Vector diagram lc. Vector diagrams
IN active support voltage and strum vary in phase, so the voltage vectors Ū R i struma Ī straightening into one roll (Fig. 2.1). They can lie on one straight line or on parallel lines. When linking vectors Ū R ta Ī maybe the mother is more direct, but in all situations, the cut between the vectors is closer to zero .
Note. In order for different vectors, which lie on one straight line, not to get angry and easily irritate one in one, it is recommended to carry them out on the deyakіy, to finish a small one in one of one.
2.2. inductance
In the inductance of the strum, it is in phase with the voltage for a quarter of the period. On the vector diagram cut between vectors Ū L ta Ī become 90 º. І here zv'yazuvannya vectorіv Ū L ta Ī you can be oriented as usual, that one is mutually raztashuvannya invariably. When wrapping the diagrams against the anti-Godinnikov arrow in front of the ide, the stress vector Ū L , and after it, by 90 º Ī (Fig.2.2).
2.3. Amnesty
The capacity has a voltage in the stream for a quarter of the period. Kut mizh vectors Ū C i Ī also doro_vnyuє 90º, but when wrapped with diagrams of the anti-godinnikov arrows in front, there is a struma vector, and this is the stress vector (Fig. 2.3).
Vkazane mutual roztashuvannya vectors on the diagrams of the month with the same direction of the arrows of the voltage and the stream on the scheme of the analyzed element.
3. Electric lance with the last connection of elements
Task 3.1. It is necessary to induce the Lantzug vector diagram, which is made up of successive elements (Fig. 3.1.).
Let's write down the equalness of another Kirchhoff's law in the vector form: the voltage applied to the lance, the sum of the voltages on all elements:
Ū = Ū R1 + Ū L+ Ū R2 + Ū C(3.1)
The sum of the voltages at the right part of the equation is recorded in the order in which, when going around the contour, the points but (of the first entry press) to the point d (Another entrance zatyskach) are sharpening the vital elements. In the same order, there are vectors. When prompted by the diagrams, the circuit is bypassed straight ahead. Great respect, that the direct arrows of the tension of the skin element of the lancet move from the direct arrows of the strum.
Pobudov's diagrams are repaired from the strum vector, because in successive lancer Strum is a hot one for all elements (Fig. 3.2, a).
The first element, which is mimic when bypassing the lancet, is the active opir R one . Yoga clamp vector Ū R 1 Ī , Summing the cob of two vectors (Fig. 3.2, b). Step element - inductance L . Voltage Ū L on nіy zgіdno s rіvnyanyam 3.1 mi owe to add to the voltage Ū R1. To the cob vector Ū L one by one with the end of the vector Ū R 1 and up to item 2.2. we direct yoga uphill - at the bik viperedzhennya struma (Fig. 3.2, c). Until the end of the vector Ū L arrives vector Ū R 2 Ī (Fig. 3.2, d).
Remaining vector - Ū From the end of the vector Ū R 2 down (Fig. 3.2, bud). Vector Ū swipes on the cob vector Ū R 1 at the end of the vector Ū C , i equal amount all three vectors determine the input strain of the lancer (Fig. 3.2, f).
The resulting vector diagram allows you to designate the stress on okreme plots electric lansyug. For example, the voltage between points a і b is added to the voltage on the active support R 1 and inductance L the vector Ū ab , cob vector Ū R 1 at the end of the vector Ū L (indications dotted). Similarly carried out i vector Ū bd , equal sum of vectors Ū R 2 that Ū C.
Task 3.2. Behind the given vector diagram (Fig. 3.3), cross the lancet, for which you are prompted.
On the diagram of indications, one vector of the struma and five vectors of the voltage, yakі y sum i give the vector Ū :
Ū = Ū 1 + Ū 2 + Ū 3 + Ū 4 + Ū 5.
From this world robimo visnovok, that the electric lancet is made up of five successive elements, which flow through that very stream.
Voltage Ū 1st element goes into the struma at 90º, also, the tse is the capacity. The other element is the active opir, so the vector Ū 2 parallel to the strum vector Ī zbіgaєtsya with him in phase. Voltage Ū 3 viperedzhaє strum at 90 º, also, the third element is inductance. The fourth element is capacity, because voltage Ū 4 vіdstaє vіd struma 90º Ū 3). І, nareshti, the remaining element - again active opіr, tk. the voltage on the new one is fluctuating in phase with the strum. Ū 5 that Ī parallel and straightened into one bill. The bright view of the scheme is shown in Fig. 3.4.
trikutnik naprugі tricot support,:
The last row of R, C on the streak: vector diagram of the strum and the voltage, the tricot of the voltage. Ohm's law complex form.
if there is a flow in such a strum, then the voltage drop will be formed from:
de; to the induced visualization, you can set the value of the virase: trikutnik naprugі tricot support,:
Ohm's law for the complex form:
The last lance R, L, C on the replacement stream: the vector diagram of the stream and the voltage. Reactive Opir lanceugs. Voltage resonance.
voltage drop on the lances: , de: , a . There are three different fluctuations:
In lanceuzi, inductance is more important, tobto. , but also . Which mode is supported by the vector diagram baby a.
The Lancuse has more capacity, tobto. , which means . Tsej vіpadok vіdobrazhaє vector diagram baby b.
Vipadok resonance voltage ( little ones in).
Umov resonance voltage: , for whom . At resonance of the voltage or modes close to new, the strum near the lanzug grows sharply. Theoretically, at R=0, the value of the correct inconsistency. Vidpovidno up to the growth of the struma, the voltages on the inductive and terminal elements increase, which can sometimes outweigh the magnitude of the voltage of the zherel zhivlennia. The physical nature of the resonance influences the periodic exchange of energy between the magnetic field of the inductance coil and the electric field of the capacitor, and the amount of energy of the field is filled with constant.
- resonance curves called fallow strum and voltage and frequency:
Rozgaluzheni elektrichnі lanceugs snake struma: complex conductivity of the sequential rod R, L, tricot conductivity, equivalent parallel circuitіz conductivities.
- new opir such a lancer: ;
- povna conductivity: ;
When depicting a tricot of conductivities on a complex area, they show an active, inductive and even conductance: (div. fig.)
The last R and L connection scheme can be replaced by a parallel transformation of the strum through the lancet as the sum of the active and reactive strum:
carry out the re-development of the re-development of the schemes manually, leading them up to equivalent parallel:
Parallel electric line from capacitor and inductance coil: equivalent parallel circuit, vector flow diagram. Strum resonance.
Complex strumu through this thread: ;
Conductivity of such a lancet: , a
Fallow in the spivvіdnoshennia values and possible three different fluctuations.
In lanceuzi, inductance is more important, tobto. , and also, . Which mode is supported by the vector diagram baby a .
The Lancuse has more capacity, tobto. , which means . Tsej vpadok ilustraє vector diagram on baby b .
І - decline to the resonance of strums ( little ones in ).
Umov resonance strumіv abo. Also, at the resonance of the strum, the input conductivity of the lancet is minimal, and the input opir, on the other hand, is maximum. Zokrema for the presence of a small resistor Rїї introductory opir as a resonance of pragne insincerity, that is. at resonance of strums, the strum at the entrance of the lancet is minimal.
Induced to mind resonance is valid only for the simplest circuits from the last or parallel circuits of the inductive and the mnemonic elements.
The tightness of the electric lance of the strumu: mitteva tightness in the elements R, L, C. Reactive pressure inductance and capacitance. Stretcher of tightness. Active, reactive, total complex tension of the entire lancet.
The intensity of transmission or the transformation of energy is called straining :
- mittve meaning of tightness in the electric lance: , Having taken the cob phase of the voltage for zero, and zsv phases between the voltage and the stream for , We take:
Including, mitteva tension may be constant warehouse and harmony warehouse, the apex frequency is 2 times greater than the apex frequency of the voltage and struma.
If mitteva tension is negative, but tse maє mistse (div. figure), if uі i different signs, tobto. if there is a direct voltage and a stream at the bipole is proliferating, the energy is turned from the bipole of the life.
Such a turn of energy to the dzherel is due to the fact that energy is periodically stored in magnetic and electric fields, ranging up to inductive and єmnіshnіh elementіv, how to enter the warehouse of the two-terminal network;
Energy, which is seen by the bipolar man for an hour t goodbye.
Average for the period mitteva tightness called active sweating: , [W]; I’ll look at what, we’ll take it:. The tension is active, supported by a passive bipolar, which can be negative (in this case, the bipolar will generate energy), either. at the input of a passive two-terminal network. vipadok P=0, theoretically possible for a two-terminal network, which does not have active supports, but only ideal inductive and imaginary elements can be avenged.
- strain on resistors(Ideal active support) Strum and voltage change in phase:
- pressure on coils of inductance(Ideal inductance) does not work:
Because Strum vіdstає vіd vіd narugi on phase on , then: ; At the distance of 1-2 energy, which is stored in the magnetic field of the coil, builds up. At 2-3 - change, turning around at the neck.
- pressure on the condenser(Ideal capacity) also does not fit:
Strum here viperedzha naprugu, to that, i. Including, in the coil inductance and capacitors, there is no irreversible conversion of energy to other types of energy. Here, there is less circulation of energy: electrical energy is stored in the magnetic field of the coil or electric field condenser stretching out the fourth period, and stretching out the coming fourth period, the energy will again turn to the edge. After all, the inductance coil and the capacitor are called reactive elements, and they are supported X L , a , then the complex again:
- tricot tension- Examination of the complex value of tensions on the complex plane (if there is a slight onset of expiration).
For the sake of simplicity, analyze and analyze the rozrahunka of the lanceuge in the chrystal strum dotally vikoristovuvat vectori.
In electrical engineering, the vectors are depicted as sinusoidally changing EPC, voltages and streams, but on the other hand, in vectors, as the forces and speeds in mechanics are depicted, q vectors wrap around with a constant cusp frequency and do not mean straight away.
It is assumed that the radius vector OA (Fig. 2.3, a), which is on the scale of the amplitude value of EPC E t, wraps around with a constant peak frequency ω = 2 πf anti-year arrow. The projection of the vector OA on the vertical at) will be equal
Pro a \u003d OA sin α.
Virazivshi OA through the amplitude value of EPC E T and α through ωt, We take away the value of EPC, which changes sinusoidally:
e \u003d E t sin ωt.
Graph mittevih EPC value is shown in fig. 2.3b. For the cob, the moment of the hour is chosen, if the radius vector falls with the horizontal axis (all x).
Rice. 2.3. Vectors (a), which wrap around, and the graph of the mittev and the value of the sinusoidal EPC (b)
Yakscho at the moment t=0 radius-vector OA zbіgaєtsya s linієyu, raztashovanoyu under the kutom ψ to axis x, then the projection Oa" and, later, EPCs will be equally equal
Oa \u003d OA sin (ωt + ψ), e \u003d Em sin (ωt + ψ).
In a similar way, one can imagine that looking at the vectors that wrap around the anti-Godinnikov arrows with a constant apex frequency, voltage and strum.
Rozrahunok Lanzyugiv sinusoidal struma fluctuate with fluctuating EPC values, voltage and strum. With whom E, U, I it’s easier to do it for help of vectors that are wrapped around, instead of the one who made the mittve meaning e, і, i, determine the effective values of the resulting E, U, I integration of harmonic functions. The adequacy of qih diy can be rounded up like this.
Assume that in some node of the lancelet of the snake strum (Fig. 2.4 a) we can see the values of the strum i 1 i i 2:
i 1 \u003d I 1m sin (ωt + 1);
i 2 \u003d I 2 m sin (ωt + ψ 2).
It is necessary to designate a strum i.
On the basis of the first law of Kirchhoff mittve, the meaning of the strum
i \u003d i 1 + i 2,
i \u003d I 1m sin (ωt + ψ 1) + I 2m sin (ωt + ψ 2).
Strum i can be assigned analytically by a trigonometric pattern, or graphically folding graphs in mittevikh values of strum i 1 і i 2 as shown in fig. 2.4, b. The resulting strum also changes sinusoidally and sinusoidally to fig. 2.4, b
Rice. 2.4. Folding sinusoidal strums for additional vectors (a): graphs of mittiev values of strums (b)
i \u003d I m sin (?t +?).
It is much easier to fold the streams i 1 і i 2 to represent the amplitudes of the streams in the visual vectors and add them according to the parallelogram rule. On fig. 2.4 and the amplitude of the strums I 1 m і I 2 m are shown in the view of the vectors under the cod phases 1 and 2 along the x axis. After the hour t, the vectors turn around α = ωt. Projections of amplitudes on all fold
i 1 \u003d I 1 m sin (ωt + ψ 1);
i 2 \u003d I 2 m sin (ωt + ψ 2).
Having added the vectors I 1 m і I 2 m according to the parallelogram rule (div. Fig. 2.4 a), we subtract the amplitude of the resulting stream I m . The sum of the projections of the strum I 1 m і I 2 m
i = i1 + i2.
Otrimane viraz in accordance with the first Kirchhoff's law for the node of the lancet, which is seen (div. Fig. 2.4, a). 3 fig. 2.4. but it is clear that mutually the expansion of vectors I 1 m, I 2 m ta I m at any hour, it becomes imminent, shards of stink wrap around with a constant kutovy frequency ω. Similarly, you can calculate the sum of the number of sinusoidally changing voltages with the same frequency or EPC. For example, the last lance of the snake struma has three tensions:
u 1 \u003d U 1 m sin (ωt + ψ 1);
u 2 \u003d U 2 m sin (ωt + ψ 2);
u 3 \u003d U 3m sin (ωt + ψ 3).
The sum u \u003d u 1 + u 2 + u 3 voltage can be determined by the way of folding the vector in їх amplitudes (Fig. 2.5)
Rice. 2.5. Voltage vector diagram
Ūm = Ū1m + Ū2m + Ū3m
and the offensive recording of the resulting strain u \u003d U m sin (ωt + ψ).
The sequence of several vectors, which are used to represent the equals of an electric lance, is called a vector diagram.
Sound vector diagrams will not be for amplitude, but for exploding values. Vectors and meanings that deyut, vіdrіznyayutsya vіd vektorіv amplitude values only in scale, to that
I = I m / .
When prompted by vector diagrams, sound one of the outward vectors on the flat enough, and other vectors - under the outward turns to the outward one. If you need more important fluctuations, you can do without drawing the coordinate axes Xі at.
