In all radio engineering and electronic devices, except for transistors and microcircuits, capacitors are used. In some circuits there are more of them, in others there are fewer, but almost no electronic circuit can exist without capacitors at all.
At the same time, capacitors can perform a variety of tasks in devices. First of all, these are capacities in filters of rectifiers and stabilizers. With the help of capacitors, a signal is transmitted between the amplifying stages, low and high-frequency filters are built, time intervals in time delays are set, and the frequency of oscillations in various generators is selected.
Capacitors trace their ancestry back to the Dutch scientist Peter van Muschenbruck used in his experiments in the middle of the 18th century. He lived in the city of Leiden, so it's not hard to guess why this bank was called that.
Actually, it was an ordinary glass jar, lined inside and outside with tin foil - staniol. It was used for the same purposes as modern aluminum, but then aluminum was not yet discovered.
The only source of electricity in those days was an electrophore machine, capable of developing voltages up to several hundred kilovolts. It was from her that they charged the Leyden jar. Physics textbooks describe the case when Mushenbrook discharged his can through a chain of ten guardsmen holding hands.
At the time, no one knew that the consequences could be tragic. The blow turned out to be quite sensitive, but not fatal. It did not come to that, because the capacity of the Leyden jar was insignificant, the impulse turned out to be very short-lived, so the discharge power was low.
How a capacitor works
The device of the capacitor is practically no different from the Leyden jar: all the same two plates, separated by a dielectric. This is how capacitors are depicted on modern electrical circuits. Figure 1 shows a schematic design of a flat capacitor and the formula for calculating it.
Figure 1. The device of a flat capacitor
Here S is the area of the plates in square meters, d is the distance between the plates in meters, C is the capacitance in farads, ε is the dielectric constant of the medium. All quantities included in the formula are indicated in the SI system. This formula is valid for the simplest flat capacitor: you can simply place two metal plates side by side, from which conclusions are drawn. Air can be used as a dielectric.
From this formula, it can be understood that the capacitance of the capacitor is the greater, the larger the area of the plates and the smaller the distance between them. For capacitors with a different geometry, the formula may be different, for example, for the capacitance of a single conductor or. But the dependence of the capacitance on the area of the plates and the distance between them is the same as for a flat capacitor: the larger the area and the smaller the distance, the greater the capacitance.
In fact, the plates are not always flattened. For many capacitors, for example, metal-paper ones, the plates are aluminum foil rolled together with a paper dielectric into a tight ball, in the form of a metal case.
To increase the dielectric strength, thin capacitor paper is impregnated with insulating compounds, most often transformer oil. This design allows you to make capacitors with a capacity of up to several hundred microfarads. Capacitors with other dielectrics are arranged in approximately the same way.
The formula does not contain any restrictions on the area of the plates S and the distance between the plates d. If we assume that the plates can be separated very far, and at the same time the area of the plates is made quite insignificant, then some capacity, albeit small, will still remain. Such reasoning suggests that even just two conductors located in the neighborhood have electrical capacitance.
This circumstance is widely used in high-frequency technology: in some cases, capacitors are made simply in the form of printed wiring tracks, or even just two wires twisted together in polyethylene insulation. A conventional noodle wire or cable also has capacitance, and it increases with length.
In addition to capacitance C, any cable also has a resistance R. Both of these physical properties are distributed along the length of the cable, and when transmitting pulsed signals, they work as an integrating RC-chain, shown in Figure 2.
Figure 2.
In the figure, everything is simple: here is the circuit, here is the input signal, and here it is at the output. The impulse is distorted beyond recognition, but this was done on purpose, for which the circuit was assembled. In the meantime, we are talking about the influence of the cable capacitance on the pulse signal. Instead of a pulse at the other end of the cable, such a "bell" will appear, and if the pulse is short, then it may not reach the other end of the cable at all, completely disappear.
Historical fact
It is quite appropriate here to recall the story of how the transatlantic cable was laid. The first attempt in 1857 failed: telegraph dots - dashes (rectangular pulses) were distorted so that nothing could be discerned at the other end of the 4000 km long line.
The second attempt was made in 1865. By this time, the English physicist W. Thompson had developed a theory of data transmission over long lines. In the light of this theory, the cable laying turned out to be more successful, the signals were received.
For this scientific feat, Queen Victoria conferred the scholar the knighthood and title of Lord Kelvin. This was the name of the small town on the coast of Ireland, where the cable laying began. But this is just a word, and now let's return to the last letter in the formula, namely, to the dielectric constant of the medium ε.
A little about dielectrics
This ε is in the denominator of the formula, therefore, its increase will entail an increase in capacity. For most of the dielectrics used, such as air, lavsan, polyethylene, fluoroplastic, this constant is practically the same as that of a vacuum. But at the same time, there are many substances, the dielectric constant of which is much higher. If the air condenser is poured with acetone or alcohol, then its capacity will increase every 15 ... 20.
But such substances, in addition to high ε, also have a fairly high conductivity, therefore such a capacitor will not be well charged, it will quickly discharge through itself. This harmful phenomenon is called leakage current. Therefore, for dielectrics, special materials are being developed that allow, at a high specific capacitance of capacitors, to provide acceptable leakage currents. This is what explains such a variety of types and types of capacitors, each of which is designed for specific conditions.
They have the highest specific capacity (capacity / volume ratio). The capacity of "electrolytes" reaches up to 100,000 microfarad, operating voltage up to 600V. Such capacitors only work well at low frequencies, most often in power supply filters. Electrolytic capacitors are switched on with respect to polarity.
The electrodes in such capacitors are a thin film of metal oxide; therefore, these capacitors are often called oxide capacitors. A thin layer of air between such electrodes is not a very reliable insulator; therefore, an electrolyte layer is introduced between the oxide plates. Most often these are concentrated solutions of acids or alkalis.
Figure 3 shows one such capacitor.
Figure 3. Electrolytic capacitor
To estimate the size of the capacitor, a simple matchbox was photographed next to it. In addition to a fairly large capacity, the figure also shows a percentage tolerance: no less than 70% of the nominal.
In those days, when computers were large and were called computers, such capacitors were in disk drives (in the modern HDD). The information capacity of such drives can now only cause a smile: 5 megabytes of information were stored on two disks with a diameter of 350 mm, and the device itself weighed 54 kg.
The main purpose of the supercapacitors shown in the figure was to remove the magnetic heads from the working area of the disk in case of a sudden power outage. Such capacitors could store a charge for several years, which has been proven in practice.
Below, with electrolytic capacitors, it will be suggested to do some simple experiments in order to understand what a capacitor can do.
For work in AC circuits, non-polar electrolytic capacitors are produced, but for some reason it is very difficult to get them. To somehow get around this problem, conventional polar "electrolytes" include counter-sequential: plus-minus-minus-plus.
If a polar electrolytic capacitor is included in the alternating current circuit, then first it will warm up, and then an explosion will sound. Domestic old capacitors flew in all directions, while imported ones have a special device to avoid loud shots. This, as a rule, is either a cross notch on the bottom of the condenser, or a hole with a rubber stopper located in the same place.
They really do not like electrolytic capacitors with increased voltage, even if the polarity is observed. Therefore, it is never necessary to put "electrolytes" in a circuit where the expected voltage is close to the maximum for a given capacitor.
Sometimes in some, even reputable forums, beginners ask the question: "The diagram shows a 470µF * 16V capacitor, and I have 470µF * 50V, can I put it?" Yes, of course you can, but the reverse replacement is unacceptable.
A capacitor can store energy
A simple diagram shown in Figure 4 will help to deal with this statement.
Figure 4. Circuit with capacitor
The main protagonist of this circuit is an electrolytic capacitor C of a sufficiently large capacity so that the charging and discharging processes proceed slowly, and even very clearly. This makes it possible to observe the operation of the circuit visually using a conventional light bulb from a flashlight. These lanterns have long given way to modern LED lamps, but bulbs for them are still being sold. Therefore, it is very easy to assemble a circuit and carry out simple experiments.
Maybe someone will say: “Why? After all, and so everything is obvious, but if you also read the description ... ". There seems to be nothing to argue here, but any, even the simplest thing remains in the head for a long time, if its understanding came through the hands.
So, the diagram is assembled. How does it work?
In the position of the SA switch shown in the diagram, the capacitor C is charged from the power supply GB through the resistor R along the circuit: + GB __ R __ SA __ C __ -GB. The charging current in the diagram is shown by an arrow with the index iз. The process of charging a capacitor is shown in Figure 5.
Figure 5. Capacitor charging process
The figure shows that the voltage across the capacitor rises along a curved line, in mathematics called an exponential. The charge current directly mirrors the charge voltage. As the voltage across the capacitor rises, the charge current becomes less and less. And only at the initial moment it corresponds to the formula shown in the figure.
After a while, the capacitor will charge from 0V to the power supply voltage, in our circuit up to 4.5V. The whole question is how to determine this time, how long to wait, when the capacitor will be charged?
Time constant "tau" τ = R * C
This formula simply multiplies the resistance and capacitance of the series-connected resistor and capacitor. If, without neglecting the SI system, substitute the resistance in Ohms, the capacitance in Farads, then the result will be in seconds. It is this time that is required for the capacitor to charge up to 36.8% of the power supply voltage. Accordingly, it will take 5 * τ time to charge up to almost 100%.
Often, neglecting the SI system, they substitute the resistance in ohms into the formula, and the capacitance in microfarads, then the time will turn out in microseconds. In our case, it is more convenient to get the result in seconds, for which you have to simply multiply the microseconds by a million, or, more simply, move the comma six characters to the left.
For the circuit shown in Figure 4, with a capacitor capacitance of 2000μF and a resistor resistance of 500Ω, the time constant will turn out to be τ = R * C = 500 * 2000 = 1,000,000 microseconds or exactly one second. Thus, you will have to wait approximately 5 seconds for the capacitor to be fully charged.
If after the specified time the switch SA is moved to the right position, the capacitor C will be discharged through the EL lamp. At this moment, a short flash will turn out, the capacitor will be discharged and the lamp will go out. The direction of discharge of the capacitor is shown by an arrow with the index ip. The discharge time is also determined by the time constant τ. The discharge graph is shown in Figure 6.
Figure 6. Capacitor discharge graph
The capacitor does not pass direct current
An even simpler circuit, shown in Figure 7, will help to verify this statement.
Figure 7. Diagram with a capacitor in a DC link
If you close the SA switch, then a short flash of the light will follow, which indicates that the capacitor C has been charged through the light. The charge graph is also shown here: at the moment the switch closes, the current is maximum, as the capacitor is charged, it decreases, and after a while it stops completely.
If the capacitor is of good quality, i.e. with a low leakage current (self-discharge), re-closing the switch will not result in a flash. To get another flash, the capacitor will have to be discharged.
Capacitor in power filters
The capacitor is usually placed after the rectifier. Most often, rectifiers are made full-wave. The most common rectifier circuits are shown in Figure 8.
Figure 8. Rectifier circuits
Half-wave rectifiers are also used quite often, as a rule, in cases where the load power is insignificant. The most valuable quality of such rectifiers is simplicity: just one diode and a transformer winding.
For a full-wave rectifier, the capacitance of the filter capacitor can be calculated using the formula
C = 1000000 * Po / 2 * U * f * dU, where C is the capacitance of the capacitor μF, Po is the load power W, U is the voltage at the output of the rectifier V, f is the frequency of the alternating voltage Hz, dU is the amplitude of the ripple V.
A large number in the numerator 1,000,000 converts the capacitance of the capacitor from system farads to microfarads. The two in the denominator represents the number of half-cycles of the rectifier: for a half-cycle, one will appear in its place
C = 1,000,000 * Po / U * f * dU,
and for a three-phase rectifier, the formula will take the form C = 1,000,000 * Po / 3 * U * f * dU.
Supercapacitor - supercapacitor
Recently, a new class of electrolytic capacitors has appeared, the so-called. In terms of its properties, it is similar to a battery, albeit with several restrictions.
The supercapacitor is charged to the rated voltage within a short time, literally in a few minutes, so it is advisable to use it as a backup power source. In fact, a supercapacitor is a non-polar device, the only thing that determines its polarity is charging at the factory. In order not to confuse this polarity in the future, it is indicated by a + sign.
The operating conditions of the supercapacitors play an important role. At a temperature of 70˚C at a voltage of 0.8 of the nominal, the guaranteed service life is not more than 500 hours. If the device operates at a voltage of 0.6 of the nominal, and the temperature does not exceed 40 degrees, then correct operation is possible for 40,000 hours or more.
The most common application of a supercapacitor is in backup power supplies. These are mainly memory chips or electronic clocks. In this case, the main parameter of the supercapacitor is a low leakage current, its self-discharge.
The use of supercapacitors in conjunction with solar batteries is quite promising. It is also affected by the non-criticality to the charge condition and the practically unlimited number of charge-discharge cycles. Another valuable property is that the supercapacitor is maintenance-free.
So far it has turned out to tell how and where electrolytic capacitors work, and, moreover, mainly in direct current circuits. The work of capacitors in AC circuits will be discussed in another article -.
The simplest capacitor is a system of two flat conducting plates located parallel to each other at a small distance compared to the dimensions of the plates and separated by a dielectric layer. Such a capacitor is called flat ... The electric field of a flat capacitor is mainly localized between the plates (Fig. 1.6.1); however, a relatively weak electric field also arises near the edges of the plates and in the surrounding space, which is called scattering field ... In a number of problems, one can approximately neglect the stray field and assume that the electric field of a flat capacitor is entirely concentrated between its plates (Fig. 1.6.2). But in other problems, neglecting the scattering field can lead to gross errors, since this violates the potential character of the electric field ( see § 1.4).
Each of the charged plates of a flat capacitor creates an electric field near the surface, the modulus of strength of which is expressed by the ratio
According to the principle of superposition, the field strength created by both plates is equal to the sum of the strengths and fields of each of the plates:
Outside the plates are vectors and are directed in different directions, and therefore E= 0. The surface density σ of the charge of the plates is equal to q / S, where q- charge, and S Is the area of each plate. The potential difference Δφ between the plates in a uniform electric field is equal to Ed, where d Is the distance between the plates. From these ratios, you can get the formula for the electrical capacity of a flat capacitor:
Spherical and cylindrical condenser.
Examples of capacitors with different plate configurations are spherical and cylindrical capacitors. Spherical capacitor Is a system of two concentric conducting spheres of radii R 1 and R 2 . Cylindrical condenser - a system of two coaxial conducting cylinders of radii R 1 and R 2 and length L... The capacitances of these capacitors, filled with a dielectric with a dielectric constant ε, are expressed by the formulas:
Parallel and series connection of capacitors.
Capacitors can be interconnected to form capacitor banks. At parallel connection capacitors (Fig. 1.6.3) the voltages across the capacitors are the same: U 1 = U 2 = U and the charges are q 1 = C 1 U and q 2 = C 2 U... Such a system can be considered as a single capacitor of electrical capacity C charged with charge q = q 1 + q 2 when the voltage between the plates is equal to U... this implies
When connected in series (Fig. 1.6.4), the charges of both capacitors are the same: q 1 = q 2 = q, and the voltages across them are equal and Such a system can be considered as a single capacitor charged with a charge q with tension between plates U = U 1 + U 2. Hence,
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When capacitors are connected in series, the reciprocal values of the capacitances are added.
The formulas for parallel and series connection remain valid for any number of capacitors connected to the battery.
Electrical capacity
When a charge is imparted to a conductor, a potential φ appears on its surface, but if the same charge is communicated to another conductor, then the potential will be different. It depends on the geometric parameters of the conductor. But in any case, the potential φ is proportional to the charge q.
The SI unit of capacitance is farad. 1 F = 1Cl / 1V.
If the potential of the surface of the ball
 |
(5.4.3) |
 |
(5.4.4) |
More often in practice, smaller units of capacitance are used: 1 nF (nanofarad) = 10 –9 F and 1pcF (picofarad) = 10 –12 F.
There is a need for devices that store charge, and solitary conductors have a small capacity. Empirically, it was found that the electrical capacity of a conductor increases if another conductor is brought to it - due to electrostatic induction phenomena.
Capacitor Are two conductors called covers located close to each other .
The design is such that the external bodies surrounding the capacitor do not affect its electrical capacity. This will be done if the electrostatic field is concentrated inside the capacitor, between the plates.
Capacitors are available in flat, cylindrical and spherical capacitors.
Since the electrostatic field is inside the capacitor, the lines of electrical displacement start at the positive plate, end at the negative plate, and do not disappear anywhere. Consequently, the charges on the plates opposite in sign, but equal in magnitude.
The capacitance of a capacitor is equal to the ratio of the charge to the potential difference between the capacitor plates:
 |
(5.4.5) |
In addition to capacitance, each capacitor is characterized by U slave (or U etc . ) Is the maximum allowable voltage, above which breakdown occurs between the capacitor plates.
Connecting capacitors
Capacitive batteries- combinations of parallel and series connections of capacitors.
1) Parallel connection of capacitors (fig.5.9):
In this case, the common voltage is U:
Total charge:
Resulting capacity:
Compare with parallel connection of resistances R:
Thus, when capacitors are connected in parallel, the total capacitance
The total capacity is greater than the largest capacity in the battery.
2) Series connection of capacitors (fig.5.10):
Common is charge q.
Or 
, from here
| (5.4.6) |
Compare with serial connection R:
Thus, when capacitors are connected in series, the total capacity is less than the smallest capacity included in the battery:
Calculation of capacities of various capacitors
1.Capacitance of a flat capacitor
Field strength inside the capacitor (Figure 5.11):
Voltage between plates:
where is the distance between the plates.
Since the charge, then
 .
|
(5.4.7) |
As you can see from the formula, the dielectric constant of a substance has a very strong effect on the capacitance of a capacitor. This can be seen experimentally: we charge the electroscope, bring a metal plate to it - we got a capacitor (due to electrostatic induction, the potential has increased). If a dielectric with ε is introduced between the plates, more than that of air, then the capacitance of the capacitor will increase.
From (5.4.6) it is possible to obtain the units of measurement ε 0:
| (5.4.8) |
.
2. Cylindrical capacitor capacity
The potential difference between the plates of the cylindrical capacitor shown in Figure 5.12 can be calculated using the formula:
One of the most common electronic components is a capacitor. In conversation, such elements are called "capacity". The simplest design for manufacturing and calculations is a flat capacitor.
What is a flat capacitor
This concept refers to a structure consisting of two plates parallel to each other. The distance between them should be many times greater than the dimensions of the plates themselves. In this case, edge effects can be neglected. Otherwise, these effects become very important, and the formulas for calculating the capacity become too complex.
Important! Another name for these plates is plates.
Each of the electrodes creates around itself an electric field of the same magnitude and opposite direction: in the positively charged plate, q +, and in the negative - q-.
In a flat capacitor, the electric field is between the plates and is uniform. Its intensity is calculated by the formula:
E∑ = qεε0 * S, where:
- q is the charge of the electrodes;
- S is the area of the plates;
- ε is the dielectric constant of the material between them - a parameter that determines how many times the effect of charges on each other is stronger than in vacuum ;
- Fmε0 = 8.85 * 10−12 f / m - electrical constant.
What determines the capacitance of a capacitor
To calculate the capacity, the formula is applied:
C = ε * ε0 * Sd, where:
- S is the area of the plates;
- d is the distance between them;
- Fmε0 = 8.85 * 10−12 f / m - electrical constant;
- ε is the dielectric constant of the insulating material between the electrodes.
Thus, the capacitance depends on the area of the plates, the distance between them and the dielectric constant of the insulating material.
To reduce the size of the "sandwich" of flat electrodes with an insulator between them is rolled up. Provided that the thickness of the insulator is many times smaller than the radius of the cylinder, the latter can be neglected.
Another way to increase the capacitance is to reduce the distance between the plates, while the electrical strength decreases - the voltage at which the capacitor breaks down and fails.
Interesting. In a new type of capacitors - supercapacitors, activated carbon or graphene are used as plates, the porous structure of which allows the capacitance of the elements to be increased many times over (up to several farads).
Charge and discharge of capacitors
Free electrons are charge carriers in metals. When the device is connected to a voltage source: a battery, accumulator or network, electrons from the plate connected to the positive pole of the battery will rush into the power source, and the plate will be charged positively. Electrons will begin to flow into the plate connected to the negative pole. This process is depicted in the figure below.
This increases the strength of the electric field in the device between the electrodes and the voltage across the device. This process will end when the voltage between the terminals of the element becomes equal to the mains voltage. In this case, a certain amount of energy will be stored inside it, which is calculated by the formula:
E = (U² * C) / 2, where:
- E - energy (J);
- U - voltage (V);
- C - capacitance (μF).
When the device is connected to the load circuit, excess electrons from the negative terminal through the load will begin to flow to the positive terminal. This movement will end when the potential is equalized between the terminals.
This process cannot happen instantly, which allows the use of capacitors as a filter that smooths out voltage ripples in the network.
Important! A charged capacitor does not pass direct current, since the dielectric between its plates opens the circuit.
Calculation of the capacity of flat capacitors
The capacity of an ideal device, in which there is air between the plates, can be calculated using the formula:
Co = Q / U, where:
- Co - capacity;
- Q is the charge on one of the plates of the device;
- U is the potential difference or voltage between the terminals.
This parameter depends only on the voltage and the accumulated charge, but they change with changes in the distance between the plates and the type of dielectric between them. This is taken into account in the formula:
С = Co * ε, where:
- С - real capacity;
- So - perfect;
- ε is the dielectric constant of the insulating material.
The unit of capacity is 1 farad (1F, 1F). There are also smaller values:
- Microfarads (1mkF, 1mkF). 1000000mkF = 1F;
- Picofarads (1pF, 1pF). 1000000pF = 1mkF.
Allowable voltage
In addition to capacity, an important parameter affecting the use of an element and its dimensions is the permissible voltage. This is the value of the potential difference at the terminals of the device, if exceeded, there will be an electrical breakdown of the dielectric between the plates, a short circuit inside the structure and its failure.
In the absence of an element with the required parameters, the existing devices can be connected together.
There are three types of connections: serial, parallel and mixed, which is a combination of parallel and serial.
Serial connection calculation
With this type of connection, the charges on all plates are the same:
This is because the power supply voltage is supplied only to the outer terminals of the outermost elements. In this case, there is a transfer of charge from one electrode to another.
In this case, the voltage is distributed inversely proportional to the capacity:
U1 = Q / C1, U2 = Q / C2,…, Un = Q / Cn.
The final voltage is equal to the mains voltage:
Uset = U1 + U2 +… + Un.
Equivalent capacity is determined by the formulas:
- С = Q / U = Q / (U1 + U2 + ... + Un),
- С = 1 / С1 + 1 / С2 + ... + 1 / Cn,
- or the addition of conductivities.
Reference. Conductivity is the reciprocal of resistance.
Parallel connection calculation
When connected in parallel, the plates of the elements are connected in pairs. The voltage on all devices is equal to each other, and the charges differ depending on the capacity:
Q1 = C1U, Q2 = C2U,… Qn = CnU.
The total charge of the system is equal to the total amount on all elements:
a the total capacity is equal to the total for all devices:
C = Q / U = (Q1 + Q2 +… + Qn) / U = C1 + C2 +… Cn.
How to check the capacitance of a capacitor
In the absence of markings on the case of the device or in doubt about its serviceability, the capacitance of the capacitor is determined with a multimeter, which has the appropriate functions, or with an ordinary voltmeter and ammeter.
Checking by measuring the charging time
When a capacitive element is connected to a DC network through a resistance, the voltage at its terminals grows exponentially and over a period of time 3R * C will become equal to 95% of U of the network.
Accordingly, knowing the value of the resistor, the parameters of the capacitor are determined by the formula:
The resistor value depends on the expected parameters of the measured element and is determined empirically.
Important! In this way, you can determine the capacitance of the capacitor from 0.25 μF and above.
Capacitance measurement
In addition to determining the charging time, you can find out the capacitive resistance. It depends on the frequency of the voltage at the terminals of the device:
Xc = 1/2 * π * f * C, where:
- Xc - capacitive resistance;
- π - number "pi" (3.14);
- f - mains frequency (in 50Hz socket);
- C is the capacitance of the capacitor.
Having connected the capacitor to the network, Xc can be determined in two ways:
- knowing the voltage of the network and the current flowing in it according to Ohm's law:
- connect a 10 kOhm resistor in series with the measured element, measure the voltage on all parts, and the capacitive resistance is determined by the formula Xc = (Ur * Uc) / R.
Serviceability check with a tester
If it is necessary to check the serviceability of an electronic device, but it is not possible to make long-term measurements, then this can be done with a tester or LED dial tone. To do this, you need to connect the tester to the terminals. On a working device, the tester will show a circuit during charging, and after its completion, an open circuit. Reversing the polarity doubles the charging time.
Knowledge of how the capacity of a flat capacitor is calculated and checked is necessary in the design and repair of electrical appliances and electronic equipment.
Video
As you know, there is an electric field around charged bodies that has energy.
Is it possible to accumulate charges and energy of an electric field? The device that allows the accumulation of charges is capacitor(from Lat.condensare - condensation). The simplest flat capacitor consists of two identical metal plates - plates, located at a small distance from each other and separated by a dielectric layer, for example, air (Fig. 83). The dielectric thickness is small in comparison with the dimensions of the plates.
Rice. 83. The simplest capacitor and its designation in the diagram
Let us demonstrate by experience the ability of a capacitor to store charges. To do this, connect two metal plates to different poles of the electrophoretic machine (Fig. 84). The plates will receive charges of the same modulus, but different in sign. An electric field will appear. The capacitor's electric field is practically concentrated between the plates inside the capacitor.
Rice. 84. Charging a capacitor from an electric machine
After turning off the electrophoretic machine, the charges on the plates and the electric field between them will remain.
If the plates of a charged capacitor are connected with a conductor, then a current will flow through the conductor for some time. This means that a charged capacitor is a current source.
Depending on the dielectric, there are several types of capacitors: with solid, liquid and gaseous dielectric. They are also distinguished by the shape of the plates: flat, cylindrical, spherical, etc. (Fig. 85).
Rice. 85. Different types of capacitors
The property of a capacitor to accumulate electrical charges is characterized by electrical capacity, or capacity. In order to understand what this physical quantity depends on, let us turn to experience.
We connect two metal plates, fixed on insulating supports parallel to each other, with an electrometer. We connect one of the plates to the rod of the electrometer, and the other to ground by connecting it to the body of the device (Fig. 86, a). Let us touch the outer side of plate A with an electrified ball, thereby imparting a positive charge + q to it. Under the action of the electric field of plate A, a redistribution of charges will occur in plate B: negative charges will be located on the inner side of the plate. Free electrons will come from the ground to neutralize the positive charges on the outside of plate B. Thus, an equal negative charge -q will appear on plate B.
Rice. 86. Dependence of the capacitance of the capacitor on the area, the distance between the plates, the dielectric between the plates
The electrometer needle will deviate from the zero position. With the help of equally charged balls, we will continue to transfer charges to the capacitor in successive equal portions. We will notice that with an increase in the charge by 2, 3, 4 times, respectively, the readings of the electrometer will increase by 2, 3, 4 times, i.e., the voltage between the capacitor plates will increase. Moreover, the ratio of charge to voltage will remain constant:
The value measured by the ratio of the charge of one of the capacitor plates to the voltage between the plates is called the capacitance of the capacitor.
The capacitance of a capacitor is calculated by the formula:
The unit of capacity in SI is the farad (F), the name is given in honor of the English physicist Michael Faraday. The capacitance of a capacitor is equal to unity if, when a charge of 1 C is imparted to it, a voltage of 1V occurs.
1 F is a very large capacity, therefore, in practice, microfarad (μF) and picofarad (pF) are used.
1 μF = 10 -6 F; 1 pF = 10 -12 F.
Let's find out what determines the capacity of the condenser. To do this, take a capacitor with plates having a large area (Fig. 86, b). Let's repeat the experience. The charge-to-voltage ratio remains constant in this case.
but the ratio of charge to voltage is now greater than in the first experiment, i.e. C1> C. The larger the area of the plates, the larger the capacitance of the capacitor..
Let's do the first experiment again, but now we will change the distance between the plates (Fig. 86, c). As the distance between the plates decreases, the stress between them decreases. With a decrease in the distance between the plates of the capacitor with a constant charge, the capacitance of the capacitor increases.
Let's do one more experiment. Let's install the plates of the capacitor A and B at some distance from each other. We charge plate A. Note the readings of the electrometer when there is air between the plates. We place a sheet of plexiglass or another dielectric between the plates (Fig. 86, d). We will notice that the tension between the plates will decrease. Consequently, the capacitance of the capacitor depends on the properties of the introduced dielectric.
When a dielectric is introduced, the capacitance of the capacitor increases.
A capacitor, like any charged body, has energy. Let's check it out by experience. Let's charge the capacitor and connect a light bulb to it. The light will flash brightly. This indicates that the charged capacitor has energy. The energy from the capacitor is converted into internal energy from the lamp filament and wires. In order to charge the capacitor, work had to be done to separate the positive and negative charges. In accordance with the law of conservation of energy, the work done A is equal to the energy of the capacitor E, i.e.
where E is the energy of the capacitor.
The work that the electric field of a capacitor does can be found by the formula:
where Uav is the average voltage value.
Since the voltage does not remain constant during the discharge process, it is necessary to find the average voltage value:
Uav = U / 2; then A = qU cf = qU / 2,
since q = CU, then A = CU 2/2.
This means that the energy of a capacitor with a capacity of C will be equal to:
Capacitors can store energy for a long time, and when they are discharged, they give it up almost instantly. The property of a capacitor to accumulate and quickly release electrical energy is widely used in electrical and electronic devices, in medical technology (X-ray equipment, electrotherapy devices), in the manufacture of dosimeters, and aerial photography.
Questions
- What are capacitors for?
- What characterizes the capacitance of a capacitor?
- What is the SI unit of electrical capacity?
- What determines the capacitance of a capacitor?
Exercise # 38
- The plates of a flat capacitor are connected to a voltage source of 220 V. The capacitance of the capacitor is 1.5 10 -4 μF. What will the capacitor charge be equal to?
- The charge of a flat capacitor is 2.7 10 -2 C, its capacity is 0.01 μF. Find the voltage between the plates of the capacitor.
Exercise
- Using the Internet, find out how the first capacitor was arranged - the Leyden bank. Make it.
- Prepare a talk about the history of the capacitor.
