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The oscillatory circuit is ... The principle of action

The oscillatory circuit is a device designed to generate (create) electromagnetic oscillations. From the moment of its creation to the present day it is used in many fields of science and technology: from everyday life to huge factories producing a variety of products.

What does it consist of?

The oscillatory circuit consists of a coil and a capacitor. In addition, it can also contain a resistor (an element with a variable resistance). The inductor (or solenoid, as it is sometimes called) is a rod on which several layers of winding are wound, which, as a rule, is a copper wire. It is this element that creates oscillations in the oscillatory circuit. The rod in the middle is often called the throttle, or core, and the coil is sometimes called a solenoid.

The coil of the oscillating circuit creates oscillations only if there is a stored charge. When passing current through it, it accumulates a charge, which then gives to the circuit if the voltage drops.

Coil wires usually have a very small resistance, which always remains constant. In the circuit of the oscillatory circuit, the voltage and current intensity change very often. This change is subject to certain mathematical laws:

  • U = U 0 * cos (w * (tt 0 ), where
    U is the voltage at a given time t,
    U 0 is the voltage at time t 0 ,
    W is the frequency of electromagnetic oscillations.

Another integral component of the circuit is the electric capacitor. This is an element consisting of two plates, which are separated by a dielectric. The thickness of the layer between the plates is less than their dimensions. This design allows you to accumulate on the dielectric electric charge, which then can be given in a chain.

The difference between a capacitor and a battery is that it does not convert substances under the influence of an electric current, but a direct accumulation of a charge in an electric field occurs. Thus, with the help of a capacitor, you can accumulate a sufficiently large charge, which can be sent all at once. At the same time, the current strength in the circuit greatly increases.

Also, the oscillatory circuit consists of one more element: a resistor. This element has resistance and is designed to control the current and voltage in the circuit. If at a constant voltage increase the resistance of the resistor, then the current will decrease in Ohm's law:

  • I = U / R, where
    I is the amperage,
    U is the voltage,
    R is the resistance.

Inductor

Let's take a closer look at all the subtleties of the inductor and better understand its function in the oscillatory circuit. As we have already said, the resistance of this element tends to zero. Thus, when connected to a DC link, a short circuit would occur . However, if you connect the coil to an alternating current circuit, it works properly. This allows us to conclude that the element provides resistance to alternating current.

But why does this occur and how does the resistance arise at AC? To answer this question, we need to address to such a phenomenon as self-induction. As the current passes through the coil, an electromotive force (EMF) appears in it , which creates an obstacle to the change in current. The magnitude of this force depends on two factors: the inductance of the coil and the derivative of the current with respect to time. Mathematically, this dependence is expressed in terms of the equation:

  • E = -L * I '(t), where
    E is the EMF value,
    L is the inductance value of the coil (for each coil it is different and depends on the number of winding coils and their thickness),
    I '(t) is the derivative of the current strength with respect to time (the rate of change of the current strength).

The strength of the direct current does not change with time, therefore resistance does not arise when it acts.

But with alternating current, all its parameters are constantly changing in sinusoidal or cosine law, resulting in an EMF that prevents these changes. This resistance is called induction and is calculated by the formula:

  • X L = w * L, where
    W is the oscillation frequency of the circuit,
    L - coil inductance.

The current in the solenoid increases linearly and decreases according to various laws. This means that if you stop supplying current to the coil, it will continue to charge for a while in the circuit. And if, at the same time, the supply of current is abruptly interrupted, there will be a blow due to the fact that the charge will try to dispense and exit the coil. This is a serious problem in industrial production. Such an effect (although not entirely related to the oscillatory circuit) can be observed, for example, when pulling the plug out of the socket. At the same time, a spark is leaping, which on such a scale is not capable of harming a person. It is due to the fact that the magnetic field does not disappear immediately, but gradually dissipates, inducing currents in other conductors. On industrial scales, the current is many times greater than the usual 220 volts, so when the circuit is interrupted, sparks of such intensity may appear on the production line that will cause considerable harm to both the plant and the person.

The coil is the basis of what the oscillatory circuit consists of. The inductances of series-connected solenoids are added. Next, we will take a closer look at all the details of the structure of this element.

What is inductance?

The inductance of the coil of the oscillatory circuit is an individual index numerically equal to the electromotive force (in volts) that arises in the circuit when the current strength changes by 1 A per second. If the solenoid is connected to a direct current circuit, then its inductance describes the energy of the magnetic field, which is created by this current according to the formula:

  • W = (L * I 2 ) / 2, where
    W is the energy of the magnetic field.

The coefficient of inductance depends on many factors: on the geometry of the solenoid, on the magnetic characteristics of the core, and on the number of coils of wire. Another property of this indicator is that it is always positive, because the variables on which it depends can not be negative.

Inductance can also be defined as the property of a conductor with a current to store energy in a magnetic field. It is measured in Henry (named after the American scientist Joseph Henry).

In addition to the solenoid, the oscillatory circuit consists of a condenser, which will be discussed later.

Electric Capacitor

The capacitance of the oscillating circuit is determined by the capacitance of the electric capacitor. About its appearance was written above. Now let's analyze the physics of the processes that take place in it.

Since the capacitor plates are made of a conductor, an electric current can flow through them. However, there is an obstacle between two plates: dielectric (it can be air, wood or other material with high resistance.) Due to the fact that the charge can not pass from one end of the wire to the other, it accumulates on the capacitor plates, thereby increasing the power of magnetic and electric Fields around it.Thus, when the charge comes to an end, all the electricity accumulated on the plates begins to be transferred to the circuit.

Each capacitor has a nominal voltage, optimal for its operation. If this element is operated for a long time at a voltage higher than the rated voltage, its service life is significantly reduced. The capacitor of the oscillatory circuit is constantly influenced by the currents, and therefore, when choosing it, one must be extremely careful.

In addition to conventional capacitors, which were discussed, there are also ionistors. This is a more complex element: it can be described as a cross between the battery and the capacitor. As a rule, organic substances are the dielectric in the ionistor, between which there is an electrolyte. Together, they create a double electrical layer, which allows you to accumulate in this design at times more energy than in a traditional capacitor.

What is the capacitance of the capacitor?

Capacitor capacitance is the ratio of the capacitor charge to the voltage under which it is located. To calculate this value can be very simple with the help of a mathematical formula:

  • C = (e 0 * S) / d, where
    E 0 is the permittivity of the dielectric material (tabular value),
    S is the area of the capacitor plates,
    D is the distance between the plates.

The dependence of the capacitance of the capacitor on the distance between the plates is explained by the phenomenon of electrostatic induction: the smaller the distance between the plates, the more they influence each other (according to Coulomb's law), the greater the charge of the plates and the lower the voltage. And as the voltage decreases, the capacitance increases, because it can also be described by the following formula:

  • C = q / U, where
    Q - charge in coulombs.

It is worth talking about units of this magnitude. The capacity is measured in farads. 1 farad is a large enough quantity, therefore existing capacitors (but not ionistors) have a capacitance, measured in picofarads (one trillionth Faraday).

Resistor

The current in the oscillating circuit also depends on the resistance of the circuit. And in addition to the described two elements, of which the oscillatory circuit (coil, capacitor) consists, there is also a third - a resistor. He is responsible for creating resistance. The resistor differs from other elements in that it has a great resistance, which in some models can be changed. In the oscillatory circuit, it acts as a regulator of the power of the magnetic field. It is possible to connect several resistors in series or in parallel, thereby increasing the resistance of the circuit.

The resistance of this element also depends on the temperature, so you have to be careful about its work in the circuit, because when it passes the current it heats up.

Resistor resistance is measured in Ohms, and its value can be calculated by the formula:

  • R = (p * l) / S, where
    P is the resistivity of the resistor material (measured in (Ohm * mm 2 ) / m);
    L is the length of the resistor (in meters);
    S is the cross-sectional area (in square millimeters).

How to associate contour parameters?

Now we have come very close to the physics of the oscillatory circuit. Over time, the charge on the capacitor plates changes according to a second-order differential equation.

If we solve this equation, it yields several interesting formulas describing the processes taking place in the circuit. For example, the cyclic frequency can be expressed in terms of capacitance and inductance.

However, the simplest formula that allows us to calculate many unknown quantities is Thomson's formula (named after the English physicist William Thomson, who deduced it in 1853):

  • T = 2 * n * (L * C) 1/2 .
    T is the period of electromagnetic oscillations,
    L and C are, respectively, the inductance of the coil of the oscillatory circuit and the capacity of the contour elements,
    N is the number pi.

Quality

There is another important value that characterizes the work of the circuit, - Q-factor. In order to understand what it is, one should turn to such a process as resonance. This phenomenon, in which the amplitude becomes maximum with the same magnitude of force that this oscillation maintains. Explain the resonance can be a simple example: if you start to push the swing in time with their frequency, then they will accelerate, and their "amplitude" will increase. And if you push not in tact, then they will slow down. At resonance, very much energy is scattered very often. In order to be able to calculate the magnitude of losses, came up with a parameter such as Q-factor. It is a coefficient equal to the ratio of the energy in the system to the losses occurring in the circuit in one cycle.

The quality of the contour is calculated by the formula:

  • Q = (w 0 * W) / P, where
    W 0 is the resonant cyclic frequency of the oscillations;
    W is the energy stored in the oscillatory system;
    P is the power dissipated.

This parameter is a dimensionless quantity, since it actually shows the ratio of the energies stored to the spent energy.

What is the ideal oscillatory circuit

To better understand the processes in this system, physicists have come up with a so-called ideal oscillatory circuit . This is a mathematical model that represents the circuit as a system with zero resistance. In it, undamped harmonic oscillations arise. Such a model allows one to obtain formulas for the approximate computation of the parameters of the contour. One such parameter is the total energy:

  • W = (L * I 2 ) / 2.

Such simplifications significantly accelerate the calculations and allow us to evaluate the characteristics of the chain with given parameters.

How it works?

The whole cycle of the oscillatory circuit can be divided into two parts. Now we will take a closer look at the processes taking place in each part.

  • The first phase: the capacitor plate, charged positively, begins to discharge, giving a current to the circuit. At this moment, the current flows from the positive charge to the negative, passing through the coil. As a consequence, electromagnetic oscillations arise in the circuit. The current, passing through the coil, passes to the second plate and charges it positively (while the first plate with which the current was traveling is charged negatively).
  • The second phase: there is a direct reverse process. The current passes from the positive plate (which in the beginning was negative) to the negative, passing through the coil again. And all the charges fall into place.

The cycle is repeated until the capacitor is charged. In an ideal oscillatory circuit, this process happens endlessly, and in real life, energy losses are inevitable due to various factors: heating, which is due to the existence of resistance in the circuit (Joule heat), and the like.

Contour design options

In addition to the simple "coil-capacitor" and "coil-resistor-capacitor" circuits, there are other variants that use the oscillatory circuit as the basis. This, for example, is a parallel circuit that differs in that it exists as an element of an electrical circuit (because, if it exists separately, it would be a sequential chain, which was discussed in the article).

There are also other types of construction, including different electrical components. For example, you can connect a transistor to the network, which will open and close the circuit with a frequency equal to the frequency of oscillations in the circuit. Thus, undamped oscillations are established in the system.

Where is the oscillatory circuit applied?

The most familiar application of the contour components is the electromagnets. They, in turn, are used in doorphones, electric motors, sensors and in many other less common areas. Another application is the oscillator. In fact, this use of the circuit is very familiar to us: in this form it is used in the microwave to create waves and in mobile and radio communications to transfer information over a distance. All this is due to the fact that the oscillations of electromagnetic waves can be encoded in such a way that it will be possible to transmit information over long distances.

The inductor can itself be used as an element of a transformer: two coils with a different number of windings can transmit their charge by means of an electromagnetic field. But since the characteristics of the solenoids are different, the current indices in the two circuits to which these two inductors are connected will differ. Thus, it is possible to convert a current with a voltage, say, 220 volts into a current of 12 volts.

Conclusion

We have in detail disassembled the principle of operation of the oscillatory circuit and each of its parts separately. We learned that the oscillatory circuit is a device designed to create electromagnetic waves. However, these are only the foundations of the complex mechanics of these, seemingly simple, elements. You can learn more about the subtleties of the circuit and its components from specialized literature.

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