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What is the electrical capacity of a voltage capacitor? Capacitance of a capacitor: essence and main characteristics

Flat capacitor usually called a system of flat conducting plates - plates separated by a dielectric. The simplicity of the design of such a capacitor makes it relatively easy to calculate its electrical capacity and obtain values ​​that coincide with the experimental results.

Let's fasten two metal plates on insulating stands and connect them to the electrometer so that one of the plates will be connected to the rod of the electrometer, and the second to its metal body (Fig. 4.71). With this connection, the electrometer will measure the potential difference between the plates, which form a flat capacitor from two plates. When conducting research, it is necessary to remember that

at a constant value of the charge of the plates, a decrease in the potential difference indicates an increase in the electrical capacity of the capacitor, and vice versa.

Let us give the plates opposite charges and note the deviation of the electrometer needle. By bringing the plates closer to each other (reducing the distance between them), we will notice a decrease in the potential difference. Thus, as the distance between the plates of the capacitor decreases, its electrical capacity increases. As the distance increases, the readings of the electrometer needle increase, which is evidence of a decrease in electrical capacity.

inversely proportional to the distance between its plates.

C~ 1 / d,

Where d— distance between the plates.

This dependence can be depicted by a graph of an inverse proportional dependence (Fig. 4.72).

We will shift the plates one relative to the other in parallel planes without changing the distance between them.

In this case, the overlap area of ​​the plates will decrease (Fig. 4.73). An increase in the potential difference noted by the electrometer will indicate a decrease in electrical capacity.

Increasing the area of ​​overlap of the layers will lead to an increase in capacity.

Electrical capacity flat capacitor proportional to the area of ​​the plates that overlap.

C~S,

Where S— plate area.

This dependence can be represented by a graph of a direct proportional dependence (Fig. 4.74).

Having returned the plates to their initial position, we introduce a flat dielectric into the space between them. The electrometer will note a decrease in the potential difference between the plates, which indicates an increase in the electrical capacity of the capacitor. If another dielectric is placed between the plates, then the change in electrical capacity will be different.

Electrical capacitance of a flat capacitor depends on the dielectric constant of the dielectric.

C ~ ε ,

Where ε is the dielectric constant of the dielectric. Material from the site

This dependence is shown in the graph in Fig. 4.75.

The experimental results can be summarized in the form formulas for the capacitance of a flat capacitor:

C=εε 0 S/d,

Where S— plate area; d— the distance between them; ε — dielectric constant of the dielectric; ε 0 - electrical constant.

Capacitors, which consist of two plates, are used very rarely in practice. As a rule, capacitors have many plates connected to each other according to a certain pattern.

On this page there is material on the following topics:

  • Graph of the electrical capacity of a flat capacitor versus the area of ​​its plates

  • With an increase in the overlap area of ​​the plates, the charge on the capacitor plates

  • Theory of flat capacitors

  • How does a dielectric affect electrical capacity?

  • Message on the topic of electrical capacity

Questions about this material:

  • What is the structure of a parallel plate capacitor?

  • By changing what value in the experiment can we draw a conclusion about a change in electrical capacity?

  • Capacitance of the capacitor – physical quantity, characterizing the process of charging conductors separated by a dielectric layer. It is used in numerous mathematical calculations and is marked on the product body.

    Formulas

    The electrical capacity of a capacitor is usually expressed in terms of the stored charge q at an applied voltage U as follows:

    As for the origin of the formula, there is one mystery. We only know: from Gauss’ tension theorem electric field Let's find the electrical capacity of the capacitor. It is not stated anywhere who carried out the calculation. The physical quantity farad was initially absent from the GHS system; in 1861 it was introduced by a special commission formed by physicists.

    According to some information, it was for the first time that the electrical capacity of a capacitor was determined by the person who introduced the terms into use. We mean Alessandro Volta. In the late 70s (XVIII centuries), the scientist devoted a lot of research to the issue and established: electrical capacity can be expressed in terms of the accumulated charge and the voltage applied to the electrodes.

    In addition, you can often find the formula for the electrical capacity of a flat capacitor:

    The authors avoid judging who was involved in the calculations of the expression. Logically speaking, hardly anyone was interested in the electrical capacity of a flat-plate capacitor before Polak’s invention was born. Leyden jars distribute charge differently. Reasoning leads to the beginning of the 20th century. Perhaps Tesla and Hertz dealt with the issue. Less likely - Popov.

    Last names are named based on interest criteria alternating current. Tesla studied the safety of electricity, long-distance transmission, and designed engines. Hertz and Popov studied antennas that are obviously tuned to a certain wavelength, which is easier to obtain using an oscillating circuit. Consequently, scientists must have an idea of ​​the electrical capacity of a capacitor and inductors.

    James Maxwell, Lord Kelvin, Wilhelm Weber paid a lot of attention to improvement unified systems measurements of physical quantities There is some possibility that someone could have had a hand in the study of capacitors. One thing is clear - in the world history of natural sciences there are many blank spots when it comes to Russian-language sources. The VashTekhnik portal will be one of the first to publish the latest research in the field of correct understanding of the events that took place.

    Story

    For impatient readers, we immediately report: Alessandro Volta actually introduced the term capacity. It is not known exactly whether anyone used it before, but in his work the Italian scientist, calling electrophorus a capacitor, simultaneously applies the term capacitance to it. Like a vessel into which you can “pour” a charge from a container. It’s called a capacitor because the process is similar to vapor deposition: we’ll gradually pick up an arbitrary amount of electricity. And by by and large It's right.

    The term capacitor

    Historically, the Leyden jar should be considered the first capacitor. To this day, there is debate about who invented the device, since both scientists, carried away by events, avoided keeping neat records; one thing is indisputable - the electrical capacity of the device could not be measured, there was no corresponding concept of “electrical capacity of a capacitor.”


    Screenshot of a printed version of Volta's treatise, 1782

    The person who coined the term was powerless to pronounce the word earlier than Alessandro Volta in 1782, reporting to the Royal Scientific Society on research in the field of electrostatics. To understand where electricity comes from. It is known that over the next five years, Luigi Galvani would discover “animal electricity,” which led Volta straight to the creation of the first battery. Reporting to society, the young scientist is deprived of the mentioned knowledge, the luminary tries to understand where the charge comes from. He reasons something like this: “To date, there is a lot of evidence of the existence atmospheric electricity. People are powerless to find traces of presence. May mean: existing electroscopes are too weak, unable to detect such subtle matter. Therefore, we need to find a way to take the fluids out of the air.”

    Carrying out practically what has been said, Alessandro Volta proposes a device called an electrophorus (not to be confused with). The device captures fluids from an atmospheric conductor (air). The principle of serving Volta resembles the process of condensation: it collects electricity.

    Electrophorus

    The West calls electrophorus a capacitive type generator. The above suggests that such a definition was adopted thanks to Volta, written by the English Royal Society. The device was invented by another person - Swedish physicist John Clark Wilke. It happened two decades earlier - 1762.

    Nowadays it is believed that Volta gave the device popularity, calling his favorite an eternal generator of electricity. This is also essentially correct; you can rub rubber for thousands of years. The “capacitor” more closely resembles (see figure) a hefty seal. On top, in addition to the main central handle, there is a side one - for removing negative potential. We see three layers:

    1. The backing is optional; rubber is glued onto it.
    2. A thin layer of rubber serves as a body of electrification by friction.
    3. On top is a thin sheet of metal equipped with two handles, one (central) is insulated.


    Appearance of electrophorus

    Having started work, you need to remove the “seal” and rub the rubber with wool. Then the smooth disk is put back. The area of ​​contact with rubber is small due to the roughness present; a positive charge is not acquired quickly. We need to wait. The operator grounds the lid for a short moment with the side handle, removing the negative charge, leaving a positive charge at the bottom. When you touch the metal with one hand, you can hear a clearly audible crackling sound. After lifting the lid, the rubber carries an excess of electrons, allowing the experiment to be repeated several times (hard to believe, some sources say hundreds of repetitions).

    Separating the bodies by pulling the insulating handle with a sharp movement, the operator receives static electricity. The invention, quite revolutionary, it is noteworthy that it appeared in a matter of years after the abolition of the witch hunt law. According to Volta, the circle of rubber should be as thin as possible, about 50th of an inch. Manages to get the best result. A sheet of metal is actually also a plate. Otherwise, you need to wait a long time for the volume of the conductor to fill. In common parlance, a “capacitor” is called a rubber pie. A pie covered with a metal filling.

    Is electrophorus really an inexhaustible source of energy? IN ideal conditions, although it’s hard to believe. The negative charge of the rubber polarizes the metal plate, creating a certain potential. Forced out onto outer surface electrons are removed by touching the ground electrode. It remains to separate the components of the electrophorus. Having destroyed the positive charge by touch and heard the sound of a spark, you can start the experiment again.

    Electrophorus really resembles a capacitor. After removing the excess negative charge, it actually turns into the mentioned device. The capacitor cannot be stored for a long time, since electrons from the rubber will gradually flow onto the metal. The device will be discharged. In fact, rubber and metal are separated from each other by air, which serves as a dielectric. Instead of rubber we use various polymers, for example Teflon.

    It remains to be noted: in the time of Volta, they did not know methods for ridding rubber of static charge. The "lining" of the capacitor could for a long time store a load of electrons. Volta suggests placing the sample under Sun rays, or move a burning candle nearby. Through the ionized flame, electrons leave the capacitor. Today it is clear that it is enough to wash the rubber so that no traces of static stress remain. To work you will need to dry it again.

    Leyden jar

    It is believed that it was Felix Savary who discovered the oscillations of the resonant circuit. While discharging a Leyden jar through a twisted thread of copper, I observed the erratic movement of the compass needle. 1826, when England, France, Germany, and partly Italy feverishly explored a new phenomenon brought into the scientific world by Oersted.


    The history of creation can be read in the corresponding review. It should be said that no one really tried to understand what the electrical capacity of a capacitor is. It is not necessary for obvious reasons: the Leyden jar was mainly used by the scientific community, solving specific problems. The experience of Felix Savary remained unnoticed for a long time...

    In 1842, our old friend, Sir Joseph Henry, an inventor and telegraph enthusiast, took up the oscillatory circuit and the electrical capacity of a capacitor. Put it in writing after testing Savary’s notes in practice:

    “An anomaly that has remained unexplained for so long, which at first glance seems to exist contrary to our theory of electricity and magnetism, after careful study I have classified it as a hitherto unknown phenomenon. The discharge occurs strangely (contrary to Franklin's theory), the feeling that, upon leaving the jar, the fluid begins to wander back and forth. What we saw forces us to admit: the process begins in a normal way, then several changes of direction occur, each time the amplitude becomes smaller, until the movements die out completely. Apparently, the phenomenon cannot be explained today; physicists met with him (Savary), but were powerless.”

    Obviously, the scientist is not at all interested in the electrical capacity of the capacitor - his thoughts are absorbed in the anomaly that he would like to explore. Five years later, physicist Helmholtz, who read Henry’s report at a meeting of the Berlin Physical Society, said:

    “While performing electrolysis, I noticed unusual fluctuations. This feeling, the process of oscillation continues, until the vis viva itself disappears forever, absorbed by the total resistance of the circuit. One gets the impression that two currents of opposite directions flow along the circuit, first one, then the other takes over.”

    The dispute was put to an end by the famous William Thomson, named Lord Kelvin. Having studied the process mathematically, he stated: in the circuit, obviously, there are such things as the electrical capacity of the capacitor and the inductance of the folded copper wire. On Transient Electric Currents has become a classic. Although Lord Thomson calls inductance electrodynamic capacitance, the meaning of the formula is unambiguous. The scientist was the first to say: energy is transferred between a capacitor and an inductor, gradually attenuating by active resistance chains.

    The formula shown in the figure is given in modern values, the notations are standard. C is the electrical capacity of the capacitor, L is the inductance of the coil, q is the amount of charge, I is the circuit current. Other symbols refer to differentiation operations. The term inductance was introduced much later - in 1886 by Oliver Heaviside. Formula resonant frequency, which depends on the electrical capacitance of the capacitor and the inductance of the coil, was derived by James Maxwell in 1868.

    Electrical capacity– a quantitative measure of a conductor’s ability to hold a charge.

    The simplest ways to separate different names electric charges– electrification and electrostatic induction – make it possible to obtain a small amount of free electrical charges on the surface of bodies. To accumulate significant quantities of opposite electrical charges, they are used capacitors.

    Capacitor is a system of two conductors (plates) separated by a dielectric layer, the thickness of which is small compared to the size of the conductors. For example, two flat metal plates located parallel and separated by a dielectric layer form flat capacitor.

    If the plates of a flat capacitor are given charges equal in magnitude opposite sign, then the electric field strength between the plates will be twice as strong as the field strength at one plate. Outside the plates, the electric field strength is zero, since equal charges different sign on two plates, electric fields are created outside the plates, the strengths of which are equal in magnitude but opposite in direction.

    Capacitance of the capacitor is a physical quantity determined by the ratio of the charge of one of the plates to the voltage between the plates of the capacitor:

    With a constant position of the plates, the electrical capacity of the capacitor is a constant value for any charge on the plates.

    The unit of electrical capacity in the SI system is Farad. 1 F is the electrical capacity of such a capacitor, the voltage between the plates of which is equal to 1 V when the plates are given opposite charges of 1 C each.



    The electrical capacity of a flat capacitor can be calculated using the formula:

    S – area of ​​capacitor plates

    d – distance between plates

    – dielectric constant of the dielectric

    The electrical capacity of the ball can be calculated using the formula:

    Energy of a charged capacitor.

    If the field strength inside the capacitor is E, then the field strength created by the charge of one of the plates is E/2. In the uniform field of one plate there is a charge distributed over the surface of the other plate. According to the formula for potential energy charge in a uniform field, the energy of the capacitor is equal to:

    Using the formula for capacitance of a capacitor:

    Capacitors.

    If an insulated conductor is given a charge Dq, then its potential will increase by Dj, and the ratio Dq/Dj remains constant: Dq/Dj=C, where C is electrical capacitance of the conductor, i.e. magnitude, numerically equal to charge, which must be communicated to the conductor in order to increase its potential by one (by 1V). The electrical capacitance of conductors depends on their size, shape, dielectric properties of the medium in which they are placed, and the location of surrounding bodies, but does not depend on the material of the conductor. In SI per unit electrical capacitance 1 farad (F): [C]=1A=1kl/1V=1A 2 *s 4 /kg*m 2. A capacitance equal to 1F is very large, so in practice the units of microfarads (1 µF = 10 -6 F) or picofarads (1 µF = 10 -12 F) are more often used. A capacitor is a system of two conductors (plates) not connected to each other. Often a dielectric is placed between the plates. When these conductors are charged with equal and opposite charges, the field created by these conductors is almost completely localized in the space between them. Capacitors are storage devices for electrical charges. The ratio of the charge on the capacitor plate to the potential difference between them is constant: q/(j 1 -j 2)=C.

    Flat capacitor consists of two plates of area S, located at a small distance d from each other, charges on the plates +q and –q. In general, if the space between the plates is filled with a dielectric with dielectric constant e, then the electrostatic field strength between the plates is equal to the sum of the field strengths created by each of the plates.

    E=s/e 0 e. The capacitance of a flat capacitor is C=e 0 eS/d.

    Parallel and series connection of capacitors. In practice, capacitors are often connected different ways. Find equivalent capacity- this means finding a capacitor of such a capacity that, at the same potential difference, will accumulate the same charge q as a bank of capacitors. At serial connection N capacitors, the charge on the plates is the same, the voltage on the entire battery of capacitors is equal to the sum of the voltages on each capacitor separately: U total =U 1 +U 2 +U 3 +...+UN N, and the total capacitance of N capacitors is 1/C total =1 /С 1 +1/С 2 +1/С 3 +...+1/С N . At parallel connection capacitors, the voltage U on all capacitors is the same and the total capacity C total of the battery is equal to the sum of the capacitances of the individual capacitors, C total = C 1 + C 2 + C 3 +... + C N.

    Both in industry and in Everyday life it is often necessary to create large quantity positive and negative It is clear that this cannot be done with the help of electrification of bodies. It turns out that you need a special device. Such a device is a capacitor.

    A capacitor is a simple system consisting of a dielectric separating two plates. In this case, it is very important that the thickness of this dielectric is small compared to the dimensions of these very plates, that is, the conductors.

    The simplest type of electrical capacitive devices is which is a complex of two metal plates separated by some kind of dielectric. If we bring to these plates electricity, then the quantitative value of the intensity of the electric field that arises between them will be almost twice as large as the same intensity for one of these plates.

    The most important indicator characterizing this system, is a capacitor from the point of view of the fundamentals of electromechanics, equal to the ratio of the charge of one of the plates used to the voltage between the conductors of this device. IN general view The capacitance of the capacitor will look like this:

    If the position of the plates in space remains unchanged for a long time, then the electrical capacity of the capacitor remains constant (regardless of the quantitative indicators of the charge on the plates).

    In the International System of Physical Measurements, the electrical capacity of a capacitor is measured in farads (F). According to this classification, one farad characterizes the electrical capacity of a device in which the voltage between the dielectrics is one volt, and the amount of charge supplied to the plates is equal to one coulomb.

    In fact, one farad is a very large value, so the most commonly used units are microfarads, nanofarads and even picofarads.

    The electrical capacity of a flat capacitor will directly depend on the area of ​​its plates and will increase as the distance between them decreases. To significantly increase the electrical capacity of these devices, certain dielectrics are introduced between the conductors.


    Most often, electrodes for capacitors are made of thin foil, and paper, mica or ceramics are used as the main gasket. It is in accordance with the material that serves as the basis for dielectrics that capacitors get their names - paper, ceramic, air, mica. Quite widespread in Lately got electrolytic capacitors, which, despite their fairly compact dimensions, have significant electrical capacity. Due to these qualities, they are actively used in household appliances, and also as electric current rectifiers.

    Capacitors are among the most indispensable electrical devices, without which it would be simply impossible to create most household and electrical measuring instruments.