Electric current fluctuations occur according to the law. T

Topic 3. Electric oscillations. Alternating electric current. Main questions of the topic: 3. 1. 1. Free undamped electrical oscillations 3. 1. 2. Damped electrical oscillations 3. 1. 3. Forced electrical oscillations. Resonance 3. 1. 4. Alternating electric current.

Repetition Harmonic oscillations A - oscillation amplitude; ω - circular frequency (ωt + φ0) - oscillation phase; φ0 is the initial phase of oscillation. Differential equation of free undamped harmonic oscillations: The equation of a plane harmonic wave propagating along the X axis:

3. 1. Free undamped electrical oscillations An oscillating circuit is a circuit consisting of a capacitor and a coil. E is the electric field strength; H is the magnetic field strength; q is the charge; C is the capacitance of the capacitor; L is the inductance of the coil, I is the current in the circuit

- natural circular oscillation frequency Thomson's formula: (3) T - period of natural oscillations in the oscillatory circuit

Let's find the relationship between the amplitude values ​​of current and voltage: From Ohm's law: U=IR - wave resistance.

The energy of the electric field (the energy of a charged capacitor) at any time: The energy of the magnetic field (the energy of the inductor) at any time:

The maximum (amplitude) value of the energy of the magnetic field: - the maximum value of the energy of the electric field Total energy of the oscillatory circuit at any time: The total energy of the circuit is kept constant

Task 3. 1 An oscillatory circuit consists of a capacitor and an inductor. Determine the frequency of oscillations that occur in the circuit if the maximum current in the inductor is 1.2 A, the maximum potential difference across the capacitor plates is 1200 V, the total energy of the circuit is 1.1 m. J. Given: Im = 1.2 A UCm = 1200 In W \u003d 1.1 m. J \u003d 1.1 10 -3 J ν-?

Task In the oscillatory circuit, the capacitance increased by 8 times, and the inductance decreased by half. How will the period of natural oscillations of the circuit change? a) will decrease by 2 times; b) will increase by 2 times; c) will decrease by 4 times; d) will increase by 4 times.

(7)

(17)

Influence on oscillations the contour of the driving E.D.S., whose frequencies are different from ω0, will be the weaker, the "sharper" the resonance curve. The "sharpness" of the resonance curve is characterized by the relative width of this curve, equal to Δω/ω0, where Δω is the cycle difference. frequencies at I=Im/√ 2

Task 3. 2 The oscillatory circuit consists of a resistor with a resistance of 100 ohms, a capacitor with a capacity of 0.55 microns. Ф and coils with an inductance of 0.03 H. Determine the phase shift between the current through the circuit and the applied voltage if the frequency of the applied voltage is 1000 Hz. Given: R = 100 ohm C = 0.55 microns. Ф = 5.5 10 -7 Ф L = 0.03 H ν = 1000 Hz φ-?

1. Electromagnetic waves

2. Closed oscillatory circuit. Thomson's formula.

3. Open oscillatory circuit. Electromagnetic waves.

4. Scale of electromagnetic waves. Classification of frequency intervals adopted in medicine.

5. Impact on the human body with alternating electric and magnetic fields for therapeutic purposes.

1. According to Maxwell's theory, an alternating electric field is a set of alternating mutually perpendicular electric and magnetic fields moving in space at the speed of light

Where and are the relative permittivity and permeability of the medium.

The propagation of an electromagnetic field is accompanied by the transfer of electromagnetic energy.

All kinds of alternating currents serve as sources of an electromagnetic field (e / m radiation): alternating current in conductors, oscillatory motion of ions, electrons, and other charged particles, rotation of electrons in an atom around the nucleus, etc.

The electromagnetic field propagates in the form of a transverse electromagnetic wave, consisting of two waves that coincide in phase - electric and magnetic.

Length , period T, frequency and speed of wave propagation are related by the relation

The intensity of an electromagnetic wave or electromagnetic energy flux density is proportional to the square of the frequency of the waves.

The source of intense e / m waves should be high frequency alternating currents, which are called electrical oscillations. An oscillatory circuit is used as a generator of such oscillations.

2. The oscillatory circuit consists of a capacitor and a coil

.

First, the capacitor is charged. The field inside it is Е=Е m . In the last moment the capacitor starts to discharge. An increasing current will appear in the circuit, and a magnetic field H appears in the coil. As the capacitor discharges, its electric field weakens, and the magnetic field of the coil increases.

At time t 1, the capacitor is completely discharged. In this case, E=0, H=H m . Now all the energy of the circuit will be concentrated in the coil. After a quarter of the period, the capacitor will be recharged and the energy of the circuit will pass from the coil to the capacitor, and so on.

That. electrical oscillations with a period T occur in the circuit; during the first half of the period, the current flows in one direction, during the second half of the period - in the opposite direction.

Electric oscillations in the circuit are accompanied by periodic mutual transformations of the energies of the electric field of the capacitor and the magnetic field of the self-induction coil, just as the mechanical oscillations of a pendulum are accompanied by mutual transformations of the potential and kinetic energies of the pendulum.

The period of e / m oscillations in the circuit is determined by the Thomson formula

Where L is the inductance of the circuit, C is its capacitance. The oscillations in the circuit are damped. To implement continuous oscillations, it is necessary to compensate for losses in the circuit by recharging the capacitor with the help of a c / i device.

3. An open oscillatory circuit is a straight conductor with a spark gap in the middle, which has a small capacitance and inductance.

In this vibrator, the alternating electric field was no longer concentrated inside the capacitor, but surrounded the vibrator from the outside, which significantly increased the intensity of electromagnetic radiation.

The Hertz vibrator is an electric dipole with a variable moment.

The E/M radiation of the open vibrator 1 is recorded using the second vibrator 3, which has the same oscillation frequency as the radiating vibrator, i.e. tuned in resonance with the emitter and therefore called the resonator.

When electromagnetic waves reach the resonator, electrical oscillations occur in it, accompanied by a spark jumping through the spark gap.

Persistent electromagnetic oscillations are a source of continuous magnetic radiation.

4. It follows from Maxwell's theory that various electromagnetic waves, including light waves, have a common nature. In this regard, it is advisable to represent all kinds of electromagnetic waves in the form of a single scale.

The entire scale is conditionally divided into six ranges: radio waves (long, medium and short), infrared, visible, ultraviolet, x-ray and gamma radiation.

Radio waves are caused by alternating currents in conductors and electronic flows.

Infrared, visible, and ultraviolet radiation come from atoms, molecules, and fast charged particles.

X-ray radiation occurs during intra-atomic processes, gamma radiation is of nuclear origin.

Some ranges overlap because waves of the same length can be produced by different processes. So, the most short-wave ultraviolet radiation is blocked by long-wave X-rays.

In medicine, the following conditional division of electromagnetic oscillations into frequency ranges is accepted.

Often physiotherapeutic electronic equipment of low and audio frequency is called low-frequency. Electronic equipment of all other frequencies is called the generalizing concept of high-frequency.

Within these groups of devices, there is also an internal classification depending on their parameters and purpose.

5. Impact on the human body by an alternating magnetic field.

Eddy currents arise in massive conducting bodies in an alternating magnetic field. These currents can be used to heat biological tissues and organs. This method is called inductothermy.

With inductothermy, the amount of heat released in the tissues is proportional to the squares of the frequency and induction of the alternating magnetic field and inversely proportional to the resistivity. Therefore, tissues rich in blood vessels, such as muscles, will heat up more strongly than tissues with fat.

Exposure to an alternating electric field

In tissues in an alternating electric field, displacement currents and conduction currents arise. For this purpose, ultra-high frequency electric fields are used, so the corresponding physiotherapeutic method is called UHF therapy.

The amount of heat released in the body can be expressed as follows:

(1)

Here E is the electric field strength

l - the length of the object placed in the field

S - its section

His resistance

Its resistivity.

Dividing both parts (1) by the volume Sl of the body, we obtain the amount of heat released in 1 s in 1 m 3 of tissue:

Exposure to electromagnetic waves

The use of electromagnetic waves in the microwave range - microwave therapy (frequency 2375 MHz, \u003d 12.6 cm) and DCV therapy (frequency 460 MHz, \u003d 65.2 cm)

E/m waves have a thermal effect on biological objects. The E/M wave polarizes the molecules of matter and periodically reorients them as electric dipoles. In addition, the e / m wave affects the ions of biological systems and causes an alternating conduction current.

Thus, in a substance in an electromagnetic field, there are both displacement currents and conduction currents. All this leads to heating of the substance.

Displacement currents due to the reorientation of water molecules are of great importance. In this regard, the maximum absorption of microwave energy occurs in tissues such as muscles and blood, and less in bone and fatty hiccups, they are smaller and heat up.

Electromagnetic waves can affect biological objects by breaking hydrogen bonds and affecting the orientation of DNA and RNA macromolecules.

Considering the complex composition of tissues, it is conditionally considered that during microwave therapy, the penetration depth of electromagnetic waves is 3-5 cm from the surface, and with LCV therapy, up to 9 cm.

Centimeter e/m waves penetrate into muscles, skin, biological fluids up to 2 cm, into fat, bones - up to 10 cm.

This allows us to ignore the wave nature of the processes and describe them as electric. charges Q (in capacitive circuit elements) and currents I (in inductive and dissipative elements) in accordance with the continuity equation: I=±dQ/dt. In the case of a single oscillatory circuit, E. to. are described by the equation:

where L is self-induction, C is capacitance, R is resistance, ? - external emf.

Physical Encyclopedic Dictionary. - M.: Soviet Encyclopedia. . 1983 .

ELECTRICAL OSCILLATIONS

- electromagnetic oscillations in quasi-stationary circuits, the dimensions of which are small compared to the length of the el.-magnet. waves. This makes it possible not to take into account the wave nature of the processes and to describe them as fluctuations in electric current. charges (in capacitive circuit elements) and currents I(in inductive and dissipative elements) in accordance with the continuity equation: In the case of a single oscillatory circuit E. to. are described by the equation where L is inductance, C is capacitance, R-resistance, - variable external emf. M. A. Miller.

Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia. Editor-in-Chief A. M. Prokhorov. 1988 .

• ELECTRICAL STRENGTH

See what "ELECTRIC OSCILLATIONS" is in other dictionaries:

electrical vibrations- — [Ya.N. Luginsky, M.S. Fezi Zhilinskaya, Yu.S. Kabirov. English Russian Dictionary of Electrical Engineering and Power Industry, Moscow, 1999] Electrical engineering topics, basic concepts EN electric oscillations ... Technical Translator's Handbook

ELECTRICAL OSCILLATIONS- repeated changes in the strength of current, voltage and charge that occur in electrical (see) and are accompanied by corresponding changes in the magnetic and electric fields created by these changes in currents and charges in the environment ... ... Great Polytechnic Encyclopedia

electrical vibrations- elektriniai virpesiai statusas T sritis fizika atitikmenys: angl. electric oscillations vok. electrische Schwingungen, f rus. electrical vibrations, n pranc. oscillations electrics, f … Fizikos terminų žodynas

It has long been noted that if you wrap a steel needle with wire and discharge a Leyden jar through this wire, then the north pole is not always obtained at that end of the needle, where it could be expected in the direction of the discharge current and according to the rule ... Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron

Repeatedly repeated changes in voltage and current in electric. circuits, as well as electric tensions. and magn. fields in space near the conductors, forming an electric. chain. There are natural oscillations, forced oscillations and ... ... Big encyclopedic polytechnic dictionary

Electromagnetic oscillations in a system of conductors in the case when it is possible not to take into account electromagnetic fields in the surrounding space, but to consider only the movement of electric charges in conductors. This is usually possible in the so-called ...

VASCULATION- OSCILLATIONS, processes (in the most general sense) periodically changing their direction with time. These processes can be very diverse. If eg. hang a heavy ball on a steel coil spring, pull it back and then provide ... ... Big Medical Encyclopedia

Movements (changes in state) with varying degrees of repetition. With a pendulum, its deviations in one direction and the other from the vertical position are repeated. With K. of a spring pendulum of a load hanging on a spring, ... ... Great Soviet Encyclopedia

See Electrical Vibrations... Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron

Books

• Theoretical foundations of electrical engineering. Electrical circuits. Textbook, L. A. Bessonov. Traditional and new questions of the theory of linear and non-linear electrical circuits are considered. Traditional methods include methods for calculating currents and voltages at constant, sinusoidal, ...

The oscillation period of such a current is much longer than the propagation time, which means that the process will almost not change over time τ. Free oscillations in a circuit without active resistance Oscillatory circuit a circuit of inductance and capacitance. Let's find the oscillation equation.

Share work on social networks

If this work does not suit you, there is a list of similar works at the bottom of the page. You can also use the search button

Lecture

electrical vibrations

Plan

1. Quasi-stationary currents
2. Free oscillations in a circuit without active resistance
3. Alternating current
4. dipole radiation

1. Quasi-stationary currents

The electromagnetic field propagates at the speed of light.

l conductor length

Quasi-stationary current condition:

The oscillation period of such a current is much longer than the propagation time, which means that the process will hardly change over time τ.

Instantaneous values ​​of quasi-stationary currents obey Ohm's and Kirchhoff's laws.

2) Free oscillations in the circuit without active resistance

Oscillatory circuita circuit of inductance and capacitance.

Let's find the oscillation equation. We will consider the charging current of the capacitor positive.

Dividing both sides of the equation by L , we get

Let

Then the oscillation equation takes the form

The solution to such an equation is:

Thomson formula

Current is leading in phase U on π /2

1. Free damped vibrations

Any real circuit has active resistance, the energy is used for heating, the oscillations are damped.

At

Solution:

Where

The frequency of damped oscillations is less than the natural frequency

At R=0

Logarithmic damping decrement:

If damping is small

Quality factor:

1. Forced electrical vibrations

The voltage across the capacitance is out of phase with the current byπ /2, and the voltage across the inductance leads the current in phase byπ /2. The voltage across the resistance changes in phase with the current.

1. Alternating current

Electrical impedance (impedance)

Reactive inductive reactance

Reactive capacitance

AC power

RMS values ​​in AC circuit

with osφ - Power factor

1. dipole radiation

The simplest system emitting EMW is an electric dipole.

Dipole moment

r charge radius vector

l oscillation amplitude

Let

wave zone

Wave front spherical

Sections of the wavefront through the dipole meridians , through perpendiculars to the dipole axis parallels.

Dipole radiation power

The average radiation power of the dipole is proportional to the square of the amplitude of the electric moment of the dipole and the 4th power of the frequency.

a acceleration of an oscillating charge.

Most natural and artificial sources of electromagnetic radiation satisfy the condition

d radiation area size

Or

v average charge speed

Such a source of electromagnetic radiation Hertzian dipole

The range of distances to the Hertzian dipole is called the wave zone

Total average radiation intensity of the Hertzian dipole

Any charge moving with acceleration excites electromagnetic waves, and the radiation power is proportional to the square of the acceleration and the square of the charge

Other related works that may interest you.vshm>
6339.		MECHANICAL VIBRATIONS	48.84KB
	Oscillations are called processes of movement or change of state in varying degrees, repeating in time. Depending on the physical nature of the recurring process, the following are distinguished: - mechanical vibrations of pendulums of strings of machine parts and mechanisms of aircraft wing bridges...
5890.		ROTOR VIBRATIONS	2.8MB
	The position of the shaft section for different values ​​of the oscillation phase is shown in fig. The resonant increase in the oscillation amplitude will continue until all the energy of the oscillations is spent on overcoming the friction forces or until the shaft is destroyed.
21709.		ULTRASONIC OSCILLATIONS AND TRANSDUCERS	34.95KB
	They can be used to convert electrical energy into mechanical energy and vice versa. Substances with a strongly pronounced relationship between the elastic and electrical or magnetic states are used as materials for transducers. above the threshold of hearing for the human ear, then such vibrations are called ultrasonic ultrasonic vibrations. To obtain ultrasonic vibrations, piezoelectric magnetostrictive electromagnetic acoustic EMA and other transducers are used.
15921.		Power stations	4.08MB
	The power system is understood as a set of power plants of electrical and thermal networks interconnected and connected by a common mode in a continuous process of producing the conversion and distribution of electrical energy and heat with the general management of this mode ...
2354.		ELECTRICAL PROPERTIES OF METALLIC ALLOYS	485.07KB
	The advantages of copper provides it with wide application as a conductor material as follows: Low resistivity. Intensive oxidation of copper occurs only at elevated temperatures. Receiving copper. The dependence of the oxidation rate on temperature for iron tungsten copper chromium nickel in air After a series of smelting of ore and roasting with intense blowing, copper intended for electrical purposes is necessarily subjected to electrolytic cleaning of the cathode plates obtained after electrolysis ...
6601.			33.81KB
	The phenomenon of the stroboscopic effect is the use of lamp switching circuits in such a way that neighboring lamps receive voltage with a phase shift m. The protective angle of the lamp is the angle enclosed between the horizontal passing through the filament of the lamp and the line connecting the extreme point of the filament with the opposite edge of the reflector. where h is the distance from the filament of the lamp to the level of the lamp outlet...
5773.		Hybrid power plants on the territory of Sakhalin Island	265.76KB
	The main types of renewable natural energy resources of the VPER of the Sakhalin Region are geothermal wind and tidal. The presence of significant wind and tidal energy resources is due to the uniqueness of the island location of the region, and the presence of thermal water and steam hydrothermal resources are promising for the development of active volcanic ...
2093.		ELECTRICAL CHARACTERISTICS OF CIRCUITS OF CABLE COMMUNICATION LINES	90.45KB
	The equivalent circuit of the connection circuit R and G cause energy losses: the first heat loss in conductors and other metal parts screen shell armor second insulation loss. The active resistance of the circuit R is the sum of the resistance of the conductors of the circuit itself and the additional resistance due to losses in the surrounding metal parts of the cable, adjacent conductors, screen, shell, armor. When calculating active resistance, they usually sum up ...
2092.		ELECTRICAL CHARACTERISTICS OF FIBER-OPTIC COMMUNICATION CABLES	60.95KB
	In single-mode optical fibers, the core diameter is commensurate with the wavelength d^λ and only one type of wave mode is transmitted through it. In multimode fibers, the core diameter is larger than the wavelength d λ and a large number of waves propagate along it. Information is transmitted through a dielectric light guide in the form of an electromagnetic wave. The direction of the wave is due to reflections from the boundary with different values ​​of the refractive index at the core and cladding n1 and n2 of the fiber.
11989.		Special instant electric detonators and special water-resistant blasting caps with various degrees of delay	17.47KB
	Pyrotechnic moderators for SKD are developed on the basis of redox reactions with high combustion stability, the standard deviation is less than 15 of the total combustion time even after long-term storage in an unpressurized state in difficult climatic conditions. Two compositions have been developed: with a burning rate of 0004÷004 m s and a deceleration time of up to 10 s, the size of the retarding element is up to 50 mm; with a burning rate of 004 ​​÷ 002 m s, it has increased igniting properties.

Lecture plan

1. Oscillatory contours. Quasi-stationary currents.

2. Own electrical oscillations.

2.1. Own undamped oscillations.

2.2. Natural damped vibrations.

3. Forced electrical oscillations.

3.1. Resistance in an alternating current circuit.

3.2. Capacitance in the AC circuit.

3.3. Inductance in an alternating current circuit.

3.4. Forced vibrations. Resonance.

3.5. Cosine phi problem.

1. oscillatory contours. Quasi-stationary currents.

Fluctuations in electrical quantities - charge, voltage, current - can be observed in a circuit consisting of series-connected resistances ( R), capacities ( C) and inductors ( L) (Fig. 11.1).

Rice. 11.1.

At switch position 1 TO, the capacitor is charged from the source.

If we now switch it to position 2, then in the circuit RLC there will be fluctuations with a period T similar to the vibrations of a load on a spring.

Oscillations that occur only due to the internal energy resources of the system are called own. Initially, energy was imparted to the capacitor and localized in an electrostatic field. When the capacitor closes to the coil, a discharge current appears in the circuit, and a magnetic field appears in the coil. emf The self-induction of the coil will prevent the instantaneous discharge of the capacitor. After a quarter period, the capacitor will be completely discharged, but the current will continue to flow, supported by the electromotive force of self-induction. To the moment this emf recharge the capacitor. The current in the circuit and the magnetic field will decrease to zero, the charge on the capacitor plates will reach its maximum value.

These fluctuations in electrical quantities in the circuit will occur indefinitely if the resistance of the circuit R= 0. Such a process is called own undamped oscillations. We observed similar oscillations in a mechanical oscillatory system when there is no resistance force in it. If the resistance of the resistor R(resistance force in a mechanical oscillator) cannot be neglected, then in such systems there will be own damped oscillations.

On the graphs of Fig. 11.2. the dependences of the capacitor charge on time are presented in the case of undamped ( A) and decaying ( b,V,G) fluctuations. The nature of the damped oscillations changes with an increase in the resistance of the resistor R. When the resistance exceeds a certain critical meaning R k, there are no oscillations in the system. There is a monotonous periodic capacitor discharge (Fig. 11.2. G.).

Rice. 11.2.

Before proceeding to the mathematical analysis of oscillatory processes, we will make one important remark. When compiling the oscillation equations, we will use Kirchhoff's rules (Ohm's laws), which are valid, strictly speaking, for direct current. But in oscillatory systems, the current changes with time. However, in this case, you can use these laws for the instantaneous value of the current, if the rate of current change is not too high. Such currents are called quasi-stationary (“quasi” (lat.) - as if). But what does the speed "too" or "not too" mean? If the current changes in some section of the circuit, then the impulse of this change will reach the farthest point of the circuit after a while:

.

Here l is the characteristic size of the contour, and With is the speed of light at which the signal propagates in the circuit.

The rate of change of the current is considered not too high, and the current is quasi-stationary, if:

,

Where T- the period of change, that is, the characteristic time of the oscillatory process.

For example, for a chain 3 m long, the signal delay will be ==
= 10 -8 s. That is, the alternating current in this circuit can be considered quasi-stationary if its period is more than10 -6 s, which corresponds to the frequency= 10 6 Hz. Thus, for frequencies 010 6 Hz in the circuit under consideration, Kirchhoff's rules for instantaneous values ​​of current and voltage can be used.