An oscillatory circuit is a device designed to generate (create) electromagnetic oscillations. From its inception to the present day, it has been used in many areas of science and technology: from everyday life to huge factories producing a wide variety of products.
What is it made of?
The oscillatory circuit consists of a coil and a capacitor. In addition, it may also contain a resistor (element with variable resistance). An inductor (or solenoid, as it is sometimes called) is a rod on which are wound several layers of winding, 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 a choke or core, and the coil is sometimes called a solenoid.
The oscillatory circuit coil only oscillates when there is a stored charge. When current passes through it, it accumulates a charge, which it then gives off to the circuit if the voltage drops.
The coil wires usually have very little resistance, which always remains constant. In the circuit of the oscillatory circuit, a change in voltage and current very often occurs. This change is subject to certain mathematical laws:
-
U=U0cos(w(t-t0), where
U is the current voltage point in time t, U0 - voltage at time t0, w - frequency of electromagnetic oscillations.
Another integral component of the circuit is the electrical capacitor. This is an element consisting of two plates, which are separated by a dielectric. In this case, the thickness of the layer between the plates is less than their sizes. This design allows you to accumulate an electric charge on the dielectric, which can then be transferred to the circuit.
The difference between a capacitor and a battery is that there is no transformation of substances under the action of an electric current, but a direct accumulation of charge in an electric field. Thus, with the help of a capacitor, it is possible to accumulate a sufficiently large charge, which can be given away all at once. In this case, the current strength in the circuit increases greatly.
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 the resistance of the resistor is increased at a constant voltage, then the current strength will decrease according to the lawOma:
-
I=U/R, where
I is current, U is voltage, R is resistance.
Inductor
Let's take a closer look at all the subtleties of the inductor and better understand its function in an oscillating circuit. As we have already said, the resistance of this element tends to zero. Thus, when connected to a DC circuit, a short circuit would occur. However, if you connect the coil to an AC circuit, it works properly. This allows you to conclude that the element offers resistance to alternating current.
But why does this happen and how does resistance arise with alternating current? To answer this question, we need to turn to such a phenomenon as self-induction. When current passes through the coil, an electromotive force (EMF) arises in it, which creates an obstacle to a change in current. The magnitude of this force depends on two factors: the inductance of the coil and the derivative of the current strength with respect to time. Mathematically, this dependence is expressed through the equation:
-
E=-LI'(t), where
E is the EMF value, L is the value of the coil inductance (for each coil it is different and depends on the number of coils of the winding and their thicknesses), I'(t) - derivative of the current strength with respect to time (the rate of change of the current strength).
Direct current strength does not change over time, so there is no resistance when exposed to it.
But with alternating current, all its parameters are constantly changing according to a sinusoidal or cosine law,as a result, an EMF arises that prevents these changes. Such resistance is called inductive and is calculated by the formula:
- XL =wL
The current in the solenoid linearly increases and decreases according to various laws. This means that if you stop the current supply to the coil, it will continue to give charge to the circuit for some time. And if at the same time the current supply is abruptly interrupted, then a shock will occur due to the fact that the charge will try to be distributed 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 jumps, which on such a scale is not able to harm 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 an industrial scale, the current strength is many times greater than the 220 volts we are used to, so when a circuit is interrupted in production, sparks of such strength can occur that cause a lot of harm to both the plant and the person.
A coil is the basis of what an oscillatory circuit consists of. The inductances of the solenoids in series add up. Next, we will take a closer look at all the subtleties of the structure of this element.
What is inductance?
The inductance of the coil of an oscillatory circuit is an individual indicator numerically equal to the electromotive force (in volts) that occurs in the circuit whenchange in current by 1 A in 1 second. If the solenoid is connected to a DC circuit, then its inductance describes the energy of the magnetic field that is created by this current according to the formula:
-
W=(LI2)/2, where
W is the magnetic field energy.
The inductance factor 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 cannot be negative.
Inductance can also be defined as the property of a current-carrying conductor 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 capacitor, which will be discussed later.
Electric Capacitor
The capacitance of the oscillating circuit is determined by the capacitance of the electric capacitor. About his 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 the two plates: a dielectric (it can be air, wood or other material with high resistance. Due to the fact that the charge cannot move from one end of the wire to the other, it accumulates on the capacitor plates. This increases the power of the magnetic and electric fields around it.the electricity accumulated on the plates begins to be transferred to the circuit.
Each capacitor has a voltage rating that is 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 oscillatory circuit capacitor is constantly affected by currents, and therefore, when choosing it, you should be extremely careful.
In addition to the usual capacitors that were discussed, there are also ionistors. This is a more complex element: it can be described as a cross between a battery and a capacitor. As a rule, organic substances serve as a dielectric in an ionistor, between which there is an electrolyte. Together they create a double electrical layer, which allows you to accumulate in this design many times more energy than in a traditional capacitor.
What is the capacitance of a capacitor?
The capacitance of a capacitor is the ratio of the charge of the capacitor to the voltage under which it is located. You can calculate this value very simply using the mathematical formula:
-
C=(e0S)/d, where
e0 is the permittivity of the dielectric material (table value), S - the area of the capacitor plates, d - 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 stronger they affect each other (according to Coulomb's law), the greater the charge of the plates and the lower the voltage. And as the voltage decreasesthe capacitance value increases, since it can also be described by the following formula:
-
C=q/U, where
q is the charge in coulombs.
It is worth talking about the units of this quantity. Capacitance is measured in farads. 1 farad is a large enough value that existing capacitors (but not ionistors) have a capacitance measured in picofarads (one trillion farad).
Resistor
The current in the oscillatory circuit also depends on the resistance of the circuit. And in addition to the described two elements that make up the oscillatory circuit (coils, capacitors), there is also a third one - a resistor. He is responsible for creating resistance. The resistor differs from other elements in that it has a large resistance, which can be changed in some models. In the oscillatory circuit, it performs the function of a magnetic field power regulator. You can connect several resistors in series or in parallel, thereby increasing the resistance of the circuit.
The resistance of this element also depends on temperature, so you should be careful about its operation in the circuit, as it heats up when current passes.
Resistor resistance is measured in Ohms, and its value can be calculated using the formula:
-
R=(pl)/S, where
p is the resistivity of the resistor material (measured in (Ohmmm2)/m);
l - resistor length (in meters);
S - sectional area (in square millimeters).
How to link path parameters?
Now we come close to physicsoperation of the oscillatory circuit. Over time, the charge on the capacitor plates changes according to a second-order differential equation.
If you solve this equation, several interesting formulas follow from it, describing the processes occurring in the circuit. For example, the cyclic frequency can be expressed in terms of capacitance and inductance.
However, the simplest formula that allows you to calculate many unknown quantities is the Thomson formula (named after the English physicist William Thomson, who derived it in 1853):
-
T=2p(LC)1/2.
T - the period of electromagnetic oscillations, L and C - respectively, the inductance of the coil of the oscillatory circuit and the capacitance of the circuit elements, p - the number pi.
Q factor
There is another important value that characterizes the operation of the circuit - the quality factor. In order to understand what it is, one should turn to such a process as resonance. This is a phenomenon in which the amplitude becomes maximum with a constant value of the force that supports this oscillation. The resonance can be explained with a simple example: if you start pushing the swing to the beat of its frequency, then it will accelerate, and its "amplitude" will increase. And if you push out of time, they will slow down. At resonance, a lot of energy is often dissipated. In order to be able to calculate the magnitude of the losses, they came up with such a parameter as the quality factor. It is a ratio equal to the ratioenergy in the system to the losses occurring in the circuit in one cycle.
The quality factor of the circuit is calculated by the formula:
-
Q=(w0W)/P, where
w0 - resonant cyclic oscillation frequency;
W - energy stored in the oscillatory system;
P - power dissipation.
This parameter is a dimensionless value, as it actually shows the ratio of energy: stored to spent.
What is an ideal oscillatory circuit
For a better understanding of the processes in this system, physicists came up with the so-called ideal oscillatory circuit. This is a mathematical model that represents a circuit as a system with zero resistance. It produces undamped harmonic oscillations. Such a model makes it possible to obtain formulas for the approximate calculation of contour parameters. One of these parameters is total energy:
W=(LI2)/2.
Such simplifications significantly speed up calculations and make it possible to evaluate the characteristics of a circuit with given indicators.
How does it work?
The whole cycle of the oscillatory circuit can be divided into two parts. Now we will analyze in detail the processes occurring in each part.
- First phase: The positively charged capacitor plate begins to discharge, giving current to the circuit. At this moment, the current goes from a positive charge to a negative one, passing through the coil. As a result, electromagnetic oscillations occur in the circuit. current passing throughcoil, goes to the second plate and charges it positively (whereas the first plate, from which the current flowed, is charged negatively).
- Second phase: the reverse process takes place. The current passes from the positive plate (which was negative at the very beginning) to the negative, passing again through the coil. And all the charges fall into place.
The cycle repeats as long as there is a charge on the capacitor. In an ideal oscillatory circuit, this process goes on endlessly, but in a real one, energy losses are inevitable due to various factors: heating, which occurs due to the existence of resistance in the circuit (Joule heat), and the like.
Contour design options
Besides the simple "coil-capacitor" and "coil-resistor-capacitor" circuits, there are other options that use an oscillatory circuit as a basis. This is, for example, a parallel circuit, which differs in that it exists as an element of an electrical circuit (because, if it existed separately, it would be a series circuit, which was discussed in the article).
There are also other types of designs that include 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 oscillation frequency in the circuit. Thus, undamped oscillations will be established in the system.
Where is an oscillatory circuit used?
The most familiar application of circuit components is electromagnets. They, in turn, are used in intercoms, electric motors,sensors and in many other not so ordinary areas. Another application is an oscillation generator. 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 transmit 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 becomes possible to transmit information over long distances.
The inductor itself can be used as an element of a transformer: two coils with a different number of windings can transfer their charge using an electromagnetic field. But since the characteristics of the solenoids are different, the current indicators in the two circuits to which these two inductors are connected will differ. Thus, it is possible to convert a current with a voltage of, say, 220 volts into a current with a voltage of 12 volts.
Conclusion
We have analyzed in detail the principle of operation of the oscillatory circuit and each of its parts separately. We learned that an oscillatory circuit is a device designed to create electromagnetic waves. However, these are only the basics of the complex mechanics of these seemingly simple elements. You can learn more about the intricacies of the circuit and its components from the specialized literature.
