What is electrical resonance? Methodological development of an open lesson in physics "Alternating current on a real section of the circuit

If the frequency of natural oscillations of the circuit coincides with the frequency of change external force, then the phenomenon of resonance occurs. In an electric oscillatory circuit, the role of an external periodic force is played by a generator, which ensures a change in the electromotive force according to harmonic law:

whereas natural electromagnetic oscillations occur in the circuit with a frequency ω o. if the active resistance of the circuit is small, then the natural frequency of oscillations is determined by the formula:

The current strength during forced oscillations (or the voltage on the capacitor) should reach its maximum value when the frequency of the external emf (1) is equal to the natural frequency of the oscillatory circuit:

Resonance in an electrical oscillatory circuit is the phenomenon of a sharp increase in amplitude forced oscillations current strength (voltage on the capacitor, inductor) when the natural frequency of the circuit oscillations and the external emf coincide. Such changes during resonance can reach multiples of hundreds of times.

In a real oscillatory circuit, the establishment of amplitude oscillations in the circuit does not occur immediately. The maximum at resonance is higher and sharper, the lower the active resistance and the greater the inductance of the circuit: . Active resistance R plays a major role in the circuit. After all, it is the presence of this resistance that leads to the conversion of energy electric field in internal energy conductor (the conductor heats up). This suggests that resonance in the electrical oscillating circuit should be clearly expressed at low active resistance. In this case, the establishment of amplitude oscillations occurs gradually. Thus, the amplitude of current fluctuations increases until the energy released during the period on the resistor is equal to the energy entering the circuit during this time. Thus, at R → 0, the resonant value of the current increases sharply. Whereas with increasing active resistance maximum value current decreases, and talk about resonance when large values R doesn't make sense.

Rice. 2. Dependence of the voltage amplitude on the capacitor on the emf frequency:

1 – resonance curve with circuit resistance R1;
2 – resonance curve with circuit resistance R2;

3 – resonance curve with circuit resistance R3

The phenomenon of electrical resonance is widely used in radio communications. Radio waves from various transmitting stations excite alternating currents of different frequencies in the radio receiver antenna, since each transmitting radio station operates at its own frequency.
Inductively coupled to the antenna oscillatory circuit. Due to electromagnetic induction in the contour coil, alternating emfs of the corresponding frequencies and forced oscillations of the current strength of the same frequencies arise. But only at resonance will the fluctuations in current in the circuit and voltage in the circuit be significant. Therefore, of all the frequencies excited in the antenna, the circuit selects only oscillations whose frequency is equal to the natural frequency of the circuit. Tuning the circuit to the desired frequency ω0 is usually done by changing the capacitance of the capacitor.

In some cases, resonance in electrical circuit may cause harm. So, if the circuit is not designed to operate under resonance conditions, then the occurrence of resonance will lead to an accident: high voltages will lead to insulation breakdown. Accidents of this kind often happened in the 19th century, when people had a poor understanding of the laws of electrical vibrations and did not know how to calculate electrical circuits.

Lesson type: lesson on learning new material and initial consolidation.

Demonstrations: the phenomenon of electrical resonance.

Educational and methodological support: video presentations of educational material No., .

Technical means training:

• function generator FG-100;
• oscilloscope S1-83;
• layout of the oscillatory circuit;
• computer;
• multimedia projector;
• screen.

PROGRESS OF THE LESSON

I. Introduction: creating motivation.

“Close your eyes, free your ears, strain your hearing, and from the gentlest breath to the wildest noise, from the simplest sound to the highest harmony, from the most powerful passionate cry to the most meek words reason - all this is the speech of nature, which reveals its being, its power, its life...

She gives a wondrous spectacle; whether she sees it herself, we don’t know, but she gives it to us, and we, unnoticed, look around the corner... She appears to everyone in a special way. It hides under a thousand names and titles, and is still the same. She brought me into life, and she will take me away. I trust her. Let her do what she wants with me...” Johann Wolfgang Goethe

Physics is the science of nature, which has lifted the veil and unraveled more mysteries of the universe than any other science. We are children of nature and must be able to talk to it, understand it and take care of it.

In addition, we must not only use everything that nature gives us, admire it, but try to comprehend it and see what is hidden from us behind external images phenomena. And this is only possible with the help of a wonderful science - physics.

Only physics allows us to notice that in “natural phenomena there are forms and rhythms that are inaccessible to the eye of the contemplator, but open to the eye of the analyst. We call these forms and rhythms physical laws” (R. Feynman).

II. Repetition of previously studied material.

In past lessons, we studied in detail the processes that occur in a section of a circuit with one of the possible resistances.

Today in class we must study the main features of alternating electric current on a real section of the circuit and reveal the physical essence of processes, occurring during electrical resonance.

So let's remember.

Frontal survey

1. What are electromagnetic oscillations called?
2. What electromagnetic oscillations are called forced?
3. Give the definition of alternating electric current.
4. What is an AC circuit with active resistance?
5. Name the main features of alternating electric current in a section of a circuit with active resistance.
6. Define the effective value of alternating current.
7. What is an AC circuit with capacitance?
8. According to what laws do the instantaneous values ​​of voltage and current change in such a circuit and what is the phase shift between them?
9. What quantities does capacitive reactance depend on?
10. How is Ohm's law written for amplitude and effective values ​​of current and voltage?
11. What is an AC circuit with inductive reactance?
12. Name the main features of alternating electric current in a section of a circuit with capacitance.

You are invited to once again recall the previously studied material and watch its video presentation.

III. Learning new material.

In the workbooks we write down the date, type of work, topic of the lesson and issues discussed.

Issues covered:

• Ohm's law for an alternating current electrical circuit.
• Resonance in an AC circuit.
• Application and consideration of resonance in technology.

In fact, the section of the circuit through which the variable flows electric current, has the properties of active, capacitive and inductive resistance, although to varying degrees. In some cases, one or another resistance can be neglected, depending on the problem being solved.

Let's consider the processes occurring in a real section of the circuit, which is a series connection of a resistor, capacitor and inductor.

<Рисунок 1>

The relationships between physical quantities for such a region are much more complicated, so let us turn to the main results.

Let us describe the passage of alternating electric current through such a section of the circuit.

The voltage supplied by the external generator at any time is equal to the sum of the voltage drops in different sections of the circuit:

Let the voltage in the circuit change according to the harmonic law:

Since the voltage in each section is different, then in different sections of the circuit there is a phase shift between fluctuations in current and voltage. Therefore, the current strength in the circuit will change according to the law:

The amplitude of the applied voltage is determined in the vector diagram as the geometric sum of the amplitudes of the voltage drops across the active resistance, inductor and capacitor.

Complete electrical resistance AC circuits:

Magnitude

called reactance or reactance.

Ohm's law for an alternating current circuit will be written as:

The formulation of Ohm's law for an alternating current circuit:

The amplitude of the alternating current is directly proportional to the amplitude of the voltage and inversely proportional to the impedance of the circuit.

Ohm's law for effective values ​​of current and voltage:

The phase shift between current and voltage fluctuations can be determined from a vector diagram:

New physical phenomena occur on a real section of the circuit. One of the important ones is electrical resonance.

The phenomenon of electrical resonance was first described by the eminent English physicist James Clerk Maxwell in 1868.

From formula (7) follows the condition under which electrical resonance occurs: the current strength is maximum at minimum value total resistance of the circuit, i.e. When:

In this case:

• the circuit has only active resistance;
• (U L) res. = (U C) res.
(in absolute value), but opposite in phase.

From (10) it follows that electrical resonance occurs when the frequency of the driving voltage is equal to the natural frequency of the electrical circuit:

The amplitude of steady-state oscillations of current strength at resonance is determined by:

With electrical resonance, the circuit actually has only active resistance, i.e. there is no phase shift between current and voltage, although there is this phase shift before and after resonance.

Let's analyze formula (12):

<Рисунок 3>

Thus: resonance in an alternating current electrical circuit is the phenomenon of a sharp increase in the amplitude of forced oscillations of current in an oscillatory circuit when the frequency of the external alternating voltage coincides with the frequency of free continuous oscillations in the circuit.

Let's see how in practice we can obtain the phenomenon of voltage resonance in an alternating current electrical circuit when its elements are connected in series.

Demonstration experiment.

From the functional generator, we supply an alternating sinusoidal voltage, the frequency of which can be changed, to the input of a real oscillatory circuit. We connect an oscilloscope to the output of the oscillatory circuit, which converts the electrical signal into visible image. How will the oscillatory circuit react to a change in the frequency of the driving signal?

We change the frequency of the input signal towards increase. We observe: an increase in the amplitude of oscillations of the output signal on the oscilloscope screen.

With a further increase in the frequency of the input signal, a decrease in the amplitude of the output signal is observed. The moment when the amplitude of the output signal oscillations was maximum corresponds to the phenomenon of electrical voltage resonance.

Let us study in practice how the oscillatory circuit reacts to changes in the capacitance of the capacitor and the inductance of the coil, i.e. how the resonant frequency changes.

Let's increase the capacitance of the capacitor.

Let's increase the inductance of the coil. We observe: the resonant frequency has decreased.

Let us confirm in practice that: (U L) res. = (U C) res.

To do this, it is enough to compare the amplitudes of the output signal taken from the capacitor and the inductor.

The phenomenon of electrical resonance is widely used in radio communications in circuits for tuning radio receivers (to isolate a signal of the required frequency), amplifiers, and high-frequency oscillation generators. The operation of many measuring instruments is based on the phenomenon of resonance. For example, a resonant wavemeter is used to measure frequency and is a core part of standard signal generators.

It must be remembered that the phenomenon of electrical resonance must be taken into account when calculating the insulation of electrical circuits.

The harmful effects of resonance occur when excessively high currents or voltages occur in a circuit not designed to operate under resonance conditions.

Sharp increases in current can lead to disruption of the insulation of the inductor turns, and high voltages can lead to breakdown of capacitors.

IV. Consolidation of the studied material.

Questions for consolidation

1. What was learned in class today?
2. How would you formulate the topic of today's lesson?
3. What new concepts were introduced in the lesson?
4. What is the actual section of the circuit?
5. What new formulas and laws have you studied?
6. With what new physical phenomenon Have you met?
7. Define electrical resonance.

We present to your attention the main features of alternating electric current in a series electrical circuit. Let's look at the screen.

V. Summing up the lesson.

We are finishing our lesson. Let us trace the logic of our study of educational material.

Where did we start?

1. Previously studied material was repeated.
2. Highlighted the main theoretical principles new topic.
3. These provisions were confirmed by a demonstration experiment.
4. Found practical application electrical resonance phenomena.
5. Systematized and consolidated the acquired knowledge.

Reflection
(Cards with questions are on each student’s desk.)

1. What interesting things did you remember during the lesson?
2. What did you find useful?
3. What was the biggest challenge?
4. How do you evaluate the knowledge gained today (deep, conscious; to be realized; unconscious)?

Several students read out their answers. The teacher sums up the lesson and marks are announced to the students.

VI. Homework.

• §35. Textbook “Physics-11”. Myakishev G.Ya., Bukhovtsev B.B.
• No. 981, 982, 983. Physics. Problem book for grades 10-11. Rymkevich A.P.

Final words from the teacher:

We will conclude our lesson with the sayings of the ancient Chinese philosopher, follower of Confucius - Xun Tzu:

“Without climbing high mountain, you don’t know the height of the sky. Without looking into a deep gorge in the mountains, you will not know the thickness of the earth. Without hearing the behests of your ancestors, you will not recognize the greatness of learning.”

“You can’t stop learning.”

And indeed, there is still so much unknown and unsolved around us. What is the field of activity for skillful hands, inquisitive mind, brave and inquisitive nature! And the “great ocean of truth” still spreads out before us, completely unsolved, mysterious, magical and alluring.

I thank everyone for the lesson. Goodbye.

Literature

1. Myakishev G.Ya. Physics: textbook. for 11th grade general education institutions / G.Ya. Myakishev, B.B. Bukhovtsev. – M.: Education, 2005, p. 102-105.
2. Glazunov A.T., Kabardin O.F., Malinin A.N. etc.; Ed. Pinsky A.A., Kabardina O.F. Physics: Textbook. for 11th grade with depth studying physics. – M.: Education, 2005, p. 32-34, 39-41.
3. Disc “ Open Physics”, version 2.5, part 2. Edited by MIPT professor S.M. Kozel. Physikon LLC, 2002.
4. Comp. Kondrashov A.P., Komarova I.I. Great thoughts from great people. – M.: RIPOL classic, 2007, p. 48.

Knowledge of physics and the theory of this science is directly related to the conduct household, repair, construction and mechanical engineering. We propose to consider what resonance of currents and voltages in a series RLC circuit is, what the main condition for its formation is, as well as the calculation.

What is resonance?

Definition of the phenomenon by TOE: electrical resonance occurs in an electrical circuit at a certain resonant frequency, when some parts of the resistance or conductivity of the circuit elements cancel each other. In some circuits this occurs when the impedance between the input and output of the circuit is almost equal to zero, and the signal transmission function is close to unity. In this case, the quality factor of this circuit is very important.

Signs of resonance:

1. The components of the reactive branches of the current are equal to each other IPC = IPL, antiphase is formed only when the net active energy at the input is equal;
2. The current in individual branches exceeds the entire current of a particular circuit, while the branches are in phase.

In other words, resonance in an AC circuit implies a special frequency, and is determined by the values ​​of resistance, capacitance and inductance. There are two types of current resonance:

1. Consistent;
2. Parallel.

For series resonance, the condition is simple and is characterized by minimal resistance and zero phase, it is used in reactive circuits, and it is also used in branched circuits. Parallel resonance or the concept of an RLC circuit occurs when the inductive and capacitive inputs are equal in magnitude but cancel each other out since they are at an angle of 180 degrees from each other. This connection must be constantly equal to the specified value. It has received wider practical application. The sharp minimum impedance that it exhibits is beneficial for many electrical applications. household appliances. The sharpness of the minimum depends on the resistance value.

An RLC circuit (or circuit) is electrical diagram, which consists of a resistor, inductor, and capacitor connected in series or parallel. The RLC parallel oscillating circuit gets its name from the abbreviation physical quantities, representing resistance, inductance and capacitance, respectively. The circuit forms harmonic oscillator for current. Any oscillation of the current induced in the circuit fades over time if the movement of the directed particles is stopped by the source. This resistor effect is called attenuation. The presence of resistance also reduces the peak resonant frequency. Some resistance is unavoidable in real circuits, even if a resistor is not included in the circuit.

Application

Almost all power electrical engineering uses just such an oscillating circuit, say, a power transformer. The circuit is also necessary for setting up the operation of a TV, capacitive generator, welding machine, radio receiver; it is used by the “matching” technology of television broadcast antennas, where you need to select a narrow frequency range of some of the waves used. The RLC circuit can be used as a band-pass filter, notch filter, for low-pass or high-pass distribution sensors.

Resonance is even used in aesthetic medicine (microcurrent therapy) and bioresonance diagnostics.

Principle of current resonance

We can make a resonant or oscillating circuit at its natural frequency, say, to power a capacitor, as the following diagram demonstrates:

The switch will be responsible for the direction of vibration.

The capacitor stores all the current at the moment when time = 0. Oscillations in the circuit are measured using ammeters.

Directed particles move in right side. The inductor receives current from the capacitor.

When the polarity of the circuit returns to its original form, the current returns to the heat exchanger.

Now the directed energy goes back into the capacitor, and the circle repeats again.

In real mixed circuit circuits there is always some resistance which causes the amplitude of the directed particles to grow smaller with each circle. After several changes in the polarity of the plates, the current drops to 0. This process is called a damped sine wave signal. How quickly this process occurs depends on the resistance in the circuit. But the resistance does not change the frequency of the sine wave. If the resistance is high enough, the current will not fluctuate at all.

The AC designation means that the energy leaving the power supply oscillates at a specific frequency. An increase in resistance helps to reduce the maximum size of the current amplitude, but this does not lead to a change in the resonance frequency. But an eddy current process can form. After its occurrence, network interruptions are possible.

Resonant circuit calculation

It should be noted that this phenomenon requires very careful calculation, especially if parallel connection. In order to avoid interference in technology, you need to use various formulas. They will be useful to you for solving any problem in physics from the corresponding section.

It is very important to know the power value in the circuit. The average power dissipated in a resonant circuit can be expressed in terms of rms voltage and current as follows:

R av = I 2 contact * R = (V 2 contact / Z 2) * R.

At the same time, remember that the power factor at resonance is cos φ = 1

The resonance formula itself has the following form:

ω 0 = 1 / √L*C

Zero impedance at resonance is determined using the following formula:

F res = 1 / 2π √L*C

The resonant frequency of oscillation can be approximated as follows:

F = 1/2 r (LC) 0.5

Where: F = frequency

L = inductance

C = capacity

Generally, a circuit will not oscillate unless the resistance (R) is low enough to satisfy the following requirements:

R = 2 (L/C) 0.5

To obtain accurate data, you should try not to round the obtained values ​​due to calculations. Many physicists recommend using a method called vector diagram active currents. With proper calculation and configuration of devices, you will get good savings in alternating current.

>> Resonance in an electrical circuit

§ 35 RESONANCE IN AN ELECTRIC CIRCUIT

When studying forced mechanical vibrations, we became familiar with the phenomenon resonance. Resonance is observed when the natural frequency of oscillations of the system coincides with the frequency of change of the external force. If the friction is small, then the amplitude of the steady-state forced oscillations at resonance increases sharply. The coincidence of the form of equations for describing mechanical and electromagnetic oscillations (allows us to draw a conclusion about the possibility of resonance also in an electrical circuit, if this circuit is an oscillatory circuit with a certain natural frequency of oscillations.

At mechanical vibrations resonance is clearly expressed at low values ​​of the friction coefficient. In an electrical circuit, the role of the friction coefficient is played by its active resistance R. After all, it is the presence of this resistance in the circuit that leads to the conversion of current energy into the internal energy of the conductor (the conductor heats up). Therefore, resonance in an electrical oscillatory circuit should be clearly expressed at low active resistance R.

You and I already know that if the active resistance is small, then the natural cyclic frequency of oscillations in the circuit is determined by the formula

When forced electromagnetic vibrations resonance possible - sharp increase amplitudes of current and voltage fluctuations when the frequency of the external alternating voltage coincides with the natural frequency of oscillations. All radio communications are based on the phenomenon of resonance.

1. Can the amplitude of the current at resonance exceed the strength DC in a circuit with the same active resistance and constant voltage, equal to the amplitude AC voltage!
2. What is the phase difference between the oscillations of current and voltage during resonance!
3. Under what condition are the resonant properties of the circuit most clearly expressed!

Myakishev G. Ya., Physics. 11th grade: educational. for general education institutions: basic and profile. levels / G. Ya. Myakishev, B. V. Bukhovtsev, V. M. Charugin; edited by V. I. Nikolaeva, N. A. Parfentieva. - 17th ed., revised. and additional - M.: Education, 2008. - 399 p.: ill.

Books and textbooks according to the calendar plan for 11th grade physics download, help for schoolchildren online

About Electrical Resonance

The effects generated by resonance are increasingly being noticed by engineers and are becoming increasingly important when working with any AC equipment. Therefore, a few remarks need to be made about these effects. It is clear that if we manage to practically use the effects of electrical resonance when operating electrical appliances, the return wire, of course, will become useless, since electrical vibrations can be transmitted with one wire just as well as with two. This means that you first need to answer the question: “Is it possible to produce such effects?” Theory and experiments show that in nature this is impossible, since as the oscillations increase, the losses in the oscillating body and its environment quickly increase and necessarily stop the oscillations, which otherwise could grow indefinitely. It is a great success that resonance cannot be obtained in its pure form, because if it were possible, it would be difficult to predict what dangers would await the poor experimenter. But before to a certain extent It is possible to obtain resonance, and the degree of its manifestation is limited by the imperfection of the conductor, insufficient elasticity of the medium, or, generally speaking, frictional losses. The smaller these losses, the more impressive his manifestations. The same thing happens with mechanical vibrations. A thick metal bar can vibrate under the influence of drops of water falling on it at a certain interval; and in the case of glass, which is even more elastic, the manifestations of resonance are even more significant, because a glass goblet can be broken if you sing a note of a certain tone into it. The stronger the electrical resonance is less resistance section of the circuit and the better the insulating properties of the dielectric. When discharging a Leyden jar through a thick stranded wire with thin cores, these requirements are satisfied in the best possible way, and the resonance manifests itself most prominently. This does not happen, however, in dynamos, transformer circuits, or in general in commercial devices, where the presence of a core makes resonance difficult or impossible. As for the Leyden jars, with which the effects of resonance are often demonstrated, I would say that they are often attributed to the action of resonance, and not a consequence of it, for in this case it is very easy to make a mistake. This can be convincingly illustrated by the following experiment. Take for example two insulated metal plates or two balls A and B, place it on a specific location long distance from each other and charge them using a friction machine or electrophore generator to such a potential that even a slight change in it causes a breakdown of the air cushion or insulation between the bodies. This can be easily achieved by preliminary attempts. Now, if another plate is attached to an insulating handle and connected to one of the terminals of the secondary winding of the inductor high voltage, which is powered by a generator (preferably high-frequency), - bring it to one of the charged bodies A or IN, and closer to one of them, a discharge will certainly occur between them; at least it will happen if the plate potential is high enough. This phenomenon is easily explained by the fact that the applied plate acts inductively on the charged objects A and B, causing a spark between them. When this spark occurs, the charges that were previously transferred to the objects must be lost as a connection is established between them through the formed arc. So, this arc is formed regardless of whether there is resonance or not. But even if a spark is not formed, there is still an emf between the objects when the plate is brought up; therefore, the approach of the plate, even if it does not actually cause it, will, in any case, have a tendency to break down the gap due to inductive action. Instead of plates or balls A and B we can just as easily take the plates of a Leyden jar, and instead of a machine - preferably a high-frequency generator, since it is better suited for carrying out an experiment or for justifying it - we can take another Leyden jar or several. When such banks are discharged through a low resistance circuit, very high frequency currents pass through it. The outer plate can now be connected to one of the plates of the second can, and when it is brought nearer to the first can, previously charged to a high potential by means of an electrophoric generator, the same result is obtained as before, and the first can is discharged after a narrow interval when the second jar is affected. But both cans do not need to be brought closer to a distance closer than the lowest bass note in relation to the squeak of a mosquito, since small sparks will already appear in the gap, or at least the air in the gap will be significantly tense due to the resulting induction emf at the moment when one of the cans begins to discharge. Another mistake may have been made similar properties. If the circuits of two cans are installed parallel and close to each other, and the experimenter discharges one of them with the help of the second, and after adding a twisted wire to one of the circuits the experiment fails, the conclusion that the circuits are not tuned will be far from the truth. Since these circuits work like a capacitor, and adding turns of wire is equivalent to shorting it at the point where the turns are turned on with a small capacitor, and it, in turn, prevents breakdown from occurring, reducing the emf acting in the spark gap. Many other comments can be made, but in order not to go deeper into a discussion that is far from our subject, with your permission, they will not be made; these are made only in order to warn the unsuspecting researcher so that he does not form an incorrect opinion about his abilities when he sees that each of his experiments is successful; These remarks in no way claim to be new in the eyes of experienced experimenters.

To obtain reliable results when observing resonance, it is desirable, and indeed necessary, to use a generator that supplies harmonic vibrations, since with a discharge current the observational results cannot always be trusted, since many phenomena that depend on the rate of change can be obtained at different frequencies. Even when using such a generator, mistakes can be made. When the circuit is connected to the generator, we have infinitely large number values ​​of capacitance and self-induction, which in various proportions meet the conditions of resonance. As in mechanics it can be infinite set tuning forks that respond to a note of a certain tone, or loaded springs that have a certain amplitude of vibration. But resonance can definitely be achieved when the movement occurs with the greatest freedom. So, in mechanics, when we are talking about vibrations in an ordinary medium, that is, in the air, big difference no, does one tuning fork have a larger size than the other, since the losses in the air are negligible. You can, of course, place a tuning fork in a vacuum vessel and, thus minimizing losses from friction with air, achieve the greatest resonance. And yet the difference will be small. But it will be huge if the tuning fork is placed in mercury. When electrical vibrations occur, it is very important to ensure greatest freedom movements. The quantity of resonance, otherwise under the same conditions, depends on the amount of electricity actuated, or on the strength of the current moving in the circuit. But the circuit resists the passage of current due to its impedance and therefore, to get the best result, the resistance must be kept to a minimum. It is impossible to get rid of it completely, but it is partially possible. When the pulse frequency is very high, the flow of current is practically determined by self-induction. Self-induction can be overcome by connecting it to a capacitance. If the relationship between them is such that they cancel each other, that is, they have such values ​​that they satisfy the resonance conditions, and flows through the external circuit greatest number electricity we have best result. It is easiest and most reliable when the capacitor is connected in series with the inductance. Of course, it is clear that in such combinations, at a certain frequency, and taking into account only the basic vibrations, we will have best values when the capacitor is connected in parallel with the self-induction coil, and there will be more such values ​​than when connected in series. But the choice is determined by the requirements of practice. IN the latter case When conducting an experiment, you can take a small coil and a large capacity or a large coil and a small capacity, but the latter is more preferable, since it is inconvenient to adjust a large capacity in small steps. If you take a coil with a very high self-inductance, then the critical capacitance drops to a very small value, and the capacity of the coil itself may be sufficient. It is not difficult, with the help of some devices, to wind a coil that will lower the impedance to an ohmic resistance and for each coil, of course, there is a frequency at which maximum current flows through it. Maintaining the relationship between self-inductance, capacitance and frequency becomes especially important when operating AC devices, such as transformers or motors, since with experimental setup of parts of the equipment, the use of an expensive capacitor becomes unnecessary. So, under normal conditions, current can be passed through the winding of an AC motor the required strength with low emf and completely get rid of false currents, and the larger the motor, the easier it is practically to do this, but for this you need to use currents of high potential and frequency.

Figure 20 I shows the circuit that was used to study the phenomenon of resonance using a high-frequency generator. Cf- This is a multi-turn coil that is divided into small sections for ease of adjustment. The final adjustment was made using a few thin iron wires (although this is not always desirable) or using a closed secondary winding. Coil With one end closed to a wire L, leading to generator G, and the other to one of the capacitor plates SS, and its plate is connected to an even larger plate R. In this way, both capacitance and inductance were adjusted to the frequency of the dynamo.

As for increasing the potential through resonant action, theoretically of course, it can rise to any value, since it depends on inductance and resistance, and these quantities can have any value. But in practice the magnitude is limited, and in addition there are other factors. You can start with, say, 1,000 volts and increase the emf by 50 times, but you cannot start with 100,000 volts and increase this figure by 10 times, since the losses are environment high, especially at high frequencies. It should be possible, for example, to start with two volts in the high or low frequency circuit of a dynamo and raise the emf several hundred times. Thus, coils of the proper dimensions can be connected at one end to the supply wire of a low emf machine, and although the circuit of the machine will not be closed in the usual sense of the term, it may burn out if we get the desired resonance. I was not able to obtain and was not able to observe such a potential jump with currents received from a dynamo. It is possible or even probable that with currents received from machines containing an iron core, the disturbing effect of the latter is the reason that the theoretically existing possibilities are not realized in practice. But if so, then I attribute this solely to the phase lag and losses from Foucault currents in the core. Usually it was necessary to work up when the emf was low, and an ordinary coil was used, but sometimes it was convenient to use the circuit shown in Figure 20 P.B in this case coil C is divided into many sections, some of which serve as the primary winding. Thus, both the primary and secondary windings are configurable. One end of the coil is connected to a wire L, going to the alternator, and the other wire L connected to the middle part of the coil. Such a coil, with adjustable primary and secondary windings, can also be convenient during experiments with discharges. When true resonance is achieved, the peak of the wave must, of course, be at the free end of the coil, or, for example, at the terminal of a fluorescent lamp IN. This can be easily confirmed by measuring the potential at the end of the wire w near the coil.

In connection with the manifestations of resonance and the problem of transmitting energy through one wire, which was mentioned earlier, I would like to say a few words about a subject that constantly interests me and which concerns the well-being of all people. I mean the transmission of clear signals, and perhaps energy, to any distance without the help of wires. Every day I become convinced of the reality of such a plan; and although I am fully aware that the vast majority of scientists will not believe that such a result can be achieved in practice in short term, I still think that the amount of work in this area indicates that it is necessary to encourage research and experimentation in this direction. My conviction has become so strong that I no longer regard this method of transmitting energy or intelligent signals as merely theoretically possible, but as a serious engineering problem that must one day be solved. The idea of ​​transmitting information wirelessly is the result latest research in the field of electricity. Some enthusiasts express the belief that transmitting a telephone signal to any distance using induction through air is possible. My imagination does not stretch that far, but I firmly believe that it is practically possible, with the help of powerful machines, to excite the electrostatic field of the Earth and thus transmit information or perhaps energy. In fact, what could prevent the implementation of such a plan? Now we know that electrical vibrations can be transmitted through a single wire. Why not try to use the Earth for this? Don't be afraid of distances. For tired traveler Counting mileposts, the Earth may seem very large, but to the happiest of people, to the astronomer who looks at the stars and calculates the size of the globe from their condition, it may seem very small. It must seem the same to the electrician, for when he thinks of the speed of the electrical signal with which it penetrates the Earth, all his ideas about distance must evaporate.

Firstly, it would be very important to know what is the capacity of the Earth? And what charge does it contain when electrified? Although we have no positive evidence that there are other bodies nearby in space charged in the opposite way, it is quite possible that the Earth is such a body, for whatever the process that resulted in the separation of the Earth - and this is precisely the generally accepted view of it today origin - it had to retain a charge, as happens in all processes of mechanical division. If this is a charged body, isolated in space, then its capacity should be extremely small, less than one thousandth of a farad. But the upper layers of the atmosphere are conductors, and the medium outside the atmosphere can be the same, and it can have the opposite charge. Then the capacity can be incomparably higher. In any case, it is very important to understand how much electricity the Earth contains. It is difficult to say whether we will ever obtain such knowledge, but I hope that we will, and precisely with the help of electrical resonance. If we can ever ascertain what is the period of vibration of the earth when its charge is excited in relation to an oppositely charged circuit, we shall have a fact most likely to be most important for the welfare of all mankind. I suggest looking for this period using an electrical oscillator, or an alternating current source. One of the terminals, for example, will be connected to the ground, or a city water supply, and the other to an isolated object large sizes. It is possible that the upper atmosphere or open space, have an opposite charge and, together with the Earth, form a capacitor of enormous capacity. In such a case, the period of oscillation could be very short, and an alternating current dynamo could meet the purpose of the experiment. I would then convert the current to obtain the highest possible potential and connect the ends of the high voltage secondary winding to ground and the insulated body. By varying the frequency of the current and carefully maintaining the potential isolated body, as well as observing disturbances at various neighboring points earth's surface, resonance can be detected. If, as most scientists believe, the period is quite short, then a dynamo will not work and a corresponding electrical oscillator will have to be built, and perhaps such rapid oscillations cannot be obtained. But whether it is possible or not, whether the Earth has a charge or not, and whatever the period of its oscillations, it is absolutely possible - and we have evidence of this - to produce some kind of electrical disturbances powerful enough to be registered at any point on the earth's surface at using appropriate devices.

Let us assume that the alternating current source is connected, as in Figure 21, with one of its terminals to the ground (it is most convenient to ground the end to the water supply), and the other to the object large area R. When electrical vibrations are established, electricity will move in both directions through the object R, and alternating currents will pass through the ground, diverging or converging at point C, where the grounding is made. Thus, neighboring points on the earth's surface located in a circle with a certain radius will be disturbed. But the disturbance will weaken as it moves away, and the distance at which the effect can still be detected will depend on the amount of electricity put into action. Since the subject R isolated to set in motion significant amount electricity, the source potential must be extremely high, since the surface area of ​​the object R limited. You can configure device settings so that the source S will generate the same movement of electricity as if its circuit were closed. Thus, of course, it is practically possible to impose electrical oscillations of a certain low period on the Earth with the help of proper equipment. One can only guess at what distance these vibrations can be perceived. On another occasion, I had to think about how the Earth might react to electrical disturbances. There is no doubt that during such an experiment the electrical density at the surface may be very small, given the size of the Earth, and the air will not act as a disturbing factor, nor will there be big losses energy in the air, as it could be if the density were high. Then theoretically there will be no need huge amount energy to produce disturbances that can be read over a very large distance, if not across to the globe. So, it is quite obvious that at any point within certain circle, the center of which is the source S, You can use resonance to make an inductance and capacitance device work. But you can do not only this, but also include another source 5 (Figure 21), similar to the source S, or any number of sources operating synchronously with the first, and thus increase the vibration and spread it over a large area, or obtain an electric current from or to the source S, if its phase is opposite to the phase of the source 5". I have no doubt that it can be exploited electrical appliances throughout the city through grounding or a water supply system using resonance from a single electrical oscillator installed at a central point. But practical solution This task will be incomparably less important for humans than the transmission of information or energy over any distance through the Earth or its environment. If it's possible at all, then distance doesn't matter. First you need to build the proper instruments with which to try to solve the problem, and I thought about this for quite a long time. I firmly believe that it can be done, and we will live to see it done.