Electrical charge in the oscillatory circuit of the formula. Oscillating contour

Tomsono Virpesių Formulė Statusas T Sritis Fizika Atitikmenys: Angl. Thomson's Formula Vok. Thomsonsche SchwingungsFormel, F Rus. Thomson formula, F PRANC. Formule De Thomson, F ... Fizikos Terminų žodynas

The dependence of the diffreential scattering cross section from the scattering angle for various values \u200b\u200bof the photon cell of the cupin niche formula formula describing ... Wikipedia

- [according to VDIA eng. Physics of U. Thomson (W. Thomson; 1824 1907)] F LA, expressing the dependence of the period t of non-teaching fluctuations in the oscillatory circuit from its parameters of the inductance L and tank C: T \u003d 2PI root from LC (here l in GN, C in F ... Big Encyclopedic Polytechnic Dictionary

Thomson's effect is one of the thermoelectric phenomena in the fact that in a homogeneous unevenly heated conductor with a constant current, in addition to the warmth allocated in accordance with the law of Joule Lenza, in the volume ... Wikipedia

Expression for Differ. Section DS scattering photon on an electron (see Compton Effect). In lab. The coordinate system where the frequencies of the falling and scattered photon, the element of a bodily corner for the scattered photon, the scattering angle, parameter R0 \u003d E ... Physical encyclopedia

- (Thomson) (in 1892 for scientific merit received the title of Baron Kelvin, Kelvin (1824 1907), English Physicist, Member (1851) and President (1890 1895) of the London Royal Society, Foreign Member Correspondent (1877) and foreign honorary member ... ... encyclopedic Dictionary

- (Thomson, William), Lord Kelvin (1824 1907), English physicist, one of the founders of thermodynamics. Born in Belfast (Ireland) June 26, 1824. Lectures of the Father, Professor of Mathematics of the University of Glasgow, began to visit for 8 years, and in 10 it became ... ... Encyclopedia Color

I Thomson Alexander Ivanovich, Russian Soviet Language, member of the correspondent of the St. Petersburg Academy of Sciences (1910). He graduated from St. Petersburg University (1882). Professor of Novorossiysk University ...

Thomson, Lord Kelvin (Kelvin) William (26.6.1824, Belfast, - 12/17/1907, Largs, near Glasgow; buried in London), English physicist, one of the founders of thermodynamics and kinetic gases, a member of the Royal Society London from … Great Soviet Encyclopedia

- (Thomson, Joseph John) (1856 1940), English physicist, awarded the Nobel Prize in Physics 1906 for work, which led to the opening of an electron. Born on December 18, 1856 in the suburb of Manchester Chuthe Hill. At the age of 14 he entered Owens ... ... Encyclopedia Color

Lesson number 48-169 oscillatory contour. Free electromagnetic oscillations. Transformation of energy in the oscillatory circuit. Thompson formula.Oscillations- Movement or states repeating over time.Electromagnetic oscillations -these are electrical oscillations andmagnetic fields that soprowidged in periodic treasonthe charge, current and voltage. The oscillating circuit is a system consisting of inductance and condenser coil. (Fig. A). If the condenser is charged and closer to the coil, then the reel flows the current (Fig. B). When the capacitor is discharged, the current in the chain will not stop due to self-induction in the coil. The induction current, in accordance with the Lenz rule, will flow into the same direction and reloads the condenser (Fig. B). The current in this direction will cease, and the process will repeat in the opposite direction (Fig. d).

In this way, in a oscilbelt circuit happensound electromagnetic flashersdue to energy transformationelectric field condensator.(W E \u003d
) in the magnetic field energy coil with current (W m \u003d
), and vice versa.

Harmonic oscillations are periodic changes in physical quantity depending on the time occurring under the law of sine or cosine.

Equation describing free electromagnetic oscillations takes

q "\u003d - ω 0 2 Q (q" - the second derivative.

The main characteristics of the oscillatory movement:

Period of oscillations - the minimum period of time t, through which the process is completely repeated.

Harmonic oscillation amplitude - module the greatest value fluctuating magnitude.

Knowing a period, you can determine the frequency of oscillations, i.e. the number of oscillations per unit of time, for example per second. If one oscillation is performed during T, then the number of oscillations for 1 s ν is determined like this: ν \u003d 1 / t.

Recall that in the international system of units (s) the frequency of oscillations is equal to one if one oscillation is performed for 1 s. The frequency unit is called Herz (abbreviated: Hz) in honor of the German physics of Henry Ge Rza.

After a period of time equal to the period T,i.e. with increasing cosine argument on Ω 0 T,the charge value is repeated and the cosine takes the same value. From the course of mathematics it is known that the smallest period of cosine is 2l. Consequently, Ω. 0 T. \u003d 2π,from where Ω. 0 = \u003d 2πν thus the value Ω 0 - This is the number of oscillations, but not for 1 s, but for 2 liters. It is called cyclicor circular frequency.

Frequency of free oscillations call own frequency oscillationsystems.Often in the future for brevity we will call cyclic frequency Just frequency. Distinguish the cyclic frequency Ω 0 From the frequency ν can be on the notation.

By analogy with the solution of the differential equation for the mechanical oscillatory system cyclic frequency of free electricsky oscillationsequal: Ω 0 \u003d

The free oscillation period in the circuit is equal to: T \u003d \u003d 2π.
- thomson formula.

Phase oscillations (from the Greek word Phasis - the appearance, stage of development of any phenomenon) - the value of φ, standing under the sign of the cosine or sine. Phase is expressed in angular units - radians. The phase determines with a given amplitude the state of the oscillating system at any time.

Oscillations with the same amplitudes and frequencies may differ from each other in phases.

As ω. 0 \u003d, then φ \u003d ω 0 T \u003d 2π.. The attitude shows which part of the period passed from the moment of the start of the oscillations. Any value of the time expressed in the fractions of the period corresponds to the value of the phase expressed in radians. So, after time t \u003d (quarters of the period) φ \u003d , after half the period φ \u003d π, after a whole period φ \u003d 2π, etc., can be portrayed on the chart

charge not on time, but from the phase. The figure shows the same cosineida, as in the previous one, but on the horizontal axis postponed instead of time

various phase values \u200b\u200bφ.

Compliance between mechanical and electrical values \u200b\u200bin oscillatory processes

Mechanical values

Tasks.

942(932). The initial charge, reported by the condenser of the oscillatory circuit, decreased by 2 times. How many times changed: a) voltage amplitude; b) current strength amplitude;

c) the total energy of the electrical field of the condenser and the magnetic field of the coil?

943(933). With an increase in the voltage on the condenser of the oscillating circuit by 20 in the amplitude of the current force increased by 2 times. Find the initial voltage.

945(935). The oscillating circuit consists of a capacitor with a capacity C \u003d 400 PF and coil inductanceL. = 10 mp Find the amplitude of the oscillations of the current I t. , if the amplitude of voltage oscillations u t. \u003d 500 V.

952(942). After what time (in the fraction of the periodt / T) On the condenser of the oscillatory circuit, will the first charge equal to half an amplitude value?

957(947). What inductance coil should be included in the oscillating circuit, so that with the capacitance of the condenser 50 PF get the frequency of free oscillations of 10 MHz?

Oscillatory contour. Period of free oscillations.

1. After the condenser of the oscillating circuit was reported chargeq \u003d 10 -5 CL, fading oscillations appeared in the circuit. What amount of heat is highlighted in the circuit by the time the oscillations in it completely will fall on? Capacity of the capacitor C \u003d 0.01MCF.

2. The oscillating circuit consists of a capacitor with a capacity of 400NF and the coil with an inductance of 9MKHN. What is the period of own oscillations of the contour?

3. What inductance should be included in the oscillating circuit, so that with the capacity of 100 PF get the period of own oscillations 2 ∙ 10 -6 s.

4. Compare rigidity springsk1 / K2 two pendulums with cargo masses, respectively, 200g and 400g, if the periods of their oscillations are equal.

5. Under the action of motionless hanging load on the spring, its elongation was equal to 6.4 cm. Then the cargo was pulled out and let go, as a result of which he began to hesitate. Determine the period of these oscillations.

6. The cargo joined the spring, removed it from the equilibrium position and released. The load began to fluctuate with a period of 0.5s. Determine the extension of the spring after the cessation of oscillations. The mass of the springs is not considered.

7. For the same time, one mathematical pendulum performs 25 oscillations, and the other 15. Find their lengths if one of them is in 10 cm shorter than the other.8. The oscillatory circuit consists of a capacitor with a capacity of 10 MF and the coil of the inductance of 100 MGN. Find the amplitude of voltage fluctuations if the amplitude of the current oscillations of the current 0,1A9. Inductance of the coil of the oscillating circuit 0.5 MGN. You need to configure this outline to the frequency of 1 MHz. What should the capacitor container in this circuit be?

Examination questions:

1. Which of the expressions below determines the period of free oscillations in the oscillatory circuit? BUT. ; B.
; IN.
; G.
; D. 2.

2. Which of the above expressions determines the cyclic frequency of free oscillations in the oscillatory circuit? A. B.
IN.
G.
D. 2π.

3. The figure shows a graph of the dependence of the coordinates of the body that performs harmonic oscillations along the axis oh, on the time. What is the period of body fluctuations?

A. 1 C; B. 2 C; B. 3 S. . G. 4 s.

4. The figure shows the wave profile at a certain point in time. What is its length?

A. 0.1 m. B. 0.2 m. 2 m. 4 m. D. 5 m.
5. The figure shows a graph of the dependence of the current force through the coil of the oscillating circuit from time. What is the period of current fluctuations? A. 0.4 s. B. 0.3 s. V. 0.2 s. 0.1 s.

D. Among the answers A-g no correct.

6. The figure shows the wave profile at a certain point in time. What is its length?

A. 0.2 m. B. 0.4 m. V. 4 m. G. 8 m. D. 12 m.

7. Electric oscillations in the oscillatory circuit are set by the equationq \u003d 10 -2 ∙ COS 20T (CL).

What is the amplitude of the charge fluctuations?

BUT . 10 -2 cl. B. COS 20T CL. B.20T CL. G.20 CL. D.Sredi answers A-g no correct.

8. With harmonic oscillations along the axis oh, the coordinate of the body varies by lawX \u003d 0.2cos (5t + ). What is the amplitude of the fluctuations of the body?

A. XM; B. 0.2 m; c. COS (5T +) M; (5t +) m; D.M.

9. The frequency of oscillations of the wave source 0.2 s -1 The speed of propagation of the wave of 10 m / s. What is the wavelength? A. 0.02 m. B. 2 m. V. 50 m.

G. under the condition of the task cannot be determined by the wavelength. D. Among the answers A-g no correct.

10. The wavelength of 40 m, the distribution speed of 20 m / s. What is the frequency of fluctuations of the source of the waves?

A. 0.5 s -1. B. 2 C -1. B. 800 C -1.

G. Under the condition of the task, it is impossible to determine the frequency of oscillation of the source of the wave.

D. Among the answers A-g no correct.

3

• Electromagnetic oscillations - These are periodic changes with the time of electrical and magnetic values \u200b\u200bin the electrical circuit.

• Free are called such oscillationswhich occur in a closed system due to the deviation of this system on the state of steady equilibrium.

With oscillations, there is a continuous process of converting the energy of the system from one form to another. In the case of oscillations of the electromagnetic field, the exchange can only go between the electrical and magnetic component of this field. Simplest systemwhere this process can occur is oscillating contour.

• Perfect oscillating contour (LC-contour) - electrical circuitconsisting of coil inductance L. and capacitor capacity C..

Unlike a real oscillatory circuit, which has electrical resistance R.The electrical resistance of the ideal contour is always equal to zero. Consequently, the perfect oscillating circuit is a simplified model of a real circuit.

Figure 1 shows the scheme of an ideal oscillatory circuit.

Energy contour

Complete energy of the oscillating circuit

\\ (W \u003d w_ (e) + w_ (m), \\; \\; \\; w_ (E) \u003d \\ DFRAC (C \\ CDOT U ^ (2)) (2) \u003d \\ DFRAC (Q ^ (2)) (2c), \\; \\; \\; w_ (m) \u003d \\ dfrac (L \\ Cdot i ^ (2)) (2), \\)

Where W E. - the energy of the electrical field of the oscillating circuit at the moment, FROM - electrical capacity of the capacitor, u. - voltage value on the condenser at a given time, q. - the value of the capacitor's charge at the moment, W M. - the energy of the magnetic field of the oscillating circuit at the moment, L. - inductance of the coil, i. - Current strength in the coil at the moment.

Processes in the oscillatory circuit

Consider the processes that occur in the oscillatory circuit.

To remove the contour from the equilibrium position charge the capacitor so that on its plates will be charged Q M. (Fig. 2, position 1 ). Taking into account the equation \\ (u_ (m) \u003d \\ dfrac (q_ (m)) (C) \\) we find the voltage value on the condenser. Current in the chain at this point in time is not, i.e. i. = 0.

After closing the key under the action of the electrical field of the condenser in the chain will appear electricity, Tok power i. which will increase over time. The capacitor will start discharge at this time, because Electrons, creating a current, (remind you that the direction of current is taken by the direction of the movement of positive charges) leave with a negative condenser clamp and come to positive (see Fig. 2, position 2 ). Together with the charge q. will decrease and voltage u. \\ (\\ left (u \u003d \\ dfrac (q) (C) \\ RIGHT). \\) With an increase in the current strength through the coil, self-induction will arise, which prevents the change in the current strength. As a result, the current of the current in the oscillatory circuit will increase from zero to some maximum value not instantly, but for a certain period of time determined by the inductance of the coil.

Capacitor charge q. decreases and at some point in time it becomes zero ( q. = 0, u. \u003d 0), the current of the current in the coil will reach some value I M. (see Fig. 2, position 3 ).

Without the electric field of the condenser (and resistance), the electrons that create the current continue their inertia movement. At the same time, electrons coming to a neutral capacitor clamp report to it a negative charge, electrons leaving neutrally inform her positive charge. On the condenser begins to appear q. (and voltage u.), but the opposite sign, i.e. Condenser recharges. Now the new electrical field of the capacitor prevents the electron movement, so the current i. starts decree (see Fig. 2, position 4 ). Again, this does not happen instantly, since now EMF self-induction seeks to compensate for the decrease in current and "supports" it. And the value of the current I M. (pregnant 3 ) It turns out maximum current value in the circuit.

And again under the action of the electric field of the capacitor in the circuit, an electric current will appear, but directed in the opposite direction, the current i. which will increase over time. And the condenser at this time will be discharged (see Fig. 2, position 6 ) to zero (see Fig. 2, position 7 ). Etc.

As the charge on the condenser q. (and voltage u.) Determines its electric field energy W E. \\ (\\ left (w_ (e) \u003d \\ dfrac (q ^ (2)) (2c) \u003d \\ DFRAC (C \\ CDOT U ^ (2)) (2) \\ Right), \\) and current power in the coil i. - magnetic field energy WM. \\ (\\ left (W_ (M) \u003d \\ DFRAC (L \\ CDOT I ^ (2)) (2) \\ Right), \\) then, together with changes in charge, voltage and current, will change and energy.

Designation in the table:

\\ (W_ (e \\, \\ max) \u003d \\ dfrac (q_ (m) ^ (2)) (2c) \u003d \\ dfrac (C \\ CDOT U_ (M) ^ (2)) (2), \\; \\; \\; W_ (e \\, 2) \u003d \\ dfrac (q_ (2) ^ (2)) (2c) \u003d \\ DFRAC (C \\ CDOT U_ (2) ^ (2)) (2), \\; \\; \\ W_ (E \\, 6) \u003d \\ DFRAC (Q_ (6) ^ (2)) (2C) \u003d \\ DFRAC (C \\ CDOT U_ (6) ^ (2)) (2), \\)

\\ (W_ (m \\; \\ max) \u003d \\ dfrac (l \\ cdot i_ (m) ^ (2)) (2), \\; \\; \\; w_ (m2) \u003d \\ DFRAC (L \\ Cdot i_ (2 ) ^ (2)) (2), \\; \\; \\; w_ (m4) \u003d \\ dfrac (l \\ cdot i_ (4) ^ (2)) (2), \\; \\; \\; w_ (m6) \u003d \\ DFRAC (L \\ Cdot i_ (6) ^ (2)) (2). \\)

The total energy of the perfect oscillatory circuit is preserved over time, since it has energy losses (no resistance). Then

\\ (W \u003d w_ (e \\, \\ max) \u003d w_ (m \\, \\ max) \u003d w_ (e2) + w_ (m2) \u003d w_ (e4) + w_ (m4) \u003d ... \\)

Thus, in perfect LC- Consture will occur periodic changes in current values i., charge q. and voltage u., Moreover, the total energy of the circuit will remain constant. In this case, they say that the contour arose free electromagnetic oscillations.

• Free electromagnetic oscillations In the circuit, these are periodic changes in the charge on the condenser plates, current and voltage strength in the circuit, occurring without energy consumption from external sources.

Thus, the occurrence of free electromagnetic oscillations in the circuit is due to the recharge of the capacitor and the emergence of self-induction EMF in the coil, which "provides" this recharge. Note that the capacitor charge q. and current power in the coil i. reach their maximum values Q M. and I M. at various points in time.

Free electromagnetic oscillations in the circuit occur by harmonic law:

\\ (q \u003d q_ (m) \\ cdot \\ cos \\ left (\\ \\ \\ \\ cdot t + \\ varphi _ (1) \\ right), \\; \\; \\; u \u003d u_ (m) \\ cdot \\ cos \\ left (\\ The smallest period of time during which

- Konter returns B. LCthe initial state (To the initial value of the charge of this cover), is called a period of free (own) electromagnetic oscillations in the circuit. Period of free electromagnetic oscillations in

The system is determined by the Thomson formula: LC\\ (T \u003d 2 \\ pi \\ cdot \\ sqrt (l \\ cdot c), \\; \\; \\; \\ \\ omega \u003d \\ dfrac (1) (\\ SQRT (L \\ CDOT C)). \\)

The struts of the view of the mechanical analogy, the perfect oscillatory contouration of the spring pendulum without friction, and the real - with friction. Over the priest of the friction force fluctuations in the spring pendulum fade over time.

* Conclusion of the Thomson Formula

Since the full energy is perfect

-Conter equal to the sum of the energy of the electrostatic field of the capacitor and the magnetic field of the coil is preserved, then at any time the equality is right LC\\ (W \u003d \\ dfrac (q_ (m) ^ (2)) (2c) \u003d \\ dfrac (l \\ cdot i_ (m) ^ (2)) (2) \u003d \\ DFRAC (Q ^ (2)) (2c ) + \\ DFRAC (L \\ Cdot i ^ (2)) (2) \u003d (\\ rm const). \\)

We obtain the oscillation equation in

-The system, using the law of energy conservation. Indignantly by the expression for its total energy in time, given the fact that LC\\ (W "\u003d 0, \\; \\; \\; q" \u003d i, \\; \\; \\; i "\u003d q" ", \\)

We obtain an equation describing free oscillations in the perfect circuit:

\\ (\\ left (\\ dfrac (q ^ (2)) (2c) + \\ dfrac (l \\ cdot i ^ (2)) (2) \\ right) ^ ((")) \u003d \\ DFRAC (Q) (C ) \\ cdot q "+ l \\ cdot i \\ cdot i" \u003d \\ dfrac (q) (c) \\ cdot q "+ l \\ cdot q" \\ cdot q "" \u003d 0, \\)

\\ (\\ dfrac (q) (c) + l \\ cdot q "" \u003d 0, \\; \\; \\; \\; q "" + \\ dfrac (1) (L \\ Cdot C) \\ Cdot Q \u003d 0. \\ Swiring it in the form:

\\ (q "" + \\ omega ^ (2) \\ Cdot Q \u003d 0, \\)

We notice that this is the equation of harmonic oscillations with a cyclic frequency

\\ (\\ Omega \u003d \\ DFRAC (1) (\\ SQRT (L \\ CDOT C)). \\)

accordingly, the period of the vibrations under consideration

\\ (T \u003d \\ DFRAC (2 \\ PI) (\\ Omega) \u003d 2 \\ PI \\ CDOT \\ SQRT (L \\ CDOT C). \\)

Literature

Zhilko, V.V. Physics: studies. Manual for grade 11 general formation. shk. with rus. Yaz. Learning / V.V. Zhilko, L.G. Markovich. - Minsk: Nar. Asveta, 2009. - P. 39-43.

The main device determining the operating frequency of any generator

1. alternating current

, is the oscillating circuit. The oscillating circuit (Fig. 1) consists of inductance coil (Consider the ideal case when the coil does not have ohmic resistance) and the condenser{!LANG-b4ea81dbe1cca70d85245713e5610dad!} L.{!LANG-68c5458628edd76fb566148becc48b51!} C. And called closed. The characteristic of the coil is inductance, it is indicated L. and is measured in Henry (GG), the capacitor is characterized by a container C.which is measured in the Farades (F).

Let the capacitor are charged at the initial moment of time (Fig. 1) that on one of his plates there is a charge + Q. 0, and on the other - charge - Q. 0. At the same time, an electric field with energy is formed between the capacitor plates.

where - amplitude (maximum) voltage or potential difference on capacitor plates.

After the circuit circuit, the capacitor begins to discharge and the circuit will go the electric current (Fig. 2), the value of which increases from zero to the maximum value. Since a variable current flows in the chain, then self-induction EMP is induced in the coil, which prevents the discharge of the capacitor. Therefore, the process of dischargeing the condenser does not occur instantly, but gradually. At every moment of time, the potential difference on the capacitor plates

(where - the charge of the condenser at the moment time) is equal to the potential difference on the coil, i.e. Equal to EMF self-induction

Fig.1	Fig.2

When the condenser is completely discharged and, the current strength in the coil reaches the maximum value (Fig. 3). The induction of the magnetic field of the coil at this moment is also maximum, and the magnetic field energy will be equal to

The current of the current begins to decrease, and the charge will accumulate on the condenser plates (Fig. 4). When the current is reduced to zero, the capacitor charge reaches the maximum value Q. 0, but the label, first charged positively, will now be charged negatively (Fig. 5). The condenser is then again begins to discharge, and the current in the chain flows in the opposite direction.

So the process of flowing the charge from one condenser clamping to another through the inductor is repeated again and again. They say that the circuit occurs electromagnetic oscillations . This process is associated not only with the oscillations of the charge value and voltage on the condenser, the current forces in the coil, but also the pumping of the energy from the electric field to magnetic and back.

Fig. 3.	Fig.4

Recharge the capacitor to the maximum voltage will occur only if there is no energy loss in the oscillatory circuit. Such contour is called perfect.

In real circuits, the following energy loss takes place:

1) thermal losses, because R. ¹ 0;

2) losses in the dielectric condenser;

3) hysteresis losses in the core coil;

4) Losses on radiation, etc. If you neglect by these losses of energy, then you can write that, i.e.

Oscillations occurring in the perfect oscillatory circuit in which this condition is being done are called free, or own, oscillations of the contour.

In this case voltage U. (and charge Q.) The capacitor varies on the harmonic law:

where n is the intrinsic frequency of the oscillating circuit, W 0 \u003d 2pn - its own (circular) frequency of the oscillating circuit. The frequency of electromagnetic oscillations in the circuit is defined as

T. - time during which one complete voltage fluctuation on the condenser and current in the circuit is performed, is determined Thomson formula

The strength of the current in the circuit also changes in harmonic law, but lags behind the voltage of phase. Therefore, the dependence of the current in the circuit will be viewed

. (9)

Figure 6 presents voltage change graphs U. on the condenser and current I. In the coil for an ideal oscillatory circuit.

In the real circuit, energy with each oscillation will decrease. The amplitudes of the voltage on the condenser and current in the circuit will decrease, such oscillations are called decaying. In the specifying generators it is impossible to apply them because The device will work at best in pulse mode.

Fig.5	Fig.6.

To obtain unlucky oscillations, it is necessary to compensate for the loss of energy with a wide variety of operating frequencies, including those used in medicine.

If compared Fig. 50 with rice. 17, on which the fluctuations of the body are shown on the springs, it is not difficult to establish a large similarity in all stages of the process. You can create a kind of "dictionary", with the help of which the description of electrical oscillations can be immediately translated into mechanical description, and back. This dictionary is.

Try reread the previous paragraph with this "dictionary." At the initial moment, the capacitor is charged (the body is deflected), i.e. the system is reported by the supply of electrical (potential) energy. Begins to flow the current (the body acquires the speed), through a quarter of the current period and magnetic energy is the largest, and the capacitor is discharged, the charge on it is zero (the body rate and its kinetic energy is the largest, and the body passes through the equilibrium position), etc.

Note that the initial charge of the condenser and, therefore, the voltage on it is created by the electromotive power of the battery. On the other hand, the initial deviation of the body is created by the exempted force. Thus, the force acting on the mechanical oscillatory system plays a role similar to the electromotive force acting on the electrical oscillatory system. Our "dictionary" may therefore supplemented with another "translation":

7) force, 7) electromotive force.

The similarities of the patterns of both processes goes on. Mechanical oscillations fade due to friction: with each oscillation, part of the energy turns due to friction into heat, so the amplitude is less and less. In the same way, with each recharge of the capacitor, part of the current energy passes into heat released due to the presence of resistance from the coil wire. Therefore, electrical oscillations in the circuit also fade. Resistance plays for electrical oscillations the same role as friction for mechanical oscillations.

In 1853 English physicist William Thomson (Lord Kelvin, 1824-1907) showed theoretically that its own electrical oscillations in the circuit consisting of a capacitor capacitor and inductors are harmonic, and their period is expressed by the formula

(- In Henry, - in the Farades, - in seconds). This simple and very important formula is called Thomson's formula. The oscillatory circuits themselves with a capacity and inductance are often also called Tomsonovski, since Thomson for the first time gave the theory of electrical fluctuations in such circuits. Recently, the term "-Konutour" is increasingly used (and similarly "-Contour", "-Contour", etc.).

Comparing the Thomson formula with a formula that determines the period of harmonic oscillations of an elastic pendulum (§ 9), we see that the body weight plays the same role as inductance, and the rigidity of the spring is the same role as the value, the reverse tank (). In accordance with this in our "Dictionary" the second line can be recorded so:

2) Spring rigidity 2) The quantity of the capacitance capacitance.

Selecting different and, you can get any periods of electrical oscillations. Naturally, depending on the period of electrical oscillations, it is necessary to use different ways their observations and records (oscillographs). If you take, for example, and then the period will be

i.e. oscillations will occur with a frequency of about. This is an example of electrical oscillations whose frequency lies in the sound range. Such oscillations can be heard using the phone and write on the loop oscilloscope. The electronic oscilloscope allows you to get a scan of both such and more high-frequency oscillations. In radio engineering, extremely fast oscillations are used - with frequencies in many millions of hertz. The electronic oscilloscope allows you to observe their shape as well as we can with the help of a pendulum's track on the smoked record (§ 3) to see the shape of the pendulum oscillations. The oscilloscope of free electrical oscillations in one-time excitation of the oscillating circuit is usually not applied. The fact is that the state of equilibrium in the circuit is installed only in a few periods, or, at best, for several tens of periods (depending on the relationship between the inductance of the contour, its capacity and resistance). If, say, the attenuation process is almost ends for 20 periods, then in the above example of the contour from the periods to the entire outbreak of free oscillations, it will take a word and to keep track of an oscillogram with a simple visual observation will be very difficult. The task is easily solved if the whole process is from the excitation of oscillations to their almost complete fading - to periodically repeat. Making the deploying electronic oscilloscope voltage is also periodic and synchronous with the excitation process of oscillations, we will force the electronic beam to multiply "draw" the same oscillogram on the same screen of the screen. With a fairly frequent repetition, the picture observed on the screen will generally seem unlucky, i.e. we will break the fixed and unchanged curve, the idea of \u200b\u200bwhich gives rice. 49, b.

In the diagram with the switch shown in Fig. 49, and, repeated repetition of the process can be obtained simply, periodically throwing the switch from one position to another.

Radio engineering has for the same much more advanced and fast electric shift methods using circuits with electronic lamps. But even before the invention, the electronic lamps were invented a witty method of periodic repetition of the excitation of decaying oscillations in a circuit based on the use of spark charge. Due to the simplicity and clarity of this method, we will focus on it several more.

Fig. 51. Scheme of spark excitation of oscillations in the circuit

The oscillating circuit is broken by a small gap (spark gap 1), the ends of which are attached to the secondary winding of the increases transformer 2 (Fig. 51). The current from the transformer charges the capacitor 3 until the stress in the spark gap becomes equal to the voltage of the breakdown (see volume II, §93). At this point, a spark rank occurs in the spark gap, which closes the contour, since the column of strongly ionized gas in the spark channel spends the current almost as well as the metal. In such a closed circuit, electrical oscillations will arise, as described above. While the spark gap spends well, the secondary winding of the transformer is practically closed by spark-spin, so that all the voltage of the transformer falls on its secondary winding, the resistance of which is much more spark resistance. Consequently, with a well-conducted spark gap, the transformer practically does not cause the energy of the contour. Due to the fact that the contour has resistance, part of the oscillatory energy is spent on Jowleto heat, as well as processes in a spark, oscillations fucked and after a short time the amplitude of the current and voltage fall so much that the spark goes out. Then electrical oscillations are broken. From this point on, the transformer reappears the capacitor again until the breakdown occurs again, and the whole process will repeat (Fig. 52). Thus, the formation of sparks and its extinction play the role of an automatic switch that provides a repetition of the oscillatory process.

Fig. 52. Curve a) shows how changing high voltage On open secondary winding of the transformer. In those moments, when this tension reaches a breakdown voltage, the spark is sparking in the spark gap, the contour is closed, it turns out a flash of floating oscillations - curves b)