating does not transform into heat or other types of energy , because її average value for the period to zero.

Reactive pressure can also be represented through a reactive storage stream or a voltage

On the vіdmіnu vіd vіd zavzhdі posіtivії akіvії tinnitus, reactive tension is positive at j > 0 and negative at j< 0 .

From the mind of the equivalence of the changed warehouse left and right parts of the equivalence (10) you can know the link between P, Qі S = UI at the sight

Value S called again . Z virazu (12) shows that the total tension can be represented by the hypotenuse of a straight-cut tricot with a kutom j legs of which is active and reactive tension.

in such a manner, tension is the most active tension possible, tobto. tightness, which is seen in a purely resistive field (cosj = 0). The very tension is shown in the passport data of electric cars and devices.

Reactive storage strums and stress can be detected through active and reactive storage complex support, the same for storage pressure

The tricot of tensions can also be described with the help of complex numbers and depicted by vectors on the complex plane at the sight

de S - complex povna tightness, - pov'yazany complex strum.

Coresting manifestations of active and reactive storage tension through active and reactive storage pressures and tension (virazi (4) and (11)), tension tension can be caused in two options (Fig. 3 a) and b)). In the first depression, active and reactive warehouse tension is manifested through active and reactive warehouse tension U and the tricot of tensions should change the scale of the tricot of the tension (Fig. 3 a)). At another vipadka (Fig. 3 b)), pobudova vikonan for additional active and reactive storage struma I .

Viraz for active tension P= UI cosj allows you to set the pressure coefficient for the help of a wattmeter, a voltmeter and an ammeter.

For this, at the input of the lancet, turn on the fitting for the diagram of fig. 4 and for їх indications, the coefficient of tension in the visual

de W, V і A - indications up to the wattmeter, voltmeter and ammeter working values. From this point of view, it is also possible to designate the zsuva of phases j between the strum and the voltage at the input of the two-terminal network.

29. Two coils with supports R 1 and R 2 with inductances L 1 and L 2 that mutual inductance M z'ednani sequentially. Two types of inclusions are possible: better (Fig. 4.4a) and zustrіchne (Fig. 4.4b).

When the jet is switched on in both elements, at some point in time, however, the same time of the same time is straightened, then the magnetic fluxes of self-induction F 11 (or F 22 ) that mutual induction F 12 (or F 21 ), zchepleni z skin element folded. When the streak is turned on in both elements of the lancet, at some point in time, it is straightened out at the same time as the same visnovki, then the magnetic flows of self-induction and mutual induction, bonding with the skin element, are visible.

The inductance of two consecutively connected inductively coupled elements is determined by the ratio:

, (4.7)

de i - flow chaining of the first and the other elements, moreover ; .

The plus sign can be seen until the next day, and the minus symbol until the star is turned on. Otzhe,

L = L 1 + L 2 ± 2M.

The last opir is greater in the case of the second one, and the lower one in case of the lower one.

The voltages on the elements can be stored in three warehouses:

(4.8)

As the inductance of one of the elements is less than the mutual inductance, then with a stunted connection, there will be a “minus” effect of its own. Come on, fork, L 2< M, when you have viraz

maybe ω (L 2 -M)< 0, и, следовательно, напряжение отстает по фазе от тока , как в случае емкостного сопротивления. Конечно, reactive opir of the whole lance in the whole inductive, to that L \u003d L 1 + L 2 - 2M> 0 i strum vіdstaє in phase vіd voltage.

On (Fig. 4.5a, b) shows vector diagrams for the vocal and zustrіchny inclusion for the same value of the struma in both falls.

The input complex opir of the lancer is acceptable, vrakhovuyuchi (4.8)

; (4.9)

de (4.10)

Parallel connection of inductively coupled elements of the lancer

Two coils with supports R 1 and R 2 with inductances L 1 and L 2 that mutual inductance M is connected in parallel, moreover, one-step connections are connected to one of the same node (Fig. 4.7).

When choosing positive streaks, the streaks will be taken off the edge:

; (4.12)

; (4.13)

de (4.14)

For these equal complex stresses and taken with a plus sign, so positively direct for these stresses (vibrated to the beast down) and quiet strums, for which voltages lie, oriented similarly to one-dimensional visnovkіv however. Rozvyazavshi rivnyannya, otrimaemo

; (4.15)

; (4.16)

. (4.17)

The sounds are screaming that the input complex opera of the lanced lancet

. (4.18)

We can now look at the inclusion, when one-time visnovki are attached to different knots, then L 1 and L 2 are attached to the knot by different buntings. In this way, the positive direction of the voltage of mutual induction (vibrated to the beast down) and quiet strums, in the form of stench to fall, oriented similarly to the same vysnovkіv, the complex voltage is different go to the river (4.12) and (4.13) with a minus sign. For strums, you can see the virazi, similar to (4.15-4.17), with the same authority that Z M is replaced by - Z M that input opir lanceug

. (4.19)

30. Parallel connection of inductively coupled elements of lance

Assume that two coils or two be-like elements of a lance with supports and inductances and mutual inductance M are connected in parallel, moreover, one-way visnovki are attached to one and the same node (Fig. 6.9).
When choosing positive lines, the streams and voltages

de
For these equal complex stresses and taken with a plus sign, so positively direct for these stresses (vibrated to the beast down) and quiet strums, for which voltages lie, oriented similarly to one-dimensional visnovkіv however.
Rozvyazavshi rivnyannya, otrimaemo

The signs follow that the input complex opir of the lancet lancet

When, then, with the presence of an inductive link between the needles, the whole viraz swells a familiar sight:

We can now look at the inclusion, in which the one-time visnovkas are attached to different knots, i.e., they are attached to the knot with different frills, lower as indicated in fig. 6.9. In this way, the positive direction of the voltage of mutual induction (vibrated to the beast down) and quiet strums, in the form of stench to fall, oriented similarly to the same vysnovkіv unequally and complex, the voltage will go up to the level (6.9) and (6.10) with a minus sign. For strums, you can see the virazi, similar to (6.11), with the same note, which is replaced and the input opir of the lancer

How to change the struma to one of the elements of the electric lancet to bring E.D.S. in another element of the lance, then it seems that these elements inductively coupled one with one. Blame your E.D.S. called E.D.S. mutual induction.

On (Fig. 4.1) two coils are shown with the number of turns and the magnetic flux of the first coil is proportional to the stream, which flows through it. Part of this stream pierces the coils of another coil and pours into the stream.

Similarly, the magnetic flux of another coil pierces the coils of the first one.

Such cats are called inductively-pov'azanimy (or magnetically pov'yazanimi).

The steps of the inductive connection of the two elements of the lancet are characterized call coefficient k, which is assigned to the settings:

de M - mutual inductance of the elements of the lance, Gn.

Inductance of elements, Gn.

It is necessary to remember that the call coefficient cannot be greater for one!

Vzagali, mutual inductance The first and the other coil is called the extension of the additional flow chain of the other coil to the struma of the first coil:

Index 12 shows that the mutual inductance is induced at the first coil in the direction of the magnetic flux of the other coil.

Dosvid shows that:

Fair reprieve:

Mutual inductance of linear electric lancers do not deposit directly that value of strums, and only depend on the design of the coils mutual roztashuvannyam. About check viraz (4.5).

The inductance of the coil is determined by the following formula:

de - Vidnosna magnetic penetration of the medium (for visualization);

Absolute magnetic penetration of the medium;

S - the area of the transverse section of the coil, mm 2;

L is the length of the coil, m.m.

When folding flats for magnetically-coated lancers, it is necessary to know, logically straightened, the flows of self-induction and mutual induction. It is possible to work the visnovok correctly, as if directly winding the coils on the core, then a positive direct stream was taken from them.

On (Fig. 4.2a) the coils are turned on zgіdno, and (Fig. 4.2b) - zigzag.

On fig. 4.2 one-time zatiskachi (for example, the cob of the cob) - denoted by the same icons, for example, dots.

Yakscho on electrical circuits streams of two magnetically connected coils are straightened, however, at the same time as one-step closures, for example, the streams are straightened to points yak (Fig. 4.2a), then the coils are straightened, in a different direction it is sharp.

In fact, it is often the fault of the difficulties in the appointed visnovkіv kotushok. For which vicorist, a simple dosvіd, for which a galvanic element (or a battery) and a galvanometer (or a voltmeter) are needed.

One of the coils is connected to a voltmeter, the other one is connected to a galvanic cell (Fig. 4.3). When the key is closed, a strum briefly vibrates to the other cat, which weakens the magnetic field created by the strum. The polarity of life is directly indicated to the struma. The direction of the struma can be judged by the short-range movement of the voltmeter needle. If the arrow moves at the bik scale (so it doesn’t go off scale), then the strum is straightened to the positive voltmeter winding, at its own winding coil, adjoined to the positive voltmeter winding and zherela zhivlennya, at the same time.

On (Fig. 4.3) when the direction of the stream and the polarity of the voltmeter are set, the coils are closed.

49. Under active exhaustion P, understand the amount of energy that is generated (generated) by the object in a single hour. Mathematically, the active tension is defined as the average value of the tension for the last period.

Let the actual element of the lansyug calm down the strum i(t) with non-sinusoidal voltage u(t):

Mitta's tension p(t)=u(t)*i(t), If the tension is active, then:

Thus, the active tension of the non-sinusoidal struma is equal to the sum of active tensions of the other harmonics:

P=P0+P1+P2+P3...

The reactive tension Q of a non-sinusoidal stream is used as an analogy with the active tension P as an algebraic sum of the reactive tensions of four harmonics:

Apparently, the reactive tension Q of the sinusoidal strum characterizes the intensity of the generation of energy (Q=ωW max) with the frequency between the electromagnet field of the element and the smaller lance. At the stake of a non-sinusoidal struma, the energy is emitted at different frequencies. Folding of reactive strains of okremikh harmonics, which characterizes the coercion of energy at different frequencies, easing the physical sensation. Mathematically, it can be found that the reactive pressures of the other harmonics can different signs and give zero to the sum, if you want to get energy from your own place. Also, for a non-sinusoidal lancet, the understanding of reactive tension is relieved of the physical sensation.

For a lancet of a non-sinusoidal struma, it also stagnates and understands the new tightness, as it is shown as an additional working value of the voltage of that struma:

Apparently, for a sinusoidal sinusoidal struma of tightness P, Q, S, a straight-cut tricutnik is used, for which there is a spitting: S2 = P2 + Q2. For lances of non-sinusoidal struma, the spacing between strains is only for resistive elements, for which it is consistent with Ohm's law ( u=iR) forms of curved functions u(t) and i(t) are identical. As for the lancers, there are reactive elements L and Z, but the spiving does not win: S 2 ≥P 2 +Q 2. For the balance of which equal to the right, make an addition: S 2 ≥ P 2 + Q 2 + T 2, stars

de T - Intensity of creation - a mathematical understanding, characterizes the degree of power in the forms of stress curves u (t) and struma i (t).

The magnitude vector, which changes sinusoidally, can be represented on the complex plane. Complex manifestations allow for the simplicity and accuracy of vector diagrams, which may not be enough - to reduce the accuracy, with the possibility of conducting accurate analytical analyzes. For an hour of operation with vectors, one can speed up the theory, which is broken down for complex numbers. The vector of expansions on the complex plane uniquely represents a complex number. Appropriate to Euler's formula for a complex number, it is equally algebraic, trigonometric and shows the form of the record. When subsuming complex numbers, the form of algebra is easy, when multiplied and divided, it is shown.

Vikoristannya complex form The manifestation allows replacing geometric operations on vectors with algebraic operations on complex numbers. As a result of this, before the analysis of the lanceugs of the snake struma, all methods for the analysis of the lanceugs of the ling strum can be found.

Pay attention to those that are complex images, like vector diagrams, carry information only about two parameters of the sinusoid - the amplitude and the cob phase, without displaying the third parameter - the cutoff frequency ω. The vectors on the complex plane and the corresponding complex numbers are taken to represent the same letter, which is the amplitude of the sinusoid, which is displayed, with the point on the mountain.

The obvious unit in electrical engineering is denoted by the symbol j, the oskilki symbol i vykoristovuetsya for the recognition of the mittevogo strumu.

Strum i(t) = I m sin(ωt + φ o) can be represented by a complex number Í m on the complex plane

de amplitude of the struma I m – module, A kut φ o, scho є cob phase, - argument complex struma.

Usy parametres of lanceug are found in the complex form.

Algebraic form of writing a complex number: m = I m ' + j I m '' , when writing in a trigonometric form, the projection of the vector is expressed through the yogic length I m i kut φ pro: I m (cos φ pro + j sin φ o). The display form of the record can be seen İ m = I m e jφo.

In cih virase I m = √ (I m ' 2 + I m '' 2) - the modulus of a complex number, pro \u003d arctg (I m '' / I m ') - yogo argument, I m ' = I m cos φ o , I m '' = I m sin φ o.

- Comprehensive chinne meaning sili struma (without index m); here I = Im/√2;
- Complex dynamic value of the voltage (without index m); U = U m/√2.

For example, to reveal the complex developmental significance of the struma

at the display form. Vidpovid.

Tension in the lancers of the snake strum

Let's take a look at the energy characteristics of the bipolar passive elements (R, L, C) of the streak.

resistive elementR

As shown earlier, for a resistive element:

, moreover, complex opera- tion and conduction may be less than verbal warehouses: Y = G; Z=R.

Abo, what are you,

Mittyva tightness, tobto. tension at the function of the hour, є twir strum on the tension and is set by viraz:

(Whikoristano formula for the lower step sin 2 α = (1 – cos 2α) / 2)

Thus, the tension on the resistive element pulses from zero to the maximum value with a variable frequency, taking on a positive value (Fig. 1).

The average value of tension in the period is called active tension. From the correction of the taken value for the mitt's tightness, it is possible:

, here I- Chinne meaning struma.

Inductive elementL

Come on, like before, the stream and the voltage will be sinusoidal:

As shown earlier, the inductive element has a strum in phase with the voltage by 90°.

Complex opir of inductance is more expensive:

, then. opir is purely reactive.

Energy, which is stored in inductance, is expensive:

LI 2 .

Pressure of the inductive element:

The tension in the inductive element may be the nature of the cracking from the sub-frequency. With positive pressures of tension, if the signs of the struma and the tension are reduced, the energy will go into the inductive element and be stored (taken away) from the new one. With negative tensions of tension, if the signs of struma and tension are different, the energy goes back to the dzherel. Mean for the period of meaning of tension P=0 (energy in mnіsnumu elementі not rozsiyuєtsya, tobto. do not calm down), div. rice. 2.

The maximum value of colival tension in reactive elements with a 90° angle is called reactive tension and means P Q.

For inductive element

The reactive tension is the maximum speed of the exchange of energy between the jet and the reactive element and signifies the strum, the effect of the exchange. To make the passage of the struma up to the additional costs at the support of the annex in the transmission of energy and to that may be minimized as far as possible. Reactive sweating, on the face of active sweating, is not related to the sightings (rozsiyuvannyam) of sweating in the element, which is controlled by reactive volt-amperes (var). In this case, we can talk about inductive or inductive reactive tension.

Eminent elementC

Come on, like before, the stream and the voltage will be sinusoidal:

As it was shown earlier, in the terminal element, the strum is in phase with the voltage by 90°.

Complex Opir

, then. opіr purely reactive (єmnіsny).

Energy, which is stored in the capacity, is healthy:

Mittevi energy values fluctuate with a constant frequency between zero and maximum CU 2 .

Pressure of the omentous element:

Tension in the mucosal element may be the nature of colitis from the subwoofer frequency. With positive tensions of tension, if the signs of the struma and tension are reduced, the energy from the dzherela comes to the last element and is stored (taken away) from the new one. With negative tensions of tension, if the signs of struma and tension are different, the energy goes back to the dzherel. Mean for the period of meaning of tension P\u003d 0 (energy in the mnist element does not rise, so it does not slow down), div. rice. 3.

For the final element

Complex tension (tension in sinusoidal mode, when standing up)

In the vipadku of the electric lansyug, є yak is active, і is reactive warehouse. Tse means that the tightness of the lancelet will grow like a rose (active tightness), so it periodically accumulates in reactive elements and redistributes between them.

Come on, like before, the stream and the voltage will be sinusoidal:

Mitteva the pain is dear:

In this order, mitteva tightness of the lansy with sufficient reactivity, good:

Because of this virazu, it’s obvious that the mitt of the lance of the snake’s strum may be permanent warehouse and change the warehouse, which changes in the hour with a double frequency.

As it was determined, the average value of the mitigation tension for the period is called active sweating:

Substituting the formula (1) in this case, we take:

(2)

Active pressure in the lances of the changeable struma, the increase in the developmental values of the struma, the voltage and the cosine of the kuta zsuv of the phases between them. Active tension subsides in vata (W). Multiplier cos φ name pressure coefficient(or just "cosine φ ») .

The greater the coefficient of tension, the greater the active tension at given values of the struma and the voltage. Ideally, for lancers without reactivity, the pressure coefficient is 1.

The increase in the fluctuating values of the stream, the voltage and the sine of the kuta zsuvu of the phases between them is called reactive tension:

(3)

Reactive tension characterizes the energy, as it periodically circulates between the nerves and nerves. Vaughn vanishes at reactive volt-amperes (var)

Tvіr dіyuchikh the value of the voltage and the struma is called full strain:

(4)

External tension is reduced by volt-amperes (VA) and characterizes the limiting active tension of the lancet at a tension coefficient that is 1.

Yakscho

,

,

the same vrakhovuychi vіdomі spіvvіdnoshennia for puffiness, maybe:

, active tension

, reactive tension

,

maybe:

In electric lances with periodic sinusoidal infusion, there may be a balance of tension between tension and tension, tobto. the complex tension of the nerves of the energy is due to the complex tension of the tension and the active and reactive tensions of the necks are equal to the active and reactive tensions of the tension.

, ,

,

.

The sign of reactive tension means the predominance of the inductive (+) or the imminent (-) supports.

Active pressure in the lances of a changeable struma, the increase in the development of the fluctuations in the struma and the voltage per cosine of the cut of the phases between them. Active tension characterizes the energy, as it is transferred from the dzherel to the beginning, de transforming into another type of energy. Active tension is controlled by watts (W). The multiplier cosφ is called the tension coefficient (or simply "cosine fi"). The greater the cosφ, the greater the active tension at given values of the struma and the voltage.

Reactive pressure in the lances of the changeable struma, the increase in the developmental values of the struma and the voltage on the sine of the cut of the phases between them. The reactive tension characterizes the energy as it circulates between the nerves and the nerves. Active tension is controlled by reactive volt-amperes (var). At φ<0 (при емкостной нагрузке) реактивная мощность отрицательна, а при φ>0 (with inductive bias) reactive tension is positive.

Deyaki methods of numerical analysis (rozrahunka) of lanceugs of snake strum

Proportional re-arrangement method

The method of proportional refurbishment zastosovuєtsya to rezrahunku clumsy lancets, and navit skhodovyh lancets. The stasis method is up to lanzyugiv, in which there is one dzherelo (dzherelo struma or naprugi). In this method, the mental value of the struma is set, or the voltage of the most distant view of the jerel lansyug, and then all the other streams and stresses are insured, until the strain of the jerel (or the strum of the jerel) is insured.

Then the coefficient of proportionality will be determined between the given values of the voltage of the dzherel (struma) and the insurance. Dali, looming on the horizon, the lineage of the lancer, all the intermediary data of the rozrakhunkiv, tobto. multiply the voltage by subtracting the proportionality coefficient.

Let's explain the methodology of rozrahunkiv from the butt.

(Butt of a galvanized RC Lanziug)

Graph-analytical method pererakhunku

In this method, there is such a method itself, and instead of the method of complex amplitudes, there is a graph-analytical method. Assigning, like to the front butt, deaking the numerical value of the strum, choose the scale of the strum and the voltage. At the given scales, the selected value of the struma is added, and then all other vectors will be “nearly” the selected struma. It is safe to know the vector of the voltage or the struma of the dzherel. Vynachayut proportionality coefficient by amplitude and proportionally increase or change the scale. Determine the difference between the phases between the values of the voltage or the strum dzherel and the true phase of the given voltage or the strum dzherel, and then rotate the whole picture with vectors. As a result, right streaks and voltages appear, which vibrate with a predetermined tension or a strum dzherel.

Tension in the lancers of the snake strum

Let's take a look at the energy characteristics of the bipolar passive elements (R, L, C) of the streak.

resistive elementR

As shown earlier, for a resistive element:

, moreover, complex opera- tion and conduction may be less than verbal warehouses: Y = G; Z=R.

Abo, what are you,

Mittyva tightness, tobto. tension at the function of the hour, є twir strum on the tension and is set by viraz:

(Whikoristano formula for the lower step sin 2 α = (1 – cos 2α) / 2)

Thus, the tension on the resistive element pulses from zero to the maximum value with a variable frequency, taking on a positive value (Fig. 1).

The average value of tension in the period is called active tension. From the correction of the taken value for the mitt's tightness, it is possible:

, here I- Chinne meaning struma.

Inductive elementL

Come on, like before, the stream and the voltage will be sinusoidal:

As shown earlier, the inductive element has a strum in phase with the voltage by 90°.

Complex opir of inductance is more expensive:

, then. opir is purely reactive.

Energy, which is stored in inductance, is expensive:

LI 2 .

Pressure of the inductive element:

The tension in the inductive element may be the nature of the cracking from the sub-frequency. With positive pressures of tension, if the signs of the struma and the tension are reduced, the energy will go into the inductive element and be stored (taken away) from the new one. With negative tensions of tension, if the signs of struma and tension are different, the energy goes back to the dzherel. Mean for the period of meaning of tension P\u003d 0 (energy in the mnist element does not rise, so it does not slow down), div. rice. 2.

The maximum value of colival tension in reactive elements with a 90° angle is called reactive tension and means P Q.

For inductive element

Eminent elementC

Come on, like before, the stream and the voltage will be sinusoidal:

As it was shown earlier, in the terminal element, the strum is in phase with the voltage by 90°.

Complex Opir

, then. opіr purely reactive (єmnіsny).

Energy, which is stored in the capacity, is healthy:

Mittevi energy values fluctuate with a constant frequency between zero and maximum CU 2 .

Pressure of the omentous element:

For the final element

Complex tension (tension in sinusoidal mode, when standing up)

Come on, like before, the stream and the voltage will be sinusoidal:

Mitteva the pain is dear:

In this order, mitteva tightness of the lansy with sufficient reactivity, good:

Because of this virazu, it’s obvious that the mitt of the lance of the snake’s strum may be permanent warehouse and change the warehouse, which changes in the hour with a double frequency.

As it was determined, the average value of the mitigation tension for the period is called active sweating:

Substituting the formula (1) in this case, we take:

(2)

The greater the coefficient of tension, the greater the active tension at given values of the struma and the voltage. Ideally, for lancers without reactivity, the pressure coefficient is 1.

The increase in the fluctuating values of the stream, the voltage and the sine of the kuta zsuvu of the phases between them is called reactive tension:

(3)

Reactive tension characterizes the energy, as it periodically circulates between the nerves and nerves. Vaughn vanishes at reactive volt-amperes (var)

Tvіr dіyuchikh the value of the voltage and the struma is called full strain:

(4)

External tension is reduced by volt-amperes (VA) and characterizes the limiting active tension of the lancet at a tension coefficient that is 1.

Yakscho

,

,

the same vrakhovuychi vіdomі spіvvіdnoshennia for puffiness, maybe:

, active tension

, reactive tension

,

maybe:

, ,

,

.

The sign of reactive tension means the predominance of the inductive (+) or the imminent (-) supports.

Deyaki methods of numerical analysis (rozrahunka) of lanceugs of snake strum

Proportional re-arrangement method

Let's explain the methodology of rozrahunkiv from the butt.

(Butt of a galvanized RC Lanziug)

Graph-analytical method pererakhunku