Voltage resonance, condition of occurrence. Resonant operating modes of electrical circuits Which circuit experiences voltage resonance?

Voltage resonance is the mode of an electrical circuit of sinusoidal current with a series connection of resistive R, inductively L and capacitive WITH elements , at which the phase shift angle between the common voltage (mains voltage ) and the current in the circuit is zero .

The condition for the occurrence of voltage resonance is the equality of the inductive and capacitive reactances of the circuit:

X L = X C . (3.27)

An electrical circuit powered by a sinusoidal alternating current, which includes a capacitor and an inductor, is called oscillatory circuit .

Voltage resonance can be obtained in three ways:

1. Change frequencies w sinusoidal current;

2. Change inductance values or containers oscillatory circuit, in which the inductive XL or capacitive X C resistance;

3. When changing parameters w at the same time, L, C oscillatory circuit circuits.

From the voltage resonance condition (3.27) it follows that since

XL= w L And X C= 1/w C,

then at voltage resonance

where w res, rad/sec – resonant frequency.

Voltage resonance is characterized by a number of significant features:

1. Since during voltage resonance the phase shift angle between voltage and current is zero (j = y u – y i = 0), then The power factor at resonance takes on the highest value, equal to unity :

cos j = cos 0° = 1. (3.29)

In this case, as can be seen from the vector diagram in Fig. 3.22a, the current vector and the total voltage vector coincide in direction, since they have equal initial phases y u = y i.

2. At voltage resonance the voltage vectors on the inductive and capacitive elements turn out to be equal in magnitude and opposite in phase :

U L res = U C res (3.30)

because X L I = X C I, but in complex form (see Fig. 3.22, a).

3. The voltage across the active resistance at voltage resonance turns out to be equal to the network voltage (Fig. 4.22,a) since

. (3.31)

In a complex form.

4. The ratio of inductive or capacitive reactance to the active resistance of the circuit with R,L,C-elements at resonance is called quality factor of the oscillatory circuit Q

. (3.32)

Multiplying the numerator and denominator of these fractions by the current I, we obtain expressions for the quality factor of the oscillatory circuit through the voltage ratios

. (3.33)

At large values ​​of inductive XL and capacitive X C resistances and low values ​​of active resistance R chains ( R<<X L = X C), i.e. at high quality factors Q voltage oscillating circuit
U L res = U C res >> U:

U L res / U = XL res / R = Q >> 1; U C res / U = X C res / R = Q >> 1, (3.34)

that is the voltage on the inductance and capacitor of the series oscillating circuit with its high quality factor in the voltage resonance mode can be many times higher than the supply voltage .

For example, if the oscillatory circuit of a series circuit with
R,L,C- elements powered by sinusoidal voltage U= 220 V, R= 1 Ohm, XL res = X C res = 1000 Ohm, then the voltage across the inductance and capacitor, as follows from (3.34), is equal to:

U L res = U C res = U·Q=220·1000 = 220000 V = 220 kV.

Therefore, when working electrical equipment powered by mains voltage 220/380 volts voltage resonance is never used .

However, in a variety of radio engineering and electronics devices, where the supply voltage of the oscillatory circuit is microvolts
(1 µV = 10 -6 V), voltage resonance is widely used, allowing the input signal in the form of a sinusoidal voltage to be amplified many times over.

Rice. 3.22. Voltage resonance in a circuit with a series connection of R, L, C elements

A) - vector diagram; b) – degenerate resistance triangle (X = 0);

V) - degenerate power triangle (Q = 0)

5. Since during voltage resonance X L = X C(3.27), then The total resistance of the circuit takes a minimum value , equal to active resistance :

A the total reactance of the circuit becomes zero :

X res = | XL – X C| = 0. (3.36)

That's why the resistance triangle at voltage resonance has a degenerate character , as shown in Fig. 3.22, b.

6. Based on Ohm’s law and from formula (3.35) it follows that current I in the circuit at resonance the voltage reaches its greatest value :

I res = U/Z res = U/R. (3.37)

It follows that the current in the circuit during voltage resonance may be significantly greater than the current that could be in the absence of resonance .

This property makes it possible to detect voltage resonance when the frequency w changes, the inductance changes L or containers WITH. However resonant current is dangerous under certain conditions – it can, reaching an excessively large value, lead to overheating of circuit elements and their failure.

7. Active power at voltage resonance has the greatest value , since it is related to the square of the current

P = (I res) 2 R, (3.38)

and the current I cut is maximum.

8. Total reactive power Q at resonance the voltages are zero :

Q =½ Q L – Q C½ = ½ U L I – U C I½ = 0, (3.39)

because U L = U C. That's why The power triangle at resonance is degenerate , as shown in Fig. 3.22, v.

9. Provided R << XL = X C(i.e. with a high quality factor of the oscillating circuit) reactive inductive and capacitive power

Q L = Q C >> S = P, (3.40)

that is, these powers can be many times higher than the total power consumed S. Wherein full power S at resonance, it is completely released on the resistive element R, in the form of active power R.

Physically, this is explained by the fact that during voltage resonance, a periodic exchange of magnetic field energy in the inductive element and electric field energy in the capacitor occurs. Moreover, the intensity of this exchange, as the value of reactive powers Q L And Q C, in comparison with the active power consumed R

Q L/P = XL/R = Q; Q C/P = X C/R = Q (3.41)

is determined by the ratio of reactive and active resistance of the circuit, as for voltages U L, U C And U, that is, quality factor Q oscillatory circuit of the circuit (see paragraph 4).

Curves expressing the dependence of the total current I, circuit resistance Z, inductance voltage U L and capacitor U C, power factor cos j from the capacity of the capacitor bank WITH, are called resonance curves .

In Fig. 3.23 shows the resonance curves ( U L, U C, I, Z, cos j) = f(C), constructed in general form with U = const and w = 2p f = const.

Rice. 3.23. Resonance curves U L , U C , I , Z, cos j depending on capacity WITH
when connecting an inductor and a capacitor bank in series

Analysis of these dependencies shows that with increasing capacity WITH capacitor banks circuit impedance Z first decreases, reaches a minimum in resonance mode and becomes equal to the active resistance R, and then increases again with increasing capacity. According to the change Z the total current of the circuit changes (according to Ohm's law I inversely proportional Z): with increasing capacitor capacity, the current I initially increases, reaches a maximum in the resonance mode, and then decreases again.

Power factor cos j changes with capacitance WITH in the same order: first with increasing capacity WITH The power factor increases, reaching a maximum of unity in the resonance mode, and then decreases, tending to zero in the limit.

The voltages on the inductance and capacitors have maximums near the resonance mode and become equal to each other in this mode. It should be noted that the achieved voltage values ​​on the capacitors and inductor in the voltage resonance mode and near it can be many times higher than the input voltage applied to the entire circuit (see paragraph 4).

From the point of view of electrical safety and trouble-free operation, this should be taken into account when conducting a voltage resonance study on the bench, setting the value of the circuit supply voltage U within fairly low limits ( U= 20 ¸ 25 V).

Thus, resonance curves make it possible to establish the minimum impedance and the maximum current in the circuit at a maximum power factor of unity, when voltage resonance occurs in a circuit with a series connection of an inductor and a capacitor bank.

conclusions:

1. Voltage resonance in industrial electrical installations , powered by sinusoidal mains voltage 220/380 V – unwanted and dangerous phenomenon , since it can cause an emergency situation with possible overvoltage in certain sections of the circuit, lead to breakdown of the insulation of the windings of electrical machines and devices, insulation of cables and capacitors and is dangerous for operating personnel.

2. At the same time, Voltage resonance is widely used in radio engineering, automation and electronics for tuning oscillatory circuits into resonance at a certain frequency, as well as in various types of instruments and devices based on the resonant phenomenon.

Lab 2b is divided into four parts:

1. Preparatory part.

2. Measuring part (conducting experiments and taking instrument readings).

3. Calculation part (determination of calculated values ​​using formulas).

4. Design part (construction of vector diagrams).

Note

Electric installation work on the study of voltage resonance in a circuit with a series connection R,L,C-elements on the modernized laboratory stand EV-4 are not carried out , in contrast to work on old stands (see c - Work 2b, p. 2. Electrical installation part).

1. Preparatory part

Preparation for laboratory work includes:

1. Study of the theoretical part of this manual and literature related to the topic of this work.

2. Preliminary registration of laboratory work in accordance with existing requirements.

As a result of preliminary registration of laboratory work No. 2b in a workbook or journal (on A4 sheets with a computer printout), the student must fill out a title page, the work must indicate the name of the work and its purpose, and provide basic information on the work taken from the section above and formulas necessary for calculating the calculated values, basic and equivalent equivalent circuits are presented, tables are prepared, according to the number of experiments in the work.

In addition, free space should be left for constructing vector diagrams.

2. Measuring part

The necessary measurements of the parameters of the studied single-phase current circuit with a series connection of electrical receivers at voltage resonance are carried out using a circuit diagram (Fig. 3.24). This diagram corresponds to the panel of the modernized EV-4 stand with a similar mnemonic diagram and digital measuring instruments (see photo in Fig. 3.26).

For a more noticeable appearance of the resonance curves in the series circuit of electrical receivers, a resistor R absent (in the circuit diagram of Fig. 3.23 it is bypassed).

This circuit corresponds to an equivalent circuit with series connected, shown in Fig. 3.25.

3.24 Schematic diagram of a circuit with series connected
inductor and capacitor bank

3.25 Equivalent circuit with series connected
inductor and capacitor bank
for stress resonance studies

1. Before applying power to the circuit under study, on the bench panel with a mimic diagram and digital measuring instruments (Fig. 3.26), move all switches (S 1 ÷ S 6, S" 1 ÷ S" 6) located on this panel to the lower position ( state – “off”)

Rice. 3.26. Stand panel with digital measuring instruments and
mnemonic diagram for laboratory work 2b “Voltage resonance
in a single-phase circuit with active-reactive elements"

2. Panel stand made of daisy chain R,L,C-elements exclude resistor R, shunting it using an electrical wire (the red shunt wire in the circuit diagram of Fig. 3.24) by inserting its ends into the sockets on the sides of the voltmeter V R.

3. Set the initial total capacitance of the capacitors WITH= 40 µF by pressing the corresponding black switch buttons next to the connected capacitors on panel No. 4 of the stand with a mimic diagram of the capacitor bank (see Fig. 3.28).

4. Connect the laboratory autotransformer (LATR) installed on the horizontal panel of the power supply (Fig. 3.27) to the mains voltage (~220 V) by pressing the black “on” buttons of the switches. At the same time, two “network” indicator lamps light up. After that you must turn the knob LATRAa counterclockwise all the way , thereby reducing the voltage at its output to zero.

Rice. 3.27. Laboratory bench power supply panel

Rice. 3.28. Panel No. 4 of the stand with mimic diagrams of a capacitor bank
and inductors

5. Apply regulated voltage from the LATR to the input of the circuit under study and connect digital measuring instruments by setting the buttons of all switches (S 1 ÷ S 6, S" 1 ÷ S" 6) on the panel of the stand with the mimic diagram to the “on” position. In this case, the green numbers on the electrical measuring instruments should light up.

6. Smoothly turn the LATR regulator knob clockwise (Fig. 3.27) to set the voltage U at the circuit input about 20 ÷ 25 V, monitoring it with a digital voltmeter V(ShchP02M device installed on the left on the stand panel - Fig. 4.26). Should keep the set voltage constant in all experiments using LATR.

7. In the process of studying a circuit with an inductor and a capacitor bank connected in series, conduct 9 experiments with different capacitances of the capacitor bank (the capacitance values ​​for each experiment are indicated in Table 3.5) by pressing the corresponding switch buttons on panel No. 4 of the stand (Fig. 3.28), gradually increasing the capacitance from 40 µF to 200 µF. Before connecting additional capacitors in each experiment, it is necessary to disconnect the circuit under study from the power source (LATR output) by moving the switches (S 1, S" 1) to the lower “off” position, and before taking measurements, reconnect the circuit to the supply voltage using the same switches.

8. In all experiments, measure the input voltage U, active power consumption R and the current flowing through the circuit I, respectively, with digital measuring instruments: voltmeter V, wattmeter W and ammeter A(see the circuit diagram in Fig. 3.24 and the stand panel in Fig. 3.26).

9. Voltage across the capacitor bank U C and voltage across the inductor U K with parameters R K, LK measure with digital voltmeters, respectively V C And VK installed on the stand panel (see Fig. 3.26).

10. Enter the obtained measurement results for each experiment in Table 3.5.

11. At the end of the measuring part of this work, you need to disconnect the circuit under study from the power source and the power supply itself from the power panel using switches S 1 and S 1 "on the panel with a mimic diagram (Fig. 3.26) and the red “off” button of the switch on the panel of the unit power supply (Fig. 3.27).Inform the teacher about the completion of measurements and begin calculating the circuit parameters.

Description of the phenomenon

Let there be an oscillatory circuit with a natural frequency f, and let an alternating current generator of the same frequency operate inside it f.

At the initial moment, the circuit capacitor is discharged, the generator does not work. After switching on, the voltage across the generator begins to increase, charging the capacitor. The coil does not pass current at first due to self-induction emf. The voltage on the generator reaches its maximum, charging the capacitor to the same voltage.

Further: since the magnetic field cannot exist stationary, it begins to decrease, crossing the turns of the coil in the opposite direction. An induced emf appears at the coil terminals, which begins to recharge the capacitor. A current flows in the circuit of the oscillatory circuit, only in the opposite direction to the charge current, since the turns are crossed by the field in the opposite direction. The capacitor plates are recharged with charges opposite to the original ones. At the same time, the voltage on the generator of the opposite sign increases, and at the same speed with which the coil charges the capacitor.)

The following situation arose. The capacitor and the generator are connected in series and the voltage on both is equal to the voltage of the generator. When power supplies are connected in series, their voltages are added.

Consequently, in the next half-cycle, double the voltage will go to the coil (both from the generator and the capacitor), and oscillations in the circuit will occur at double the voltage on the coil.

In low-Q circuits, the voltage on the coil will be less than doubled, since part of the energy will be dissipated (by radiation, by heating) and the energy of the capacitor will not be completely converted into the energy of the coil). The generator and part of the capacitor are connected in series.

Notes

An oscillating circuit operating in voltage resonance mode is not a power amplifier. The increased voltages that arise on its elements arise due to the charging of the capacitor in the first quarter of the period after switching on and disappear when taken from the high power circuit.

The phenomenon of voltage resonance must be taken into account when developing equipment. Increased voltage can damage components not designed for it.

Application

When the frequency of the generator and the natural oscillations of the circuit coincide, a voltage appears on the coil that is higher than at the terminals of the generator. This can be used in voltage doublers driving high impedance loads or bandpass filters responding to a specific frequency.

see also

Literature

  • Vlasov V. F. Radio engineering course. M.: Gosenergoizdat, 1962. P. 52.
  • Izyumov N. M., Linde D. P. Basics of radio engineering. M.: Gosenergoizdat, 1959. P. 512.

Links


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    See what “Stress Resonance” is in other dictionaries: voltage resonance - voltage resonance; industry series resonance The phenomenon of resonance in an electrical circuit containing sections connected in series, having an inductive and capacitive nature ...

    See what “Stress Resonance” is in other dictionaries: Polytechnic terminological explanatory dictionary

    See what “Stress Resonance” is in other dictionaries:- Resonance in a section of an electrical circuit containing inductive and capacitive elements connected in series. [GOST R 52002 2003] Topics of electrical engineering, basic concepts EN series resonancevoltage resonance ...

    See what “Stress Resonance” is in other dictionaries:- įtampų rezonansas statusas T sritis automatika atitikmenys: engl. acceptor resonance; series resonance; voltage resonance vok. Reihenresonanz, f; Serienresonanz, f; Spannungsresonanz, f rus. series resonance, m; stress resonance, m… … Automatikos terminų žodynas - 255 voltage resonance Resonance in a section of an electrical circuit containing inductive and capacitive elements connected in series Source: GOST R 52002 2003: Electrical engineering. Terms and definitions of basic concepts original document...

    See what “Stress Resonance” is in other dictionaries: Dictionary-reference book of terms of normative and technical documentation

    - įtampų rezonansas statusas T sritis fizika atitikmenys: engl. voltage resonance vok. Spannungsresonanz, f rus. stress resonance, m pranc. résonance de tension, f … Fizikos terminų žodynas Series resonance, electrical resonance. a circuit of an inductor and a capacitor connected in series. At the resonant frequency, the reactive resistance of such a circuit is zero, and the current in it is in phase with the applied one... ...

    Big Encyclopedic Polytechnic Dictionary Voltage resonance - 1. Resonance in a section of an electrical circuit containing inductive and capacitive elements connected in series. Used in the document: GOST R 52002 2003 Electrical engineering. Terms and definitions of basic concepts...

    Telecommunications dictionary circuit tuned to voltage resonance - - [Ya.N.Luginsky, M.S.Fezi Zhilinskaya, Yu.S.Kabirov. English-Russian dictionary of electrical engineering and power engineering, Moscow, 1999] Topics of electrical engineering, basic concepts EN series oscillatory circuit ...

    Technical Translator's Guide

    Current resonance is a resonance that occurs in a parallel oscillatory circuit when it is connected to a voltage source whose frequency coincides with the circuit’s natural frequency. Contents 1 Description of the phenomenon 2 Remarks ... Wikipedia- 9 Resonance According to GOST 24346 80

By resonance in an electrical circuit we mean its state when the current and voltage are in phase and the entire circuit behaves as if it were purely active (Fig. 1.18).

Rice. 1.18. Resonant circuit ( A) and vector diagram at resonance ( b)

(from the definition of resonance);
(voltage resonance condition);

;
;

If then, i.e. the voltage on the reactive elements of the circuit may be greater than the voltage supplied to the entire circuit.
,
,
those. the circuit from the network does not consume reactive power and does not supply it to the network;
;

.

At the moment of resonance, energy is exchanged between L And C. Reactive power is not consumed from the network and is not supplied to the network, therefore, the circuit behaves as a purely active one.

35. Current resonance occurs in alternating current circuits consisting of an oscillation source and a parallel oscillating circuit. Current resonance is an increase in the current passing through the elements of the circuit, while the increase in current consumption from the source does not occur.

Figure 1 - parallel oscillatory circuit

For current resonance to occur, it is necessary that the reactance of the capacitance and inductance of the circuit be equal. And also the frequency of the circuit’s own oscillations was equal to the oscillation frequency of the current source.

During the onset of current resonance or the so-called parallel resonance, the voltage on the circuit elements remains unchanged and equal to the voltage created by the source. Because it is connected parallel to the circuit. Current consumption from the source will be minimal, since the circuit resistance will increase sharply when resonance occurs.

Figure 2 - dependence of circuit impedance and current on frequency

The resistance of the oscillatory circuit relative to the source of oscillation will be purely active. That is, it won’t, neither the capacitive nor the inductive component will fade. And there will be no phase shift between current and voltage.

At the same time, the current through the inductance will lag behind the voltage by 90 degrees. And the current in the tank will lead the voltage by the same 90 degrees. Thus, the currents in the reactive elements of the circuit will be shifted in phase by 180 degrees relative to each other.

As a result, it turns out that reactive currents of a fairly large magnitude flow in the parallel oscillatory circuit, but at the same time it consumes a small current from the voltage source, which is necessary only to compensate for losses in the circuit. These losses are due to the presence of active resistance concentrated mostly in inductance.

The source expends energy when turned on, charging the capacity. Next, the energy accumulated in the electric field of the capacitor is converted into the energy of the magnetic field of the inductance. The inductance returns the energy to the capacitor and the process repeats again. The voltage source only has to compensate for the energy losses in the active resistance of the circuit.


1. The loop current method is used in the usual way, however, we add mutual induction voltages (type) to the self-induction voltages on the coils. It is advisable to select loop currents so that each coil receives its own loop current.

When an oscillatory circuit consisting of an inductor and a capacitor is connected to an energy source (a source of sinusoidal EMF or sinusoidal current), resonance phenomena may occur. Two main types of resonance are possible: when a coil and capacitor are connected in series, there is a voltage resonance; when they are connected in parallel, there is a current resonance.

Voltage resonance.

Voltage resonance is possible in an unbranched section of the circuit, the equivalent circuit of which contains an inductive L , capacitive WITH , and resistive R elements, i.e. in a series oscillatory circuit (Fig. 2.43).

This name reflects the equality of the effective voltage values ​​on the capacitive and inductive elements at opposite phases, as can be seen from the vector diagram in Fig. 2.44, in which the initial phase of the current is chosen equal to zero.

From relation (2.766) and condition (2.77) it follows that the angular frequency at which voltage resonance is observed is determined by the equality

and is called resonant .

At voltage resonance, the current in the circuit reaches its greatest value I cut = U/R , and the voltages on the capacitive and inductive elements

U L r e z = U Av e z = ω res LI res = Uω pe z L/R

may (many times) exceed the supply voltage if

ω pe з L = 1/ω pe з С = √L/C > R.

Value ρ = ω pe з L = 1/ω pe з С = √L/C has the dimension of resistance and is called characteristic resistance oscillatory circuit. Ratio of voltage across an inductive or capacitive element at resonance to voltage U at the circuit terminals, equal to the ratio of the characteristic resistance to the resistance of the resistive element, determines the resonant properties of the oscillatory circuit and is called circuit quality factor :

If at resonance you increase the same number of times P inductive and capacitive reactance, i.e. choose

Х' L = nX Lpe з And X" C = pX Cut,

then the current in the circuit will not change, but the voltages on the inductive and capacitive elements will increase by n times (Fig. 2.44, b):U L= nU Lpe s And U" C = pU C res Therefore, in principle, it is possible to increase the voltages on the inductive and capacitive elements without limit at the same current: I = I res = U/R .


The physical reason for the occurrence of increased voltages is fluctuations in significant energy stored alternately in the electric field of the capacitive element and in the magnetic field of the inductive element.

With voltage resonance, small amounts of energy supplied from the source and compensating for energy losses in the active resistance are sufficient to maintain undamped oscillations in the system of relatively large amounts of magnetic and electric field energy.

In communication equipment, automation, etc., the dependence of currents and voltages on frequency for circuits in which resonance is possible is of great practical importance. These dependencies are called resonance curves .

Expression (2.76c) shows that the current in the circuit depends on the angular frequency I(ω) and reaches its greatest value at resonance, i.e. at ω = ω pe s And ω pe з L = 1/(ω pe з С) (Fig. 2.45).

Impedance of an ideal series circuit (R=0) at resonance it is zero (short circuit for the power supply).

The highest voltage values ​​on the inductive and capacitive elements are obtained at angular frequencies slightly different from the resonant one. So, the voltage across the capacitive element

The higher the quality factor of the oscillatory circuit Q , the less the angular frequencies differ ωC And ωL on the resonant angular frequency and the sharper all three resonant curves I(ω) , U C (ω) And U L (ω).

In electrical power devices, in most cases, voltage resonance is an undesirable phenomenon, since during resonance, the voltages of the installations can be several times higher than their operating voltages. But, for example, in radio engineering, telephony, and automation, voltage resonance is often used to tune circuits to a given frequency.

The power factor cosφ at voltage resonance is equal to unity.

2. Condition, sign and application of stress resonance. When is voltage resonance harmful? Why?

A mode in which, in a circuit with a series connection of an inductive and capacitive element, the input voltage is in phase with the current, voltage resonance.

The sudden occurrence of a resonant mode in high-power circuits can cause emergency situations, lead to breakdown of the insulation of wires and cables and create a danger for personnel.

3. In what ways can voltage resonance be achieved?

When connecting an oscillating circuit consisting of an inductor and a capacitor to an energy source, a resonant phenomenon may occur. Two main types of resonance are possible: when the coil and capacitor are connected in series, there is voltage resonance, and when they are connected in parallel, there is current resonance.

4. Why during voltage resonanceU 2 >U 1 ?

Where R is active resistance

I – current strength

XL – coil inductance

XC – capacitance of the capacitor

Z – AC impedance

At resonance: UL = UC,

Where UC is the coil voltage,

UL – capacitor voltage

The voltage can be found:

U=UR+UL+UC =>U=UR,

Where UR is the voltage of the coil to which the voltmeter V2 is connected, which means voltage V2=V1

5. What is the feature of voltage resonance? Explain it.

Consequently, the resonance mode can be achieved by changing the inductance of the coil L, the capacitance of the condensate C or the frequency of the input voltage ω.

6. Write down the expression for Ohm’s law in terms of conductivity for a circuit with a parallel connection of a capacitor and an inductive coil. What is the total conductivity?

Ohm's law through conductivity for an alternating current circuit with parallel connections of branches.

7. Condition, sign and application of current resonance.

i.e. equality of inductive and capacitive conductivity.

8 . In what ways can current resonance be achieved?

A mode in which in a circuit containing parallel branches with inductive and capacitive elements, the current of the unbranched section of the circuit is in phase with the voltage, the resonance of the currents.

9. Why during current resonanceI 2 > I 1 ?

Because, based on the vector diagram of currents at resonance, the graph will be a right triangle, where currents I and I 1 will be legs, and current I 2 will be the hypotenuse. Consequently, I 2 will also be greater than I 1.

10. What is the feature of current resonance? Explain it.

With current resonance, the currents in the branches are significantly greater than the current in the unbranched part of the circuit. This property—current strength—is the most important feature of current resonance.

11. Explain the construction of vector diagrams.

The purpose of its construction is to determine the active and reactive components of the voltage on the coil and the phase shift angle between the voltage at the circuit input and the current

Calculations

LIST OF SOURCES USED

    Electrical and Electronics. Book 1. Electric and magnetic circuits. - B 3 books: book 1 /B. G. Gerasimov and others; Ed.

    V. G. Gerasimova. M.: Energoatomizdat, 1996. – 288 p.

    Electrical engineering /Ed. Yu. L. Khotuntseva. M.: AGAR, 1998. – 332 p.

    Borisov Yu. M., Lipatov D. N., Zorin Yu. N. Electrical engineering.

    Energoatomizdat, 1985. – 550 p.



 

GOST 19880-74. Electrical engineering. Basic concepts.