A typical capacitor with the circuit designation “C” belongs to the category of the most common radio components operating in both AC and AC circuits. direct current. In the first case, it is used as a blocking element and capacitive load, and in the second - as a filter link in rectifier circuits with pulsating current. Capacitor in a circuit alternating current looks like it is shown in the figure below.

Unlike another common radio component called a resistor, a capacitor in an AC circuit introduces a reactive component into it, which leads to the formation of a phase shift between the applied emf and the current caused by it. Let's get acquainted with what the reactive component and capacitive reactance are in more detail.

Inclusion of sinusoidal EMF in the circuit

Types of inclusions

As is known, a capacitor in a direct current circuit (without an alternating component) cannot work.

Note! This statement does not apply to smoothing filters where pulsating current flows, as well as special blocking circuits.

A completely different picture is observed if we consider the inclusion of this element in an alternating current circuit, in which it begins to behave more actively and can perform several functions at once. In this case, the capacitor can be used for the following purposes:

• To block the DC component, always present in any electronic circuit;
• In order to create resistance in the path of propagation of high-frequency (HF) components of the processed signal;
• As a capacitive load element that sets the frequency characteristics of the circuit;
• As an element of oscillatory circuits and special filters (LF and HF).

From all of the above, it is immediately clear that in the vast majority of cases, a capacitor in an alternating current circuit is used as a frequency-dependent element that can have a certain effect on the signals flowing through it.

The simplest type of inclusion

The processes occurring during this switching on are shown in the figure below.

They can be described by introducing the concept of harmonic (sinusoidal) emf, expressed asU = Uo cos ω t, and look like this:

• As the EMF variable increases, the capacitor is charged by the electric current I flowing through it, which is maximum at the initial moment of time. As the capacity is charged, the value of the charging current gradually decreases and is completely zeroed at the moment when the EMF reaches its maximum;

Important! Such a multidirectional change in current and voltage leads to the formation between them of a 90-degree phase shift characteristic of this element.

• This ends the first quarter of the periodic oscillation;
• Further, the sinusoidal EMF gradually decreases, as a result of which the capacitor begins to discharge, and at this time a current increasing in amplitude flows in the circuit. In this case, the same phase lag is observed that was in the first quarter of the period;
• Upon completion of this stage, the capacitor is completely discharged (with the EMF equal to zero), and the current in the circuit reaches its maximum;
• As the reverse (discharge) current increases, the capacity is recharged, as a result of which the current gradually decreases to zero, and the EMF reaches its peak value (that is, the whole process returns to the starting point).

Further, all the described processes are repeated with a frequency specified by the frequency of the external EMF. The phase shift between current and EMF can be considered as a kind of resistance to a change in voltage on the capacitor (its lag behind current fluctuations).

Capacitance

Concept of capacity

When studying the processes occurring in circuits with a capacitor connected to them, it was discovered that the charge and discharge times for different samples of this element differ significantly from one another. Based on this fact, the concept of capacitance was introduced, defined as the ability of a capacitor to accumulate charge under the influence of a given voltage:

After this, the change in charge on its plates over time can be represented as:

But sinceQ= C.U., then through simple calculations we get:

I = CxdU/dt = ω C Uo cos ω t = Io sin(ω t+90),

that is, the current flows through the capacitor in such a way that it begins to lead the voltage by 90 degrees in phase. The same result is obtained when using other mathematical approaches to this electrical process.

Vector representation

For greater clarity, electrical engineering uses a vector representation of the processes considered, and to quantify the slowdown of the reaction, the concept of capacitance is introduced (see photo below).

The vector diagram also shows that the current in the capacitor circuit is 90 degrees ahead of the voltage in phase.

Additional Information. When studying the “behavior” of a coil in a sinusoidal current circuit, it was discovered that in it, on the contrary, it lags in phase with the voltage.

In both cases, there is a difference in the phase characteristics of the processes, indicating the reactive nature of the load in the alternating EMF circuit.

Ignoring differential calculations that are difficult to describe, to represent the resistance of a capacitive load we obtain:

It follows from it that the resistance created by the capacitor is inversely proportional to the frequency of the alternating signal and the capacitance of the element installed in the circuit. This dependence allows you to build on the basis of a capacitor such frequency-dependent circuits as:

• Integrating and differentiating chains (together with a passive resistor);
• LF and HF filter elements;
• Reactive circuits used to improve the load characteristics of power equipment;
• Resonant circuits of series and parallel type.

In the first case, using a capacitance, it is possible to arbitrarily change the shape of rectangular pulses, increasing their duration (integration) or shortening it (differentiation).

Filter chains and resonant circuits are widely used in linear circuits of various classes (amplifiers, converters, generators and similar devices).

Capacitance graph

It has been proven that current flows through a capacitor only under the influence of a harmonically varying voltage. In this case, the current strength in the circuit is determined by the capacitance of a given element, so the greater the capacitance of the capacitor, the greater its value.

But we can also trace an inverse relationship, according to which the resistance of the capacitor increases with decreasing frequency parameter. As an example, consider the graph shown in the figure below.

From the above dependence, the following important conclusions can be drawn:

• For a constant current (frequency = 0) Xc is equal to infinity, which means that it cannot flow in it;
• At very high frequencies, the resistance of this element tends to zero;
• All other things being equal, it is determined by the capacitance of the capacitor installed in the circuit.

Of particular interest are the issues of distribution of electrical energy in alternating current circuits with a capacitor included in them.

Work (power) in a capacitive load

Similar to the case with inductance, when studying the “behavior” of a capacitor in variable EMF circuits, it was discovered that there is no power consumption in them due to the phase shift of U and I. The latter is explained by the fact that electrical energy at the initial stage of the process (during charging) is stored between the plates of the capacitor, and at the second stage it is given back to the source (see figure below).

As a result, capacitance falls into the category of reactive, or wattless, loads. However, such a conclusion can be considered purely theoretical, since in real circuits there are always ordinary passive elements that have not reactive, but active or watt resistance. These include:

• Lead wire resistance;
• Conductivity of dielectric zones in a capacitor;
• Contact scattering;
• Active resistance of coil turns and the like.

In this regard, in any real electrical circuit there are always losses of active power (its dissipation), determined in each case individually.

Particular attention should be paid to internal losses associated with leaks through the dielectric and poor insulation between the plates (plates). Let us turn to the following definitions, taking into account the real state of affairs. Thus, losses associated with the qualitative characteristics of a dielectric are called dielectric. Energy costs attributed to the imperfection of the insulation between the plates are usually classified as losses due to leaks in the capacitor element.

At the end of this review, it is interesting to follow one analogy representing the processes occurring in a capacitor circuit with an elastic mechanical spring. And, indeed, a spring, like this element, accumulates potential energy in itself during one part of the periodic oscillation, and in the second phase it releases it back in kinetic form. Based on this analogy, the whole picture of the behavior of a capacitor in circuits with variable EMF can be presented.

Video

A lot has been written about capacitors, is it worth adding a couple thousand more words to the millions that already exist? I'll add it! I believe that my presentation will be useful. After all, it will be done taking into account.

What is an electric capacitor

Speaking in Russian, a capacitor can be called a “storage device”. It's even clearer this way. Moreover, this is exactly how this name is translated into our language. A glass can also be called a capacitor. Only it accumulates liquid in itself. Or a bag. Yes, a bag. It turns out it's also a storage device. It accumulates everything that we put in there. What does the electric capacitor have to do with it? It is the same as a glass or a bag, but it only accumulates an electrical charge.

Imagine the picture: a chain passes electricity, on its way there are resistors, conductors and, bam, a capacitor (glass) has appeared. What will happen? As you know, current is a flow of electrons, and each electron has an electrical charge. Thus, when someone says that a current is passing through a circuit, you imagine millions of electrons flowing through the circuit. It is these same electrons, when a capacitor appears in their path, that accumulate. The more electrons we put into the capacitor, the greater its charge will be.

The question arises: how many electrons can be accumulated in this way, how many will fit into the capacitor and when will it “get enough”? Let's find out. Very often, for a simplified explanation of simple electrical processes use a comparison with water and pipes. Let's use this approach too.

Imagine a pipe through which water flows. At one end of the pipe there is a pump that forcefully pumps water into this pipe. Then mentally place a rubber membrane across the pipe. What will happen? The membrane will begin to stretch and strain under the influence of water pressure in the pipe (pressure created by the pump). It will stretch, stretch, stretch, and eventually the elastic force of the membrane will either balance the force of the pump and the flow of water will stop, or the membrane will break (If this is not clear, then imagine a balloon that will burst if it is pumped too much)! The same thing happens in electrical capacitors. Only there instead of a membrane it is used electric field, which increases as the capacitor charges and gradually balances the voltage of the power source.

Thus, the capacitor has a certain limiting charge that it can accumulate and, after exceeding which, it will occur dielectric breakdown in a capacitor it will break and cease to be a capacitor. It’s probably time to tell you how a capacitor works.

How does an electric capacitor work?

At school you were told that a capacitor is a thing that consists of two plates and a void between them. These plates were called capacitor plates and wires were connected to them to supply voltage to the capacitor. So modern capacitors are not much different. They all also have plates and there is a dielectric between the plates. Thanks to the presence of a dielectric, the characteristics of the capacitor are improved. For example, its capacity.

Modern capacitors use different types of dielectrics (more on this below), which are stuffed between the capacitor plates in the most sophisticated ways to achieve certain characteristics.

Principle of operation

The general principle of operation is quite simple: voltage is applied and the charge is accumulated. Physical processes, which are happening now should not interest you much, but if you want, you can read about it in any book on physics in the electrostatics section.

Capacitor in DC circuit

If we place our capacitor in electrical circuit(Fig. below), connect an ammeter in series with it and apply direct current to the circuit, then the ammeter needle will twitch briefly, and then freeze and show 0A - no current in the circuit. What's happened?

We will assume that before current was applied to the circuit, the capacitor was empty (discharged), and when current was applied, it began to charge very quickly, and when it was charged (the electric field between the plates of the capacitor balanced the power source), then the current stopped (here is a graph of the capacitor charge).

This is why they say that a capacitor does not allow direct current to pass through. In fact, it passes, but for a very short time, which can be calculated using the formula t = 3*R*C (Time of charging the capacitor to 95% of the nominal volume. R is the circuit resistance, C is the capacitance of the capacitor) This is how the capacitor behaves in a DC circuit current It behaves completely differently in a variable circuit!

Capacitor in AC circuit

What is alternating current? This is when electrons “run” first there, then back. Those. the direction of their movement changes all the time. Then, if alternating current runs through the circuit with the capacitor, then either a “+” charge or a “-” charge will accumulate on each of its plates. Those. AC current will actually flow. This means that alternating current flows “unimpeded” through the capacitor.

This entire process can be modeled using the method of hydraulic analogies. The picture below shows an analogue of an AC circuit. The piston pushes the liquid forward and backward. This causes the impeller to rotate back and forth. It turns out to be an alternating flow of liquid (we read alternating current).

Let's now place a capacitor medel in the form of a membrane between the source of force (piston) and the impeller and analyze what will change.

It looks like nothing will change. Just as the liquid performed oscillatory movements, so it continues to do so, just as the impeller oscillated because of this, so it will continue to oscillate. This means that our membrane is not an obstacle to variable flow. The same will be true for an electronic capacitor.

The fact is that even though the electrons that run in a chain do not cross the dielectric (membrane) between the plates of the capacitor, outside the capacitor their movement is oscillatory (back and forth), i.e. alternating current flows. Eh!

Thus, the capacitor passes alternating current and blocks direct current. This is very convenient when you need to remove the DC component in the signal, for example, at the output/input of an audio amplifier or when you need to look only at the variable part of the signal (ripple at the output of a DC voltage source).

Capacitor reactance

The capacitor has resistance! In principle, this could be assumed from the fact that direct current does not pass through it, as if it were a resistor with a very high resistance.

An alternating current is another matter - it passes, but experiences resistance from the capacitor:

f - frequency, C - capacitance of the capacitor. If you look carefully at the formula, you will see that if the current is constant, then f = 0 and then (may militant mathematicians forgive me!) X c = infinity. And there is no direct current through the capacitor.

But the resistance to alternating current will change depending on its frequency and the capacitance of the capacitor. The higher the frequency of the current and the capacitance of the capacitor, the less it resists this current and vice versa. The faster the voltage changes
voltage, the greater the current through the capacitor, this explains the decrease in Xc with increasing frequency.

By the way, another feature of the capacitor is that it does not release power and does not heat up! Therefore, it is sometimes used to dampen voltage where the resistor would smoke. For example, to reduce the network voltage from 220V to 127V. And further:

The current in a capacitor is proportional to the speed of the voltage applied to its terminals

Where are capacitors used?

Yes, wherever their properties are required (not allowing direct current to pass through, the ability to accumulate electrical energy and change their resistance depending on frequency), in filters, in oscillatory circuits, in voltage multipliers, etc.

What types of capacitors are there?

The industry produces many different types capacitors. Each of them has certain advantages and disadvantages. Some have a low leakage current, others have a large capacity, and others have something else. Depending on these indicators, capacitors are selected.

Radio amateurs, especially beginners like us, don’t bother too much and bet on what they can find. Nevertheless, you should know what main types of capacitors exist in nature.

The picture shows a very conventional separation of capacitors. I compiled it to my taste and I like it because it is immediately clear whether variable capacitors exist, what types of permanent capacitors there are, and what dielectrics are used in common capacitors. In general, everything a radio amateur needs.

They have low leakage current, small dimensions, low inductance, and are capable of operating at high frequencies and in DC, pulsating and alternating current circuits.

They are produced in a wide range of operating voltages and capacities: from 2 to 20,000 pF and, depending on the design, withstand voltages up to 30 kV. But most often you will find ceramic capacitors with an operating voltage of up to 50V.

Honestly, I don’t know if they are being released now. But previously, mica was used as a dielectric in such capacitors. And the capacitor itself consisted of a pack of mica plates, on each of which plates were applied on both sides, and then such plates were collected into a “package” and packed into a case.

They typically had a capacity of several thousand to tens of thousands of picoforads and operated in a voltage range from 200 V to 1500 V.

Paper capacitors

Such capacitors have capacitor paper as a dielectric, and aluminum strips as plates. Long strips of aluminum foil with a strip of paper sandwiched between them are rolled up and packed into a housing. That's the trick.

Such capacitors come in capacities ranging from thousands of picoforads to 30 microforads, and can withstand voltages from 160 to 1500 V.

Rumor has it that they are now prized by audiophiles. I’m not surprised - they also have single-sided conductor wires...

In principle, ordinary capacitors with polyester as a dielectric. The range of capacitances is from 1 nF to 15 mF at an operating voltage from 50 V to 1500 V.

Capacitors of this type have two undeniable advantages. First, they can be made with a very small tolerance of only 1%. So, if it says 100 pF, then its capacitance is 100 pF +/- 1%. And the second is that their operating voltage can reach up to 3 kV (and the capacitance from 100 pF to 10 mF)

Electrolytic capacitors

These capacitors differ from all others in that they can only be connected to a direct or pulsating current circuit. They are polar. They have a plus and a minus. This is due to their design. And if such a capacitor is turned on in reverse, it will most likely swell. And before they also exploded cheerfully, but unsafely. There are electrolytic capacitors made of aluminum and tantalum.

Aluminum electrolytic capacitors are designed almost like paper capacitors, with the only difference being that the plates of such a capacitor are paper and aluminum strips. The paper is impregnated with electrolyte, and a thin layer of oxide is applied to the aluminum strip, which acts as a dielectric. If you apply alternating current to such a capacitor or turn it back to the output polarities, the electrolyte will boil and the capacitor will fail.

Electrolytic capacitors have a fairly large capacity, which is why they are, for example, often used in rectifier circuits.

That's probably all. Left behind the scenes are capacitors with a dielectric made of polycarbonate, polystyrene, and probably many other types. But I think that this will be superfluous.

To be continued...

In part two I plan to show examples of typical uses of capacitors.

This can be easily confirmed by experiments. You can light a light bulb by connecting it to an AC power supply through a capacitor. The loudspeaker or handsets will continue to work if they are connected to the receiver not directly, but through a capacitor.

A capacitor consists of two or more metal plates separated by a dielectric. This dielectric is most often mica, air or ceramics, which are the best insulators. It is quite natural that direct current cannot pass through such an insulator. But why does alternating current pass through it? This seems all the more strange since the same ceramics in the form of, for example, porcelain rollers perfectly insulate alternating current wires, and mica perfectly functions as an insulator in electric irons and other heating devices that operate properly on alternating current.

Through some experiments we could “prove” an even stranger fact: if in a capacitor a dielectric with comparatively poor insulating properties is replaced by another dielectric that is a better insulator, then the properties of the capacitor will change so that the passage of alternating current through the capacitor will not be hindered, but rather on the contrary, it is facilitated. For example, if you connect a light bulb to an alternating current circuit through a capacitor with a paper dielectric and then replace the paper with such an excellent insulator; like glass or porcelain of the same thickness, the light bulb will begin to burn brighter. Such an experiment will lead to the conclusion that alternating current not only passes through the capacitor, but that it also passes the more easily the better the insulator its dielectric is.

However, despite all the apparent convincingness of such experiments, electric current - neither direct nor alternating - does not pass through the capacitor. The dielectric separating the plates of the capacitor serves as a reliable barrier to the path of current, whatever it may be - alternating or direct. But this does not mean that there will be no current in the entire circuit in which the capacitor is connected.

A capacitor has a certain physical property that we call capacitance. This property consists of the ability to accumulate electrical charges on the plates. A source of electric current can be roughly likened to a pump that pumps electrical charges into a circuit. If the current is constant, then electrical charges are pumped all the time in one direction.

How will a capacitor behave in a DC circuit?

Our “electric pump” will pump charges onto one of its plates and pump them out from the other plate. The ability of a capacitor to hold a certain difference in the number of charges on its plates is called its capacity. The larger the capacitor capacity, the more electric charges may be on one facing versus another.

At the moment the current is turned on, the capacitor is not charged - the number of charges on its plates is the same. But the current is on. The “electric pump” started working. He drove the charges onto one plate and began pumping them out from the other. Once the movement of charges begins in the circuit, it means that current begins to flow in it. Current will flow until the capacitor is fully charged. Once this limit is reached, the current will stop.

Therefore, if there is a capacitor in a DC circuit, then after it is closed, the current will flow in it for as long as it takes to fully charge the capacitor.

If the resistance of the circuit through which the capacitor is charged is relatively small, then the charging time is very short: it lasts an insignificant fraction of a second, after which the current flow stops.

The situation is different in the alternating current circuit. In this circuit, the “pump” pumps electrical charges in one direction or the other. Having barely created an excess of charges on one plate of the capacitor compared to the number on the other plate, the pump begins to pump them in the opposite direction. Charges will circulate continuously in the circuit, which means that, despite the presence of a non-conducting capacitor, there will be a current in it - the charge and discharge current of the capacitor.

What will the magnitude of this current depend on?

By current magnitude we mean the number of electrical charges flowing per unit time through the cross section of a conductor. The greater the capacitance of the capacitor, the more charges will be required to “fill” it, which means the stronger the current in the circuit will be. The capacitance of a capacitor depends on the size of the plates, the distance between them and the type of dielectric separating them, its dielectric constant. Porcelain has a greater dielectric constant than paper, so when replacing paper with porcelain in a capacitor, the current in the circuit increases, although porcelain is a better insulator than paper.

The magnitude of the current also depends on its frequency. The higher the frequency, the greater the current will be. It is easy to understand why this happens by imagining that we fill a container with a capacity of, for example, 1 liter with water through a tube and then pump it out from there. If this process is repeated once per second, then 2 liters of water will flow through the tube per second: 1 liter in one direction and 1 liter in the other. But if we double the frequency of the process: we fill and empty the vessel 2 times per second, then 4 liters of water will flow through the tube per second - increasing the frequency of the process with the same capacity of the vessel led to a corresponding increase in the amount of water flowing through the tube.

From all that has been said, the following conclusions can be drawn: electric current - neither direct nor alternating - does not pass through the capacitor. But in the circuit connecting the AC source to the capacitor, the charge and discharge current of this capacitor flows. The larger the capacitance of the capacitor and the higher the frequency of the current, the stronger this current will be.

This feature of alternating current is extremely widely used in radio engineering. The emission of radio waves is also based on it. To do this, we excite a high-frequency alternating current in the transmitting antenna. But why does current flow in the antenna, since it is not a closed circuit? It flows because there is capacitance between the antenna and counterweight wires or ground. The current in the antenna represents the charge and discharge current of this capacitor, this capacitor.

Gentlemen, in today's article I would like to consider this interest Ask, How AC capacitor. This topic is very important in electricity, since in practice capacitors are ubiquitous in circuits with alternating current and, in this regard, it is very useful to have a clear understanding of the laws by which signals change in this case. We will consider these laws today, and at the end we will solve one practical problem determining the current through a capacitor.

Gentlemen, now the most interesting point for us is how the voltage on the capacitor and the current through the capacitor are related to each other for the case when the capacitor is in the alternating signal circuit.

Why immediately variable? Yes, simply because the capacitor is in the circuit direct current unremarkable. Current flows through it only at the first moment while the capacitor is discharged. Then the capacitor is charged and that’s it, there is no current (yes, yes, I hear people have already started shouting that the charge of the capacitor theoretically lasts for an infinitely long time, and it may also have a leakage resistance, but for now we are neglecting this). Charged capacitor for permanent current - How is that open circuit. When do we have a chance variable current - everything is much more interesting here. It turns out that in this case current can flow through the capacitor and the capacitor in this case is, as it were, equivalent resistor with some well-defined resistance (if you forget about all sorts of phase shifts for now, more on that below). We need to somehow obtain a relationship between the current and voltage across the capacitor.

For now we will assume that in the AC circuit there is only a capacitor and that’s it. Without any other components such as resistors or inductors. Let me remind you that in the case when we have only resistors in the circuit, such a problem is solved very simply: current and voltage are interconnected through Ohm's law. We have talked about this more than once. Everything is very simple there: divide the voltage by the resistance and get the current. But what about the capacitor? After all, a capacitor is not a resistor. The physics of the processes there is completely different, so it’s not possible to simply connect current and voltage with each other just like that. Nevertheless, this must be done, so let's try to reason.

First let's go back. Far back. Even very far away. To my very, very first article on this site. Old-timers may remember that this was an article about current strength. In this very article there was one interesting expression that connected the strength of the current and the charge flowing through the cross-section of the conductor. This is the very expression

Someone might argue that in that article about current strength the entry was through Δq And Δt- some very small amounts of charge and the time during which this charge passes through the cross section of the conductor. However, here we will use the notation via dq And dt- through differentials. We will need such a representation later. If you don’t go deep into the wilds of matan, then essentially dq And dt there is no particular difference here from Δq And Δt. Of course, people deeply knowledgeable in higher mathematics can argue with this statement, but right now I don’t want to concentrate on these things.

So, we remembered the expression for current strength. Let's now remember how the capacitance of a capacitor is related to each other WITH, charge q, which he has accumulated in himself, and the tension U on the capacitor, which was formed in this case. Well, we remember that if a capacitor has accumulated some kind of charge, then voltage will inevitably arise on its plates. We also talked about this all before, in this article. We will need this formula, which just connects charge with voltage

Let's express the charge of the capacitor from this formula:

And now there is a very big temptation to substitute this expression for the charge of the capacitor into the previous formula for the current strength. Take a closer look - then the current strength, the capacitance of the capacitor and the voltage on the capacitor will be interconnected! Let's do this substitution without delay:

Our capacitance is the quantity constant. It is determined solely by the capacitor itself, its internal structure, dielectric type and all that other stuff. We talked about all this in detail in one of the previous articles. Therefore, the capacity WITH the capacitor, since it is a constant, can be safely taken out as a differential sign (these are the rules for working with these same differentials). But with tension U You can't do that! The voltage across the capacitor will change over time. Why is this happening? The answer is elementary: as current flows across the plates of the capacitor, obviously, the charge will change. And a change in charge will certainly lead to a change in the voltage across the capacitor. Therefore, voltage can be considered as a certain function of time and cannot be removed from under the differential. So, having carried out the transformations specified above, we get the following entry:

Gentlemen, I hasten to congratulate you - we have just received a very useful expression that relates the voltage applied to a capacitor and the current that flows through it. Thus, if we know the law of change of voltage, we can easily find the law of change of current through a capacitor by simply finding the derivative.

But what about the opposite case? Let's say we know the law of change in current through a capacitor and we want to find the law of change in voltage across it. Readers knowledgeable in mathematics have probably already guessed that to solve this problem it is enough to simply integrate the expression written above. That is, the result will look something like this:

In fact, both of these expressions are about the same thing. It’s just that the first is used in the case when we know the law of change in voltage across the capacitor and we want to find the law of change in the current through it, and the second when we know how the current changes through the capacitor and we want to find the law of change in voltage. To better remember this whole matter, gentlemen, I have prepared an explanatory picture for you. It is shown in Figure 1.

Figure 1 - Explanatory picture

It essentially depicts conclusions in a condensed form that would be good to remember.

Gentlemen, please note - the resulting expressions are valid for any law of change in current and voltage. There does not have to be a sine, cosine, meander or anything else. If you have some completely arbitrary, even completely wild, not described in any literature, law of voltage change U(t), supplied to the capacitor, you, by differentiating it, can determine the law of change in current through the capacitor. And similarly, if you know the law of change in current through a capacitor I(t) then, having found the integral, you can find how the voltage will change.

So, we found out how to connect current and voltage with each other for absolutely any, even the most crazy options for changing them. But some special cases are no less interesting. For example, the case of someone who has already fallen in love with us all sinusoidal current Let's deal with it now.

Let the voltage across a capacitor of capacity C changes according to the law of sine in this way

We discussed in detail a little earlier what physical quantity stands behind each letter in this expression. How will the current change in this case? Using the knowledge we have already gained, let's just stupidly substitute this expression into our general formula and find the derivative

Or you can write it like this

Gentlemen, I want to remind you that the only difference between sine and cosine is that one is shifted in phase relative to the other by 90 degrees. Well, or, to put it in mathematical language, then . It is not clear where this expression came from? Google it reduction formulas. It's a useful thing, it wouldn't hurt to know. Better yet, if you are familiar with trigonometric circle, all this can be seen very clearly on it.

Gentlemen, I will immediately note one point. In my articles I will not talk about the rules for finding derivatives and taking integrals. I hope you have at least a general understanding of these points. However, even if you don’t know how to do this, I will try to present the material in such a way that the essence of things is clear even without these intermediate calculations. So, now we have received an important conclusion - if the voltage on the capacitor changes according to the sine law, then the current through it will change according to the cosine law. That is, the current and voltage on the capacitor are shifted relative to each other in phase by 90 degrees. In addition, we can relatively easily find the amplitude value of the current (these are the factors that appear in front of the sine). Well, that is, that peak, that maximum that the current reaches. As you can see, it depends on the capacity C capacitor, the amplitude of the voltage applied to it U m and frequencies ω . That is, the greater the applied voltage, the greater the capacitance of the capacitor and the greater the frequency of voltage change, the greater the amplitude of the current through the capacitor. Let's build a graph, depicting in one field the current through the capacitor and the voltage across the capacitor. Without specific numbers yet, we’ll just show the quality of the character. This graph is presented in Figure 2 (the picture is clickable).

Figure 2 - Current through the capacitor and voltage across the capacitor

In Figure 2, the blue graph is the sinusoidal current through the capacitor, and the red graph is the sinusoidal voltage across the capacitor. From this figure it is very clearly visible that the current is ahead of the voltage (the peaks of the current sinusoid are located to the left corresponding peaks of the voltage sinusoid, that is, they come earlier).

Let's now do the work in reverse. Let us know the law of current change I(t) through a capacitor with a capacity C. And let this law also be sinusoidal

Let's determine how the voltage on the capacitor will change in this case. Let's use our general formula with the integral:

By absolute analogy with the calculations already written, the tension can be represented in this way

Here we again used interesting information from trigonometry that . And again reduction formulas they will come to your aid if it is not clear why it happened this way.

What conclusion can we draw from these calculations? And the conclusion is still the same as has already been made: the current through the capacitor and the voltage on the capacitor are shifted in phase relative to each other by 90 degrees. Moreover, they are shifted for a reason. Current ahead voltage. Why is this so? What is the physics of the process behind this? Let's figure it out.

Let's imagine that uncharged We connected the capacitor to a voltage source. At the first moment there are no charges in the capacitor at all: it is discharged. And since there are no charges, then there is no voltage. But there is a current, it appears immediately when the capacitor is connected to the source. Do you notice, gentlemen? There is no voltage yet (it has not had time to increase), but there is already current. And besides, at this very moment of connection, the current in the circuit is maximum (a discharged capacitor is essentially equivalent to a short circuit in the circuit). So much for the lag between voltage and current. As current flows, charge begins to accumulate on the plates of the capacitor, that is, the voltage begins to increase and the current gradually decreases. And after some time, so much charge will accumulate on the plates that the voltage on the capacitor will be equal to the source voltage and the current in the circuit will stop completely.

Now let's get this one charged We disconnect the capacitor from the source and short-circuit it. What will we get? But practically the same. At the very first moment, the current will be maximum, and the voltage on the capacitor will remain the same as it was without changes. That is, again the current is ahead, and the voltage changes after it. As the current flows, the voltage will begin to gradually decrease and when the current stops completely, it will also become zero.

For a better understanding of the physics of ongoing processes, you can once again use plumbing analogy. Let's imagine that a charged capacitor is a tank full of water. This tank has a tap at the bottom through which you can drain water. Let's open this tap. As soon as we open it, water will flow immediately. And the pressure in the tank will drop gradually as the water flows out. That is, roughly speaking, a trickle of water from a faucet outpaces the change in pressure, just as the current in a capacitor outpaces the change in voltage across it.

Similar reasoning can be carried out for a sinusoidal signal, when the current and voltage change according to the sine law, and indeed for any signal. The point, I hope, is clear.

Let's have a little practical calculation alternating current through a capacitor and plot graphs.

Let us have a source of sinusoidal voltage, the effective value is 220 V, and frequency 50 Hz. Well, that is, everything is exactly the same as in our sockets. A capacitor with a capacity of 1 µF. For example, a film capacitor K73-17, designed for a maximum voltage of 400 V (and capacitors for lower voltages should never be connected to a 220 V network), is available with a capacity of 1 μF. To give you an idea of ​​what we are dealing with, in Figure 3 I have placed a photograph of this animal (thanks to Diamond for the photo)

Figure 3 - Looking for current through this capacitor

It is required to determine what current amplitude will flow through this capacitor and construct graphs of current and voltage.

First we need to write down the law of voltage change in an outlet. If you remember, amplitude the voltage value in this case is about 311 V. Why this is so, where it came from, and how to write down the law of voltage changes in an outlet can be read in this article. We will immediately present the result. So, the voltage in the outlet will change according to the law

Now we can use the formula obtained earlier, which will relate the voltage in the outlet to the current through the capacitor. The result will look like this

We simply substituted into the general formula the capacitance of the capacitor specified in the condition, the amplitude value of the voltage and the circular frequency of the network voltage. As a result, after multiplying all the factors we have the following law of current change:

That's it, gentlemen. It turns out that the amplitude value of the current through the capacitor is slightly less than 100 mA. Is it a lot or a little? The question cannot be called correct. By the standards of industrial equipment, where hundreds of amperes of current appear, this is very little. Yes and for household appliances, where tens of amperes are not uncommon - too. However, even such a current poses a great danger to humans! From this it follows that you should not grab such a capacitor connected to a 220 V network. However, on this principle it is possible to manufacture so-called power supplies with a quenching capacitor. Well, this is a topic for a separate article and we will not touch on it here.

All this is good, but we almost forgot about the graphs that we must build. We need to fix it urgently! So, they are presented in Figure 4 and Figure 5. In Figure 4 you can observe a graph of the voltage in the socket, and in Figure 5 - the law of change in current through a capacitor connected to such a socket.

Figure 4 - Outlet voltage graph

Figure 5 - Graph of current through a capacitor

As we can see from these pictures, the current and voltage are shifted by 90 degrees, as they should be. And perhaps the reader has an idea - if current flows through a capacitor and some voltage drops across it, probably some power should also be released across it. However, I hasten to warn you - for the capacitor the situation is absolutely not this way. If we consider an ideal capacitor, then no power will be released on it at all, even when current flows and the voltage drops across it. Why? How so? About it - in future articles. That's all for today. Thank you for reading, good luck, and see you next time!

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In all radio engineering and electronic devices In addition to transistors and microcircuits, capacitors are used. Some circuits have more of them, others have less, but there is practically no electronic circuit without capacitors.

At the same time, capacitors can perform a variety of tasks in devices. First of all, these are capacitances in the filters of rectifiers and stabilizers. Using capacitors, a signal is transmitted between amplifier stages, low- and high-pass filters are built, time intervals are set in time delays, and the oscillation frequency in various generators is selected.

Capacitors trace their origins back to , which was used by the Dutch scientist Pieter van Musschenbroeck in his experiments in the mid-18th century. He lived in the city of Leiden, so it’s not hard to guess why this jar 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 aluminum had not yet been discovered.

The only source of electricity in those days was an electrophore machine, capable of developing voltages up to several hundred kilovolts. This is where the Leyden jar was charged. Physics textbooks describe a case when Muschenbroek discharged his can through a chain of ten guardsmen holding hands.

At that time, no one knew that the consequences could be tragic. The blow was quite sensitive, but not fatal. It didn’t come to this, because the capacity of the Leyden jar was insignificant, the pulse was very short-lived, so the discharge power was low.

How does a capacitor work?

The design of a capacitor is practically no different from a Leyden jar: the same two plates separated by a dielectric. That's exactly how it is on modern electrical diagrams capacitors are shown. Figure 1 shows a schematic design of a flat-plate capacitor and the formula for its calculation.

Figure 1. Design of a parallel-plate 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, from which conclusions are drawn. Air can serve as a dielectric.

From this formula it can be understood that the larger the area of ​​the plates and the smaller the distance between them, the greater the capacitance of the capacitor. 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 that of a flat capacitor: the larger the area and the smaller the distance, the greater the capacitance.

In fact, the plates are not always made flat. For many capacitors, for example metal-paper capacitors, the plates are aluminum foil rolled together with a paper dielectric into a tight ball, shaped like a metal case.

To increase the electrical strength, thin capacitor paper is impregnated with insulating compounds, most often transformer oil. This design makes it possible to make capacitors with a capacity of up to several hundred microfarads. Capacitors work in much the same way with other dielectrics.

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 spaced very far apart, and at the same time the area of ​​the plates can be made very small, then some kind of capacity, albeit small, will still remain. Such reasoning suggests that even just two conductors located next to each other have electrical capacitance.

This circumstance is widely used in high-frequency technology: in some cases, capacitors are made simply in the form of printed circuit tracks, or even just two wires twisted together in polyethylene insulation. An ordinary noodle wire or cable also has a capacitance, and it increases with increasing length.

In addition to capacitance C, any cable also has a resistance R. Both of these physical properties distributed along the length of the cable, and when transmitting pulse 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 is the output signal. The impulse is distorted beyond recognition, but this is done on purpose, which is why the circuit was assembled. For now we're talking about about the influence of cable capacitance on a pulse signal. Instead of a pulse, a “bell” like this will appear at the other end of the cable, and if the pulse is short, then it may not reach the other end of the cable at all, it may completely disappear.

Historical fact

Here it is quite appropriate to recall the story of how the transatlantic cable was laid. The first attempt in 1857 failed: telegraph dots - dashes ( square pulses) were distorted so that at the other end of the 4000 km long line it was impossible to make out anything.

A 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 light of this theory, the cable laying turned out to be more successful; signals were received.

For this scientific feat, Queen Victoria awarded the scientist a knighthood and the title of Lord Kelvin. This was the name of a small town on the coast of Ireland where the cable laying began. But this is just a word, and now let's get back to 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 dielectrics used, such as air, lavsan, polyethylene, fluoroplastic, this constant is almost the same as that of vacuum. But at the same time, there are many substances whose dielectric constant is much higher. If an air condenser is filled with acetone or alcohol, its capacity will increase by 15...20 times.

But such substances, in addition to high ε, also have a fairly high conductivity, so such a capacitor will not hold a charge well; it will quickly discharge through itself. This harmful phenomenon is called leakage current. Therefore, special materials are being developed for dielectrics, which make it possible to provide acceptable leakage currents with high specific capacitance of capacitors. This is precisely 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 the “electrolytes” reaches up to 100,000 uF, operating voltage up to 600V. Such capacitors work well only at low frequencies, most often in power supply filters. Electrolytic capacitors are connected with correct polarity.

The electrodes in such capacitors are a thin film of metal oxide, which is why these capacitors are often called oxide capacitors. A thin layer of air between such electrodes is not a very reliable insulator, so a layer of electrolyte is introduced between the oxide plates. Most often this concentrated solutions 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 the fairly large capacity, in the figure you can also see the tolerance as a percentage: 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 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 magnetic heads from the working area of ​​the disk during a sudden power outage. Such capacitors could store a charge for several years, which was tested in practice.

Below, we will suggest doing a few simple experiments with electrolytic capacitors to understand what a capacitor can do.

Non-polar electrolytic capacitors are produced for operation in alternating current circuits, but for some reason they are very difficult to obtain. To somehow get around this problem, conventional polar “electrolytes” are switched on counter-sequentially: plus-minus-minus-plus.

If a polar electrolytic capacitor is connected to an alternating current circuit, it will first heat up, and then there will be an explosion. Old domestic capacitors scattered in all directions, while imported ones have a special device that allows them to avoid loud shots. As a rule, this is either a cross notch on the bottom of the capacitor, or a hole with a rubber plug located there.

They really don't like high voltage electrolytic capacitors, even if the polarity is correct. Therefore, you should never put “electrolytes” in a circuit where a voltage close to the maximum for a given capacitor is expected.

Sometimes in some, even reputable forums, beginners ask the question: “The diagram shows a 470µF * 16V capacitor, but I have a 470µF * 50V, can I install it?” Yes, of course you can, but reverse replacement is unacceptable.

The capacitor can store energy

It will help to understand this statement simple circuit, shown in Figure 4.

Figure 4. Circuit with capacitor

The main character of this circuit is an electrolytic capacitor C of a sufficiently large capacity so that the charge and discharge processes proceed slowly, and even very clearly. This makes it possible to observe the operation of the circuit visually using a regular flashlight light bulb. These flashlights have long given way to modern LED ones, but light bulbs for them are still sold. Therefore, collect the diagram and carry out simple experiments very simple.

Maybe someone will say: “Why? After all, everything is obvious, but if you also read the description...” There seems to be nothing to object to here, but any, even the simplest thing, remains in the head for a long time if its understanding came through the hands.

So, the circuit is assembled. How does it work?

In the position of switch SA shown in the diagram, capacitor C is charged from power source GB through resistor R in the circuit: +GB __ R __ SA __ C __ -GB. The charging current in the diagram is shown by an arrow with the index iз. The capacitor charging process is shown in Figure 5.

Figure 5. Capacitor charging process

The figure shows that the voltage across the capacitor increases along a curved line, called an exponential in mathematics. The charge current directly mirrors the charge voltage. As the voltage across the capacitor increases, the charging current becomes less. And only at the initial moment it corresponds to the formula shown in the figure.

After some time, the capacitor will charge from 0V to the voltage of the power source, in our circuit up to 4.5V. The whole question is how to determine this time, how long to wait, when will the capacitor charge?

Time constant "tau" τ = R*C

This formula simply multiplies the resistance and capacitance of a series-connected resistor and capacitor. If, without neglecting the SI system, we substitute the resistance in Ohms and the capacitance in Farads, then the result will be obtained in seconds. This is the time required for the capacitor to charge to 36.8% of the power source voltage. Accordingly, charging to almost 100% will require a time of 5* τ.

Often, neglecting the SI system, they substitute resistance in Ohms and capacitance in microfarads into the formula, then the time will be in microseconds. In our case, it is more convenient to obtain the result in seconds, for which you simply have to multiply microseconds by a million, or, more simply, move the decimal point six places to the left.

For the circuit shown in Figure 4, with a capacitor capacity of 2000 μF and a resistor resistance of 500 Ω, the time constant will be τ = R*C = 500 * 2000 = 1,000,000 microseconds or exactly one second. Thus, you will have to wait approximately 5 seconds until the capacitor is fully charged.

If, after the specified time, the switch SA is moved to the right position, the capacitor C will discharge through the light bulb EL. At this moment there will be a short flash, the capacitor will discharge and the light will go out. The direction of capacitor discharge 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 diagram shown in Figure 7 will help you verify this statement.

Figure 7. Circuit with a capacitor in a DC circuit

If you close switch SA, the light bulb will flash briefly, indicating that capacitor C has charged through the light bulb. The charge graph is also shown here: at the moment the switch is closed, the current is maximum, as the capacitor is charged, it decreases, and after a while it stops completely.

If the capacitor good quality, i.e. with a low leakage current (self-discharge), repeated closure of the switch will not lead to 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 their 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 ripple V.

The 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-wave rectifier, one will appear in its place

C = 1000000 * Po / U*f*dU,

and for a three-phase rectifier the formula will take the form C = 1000000 * Po / 3*U*f*dU.

Supercapacitor - ionistor

Recently appeared new class electrolytic capacitors, the so-called. In its properties it is similar to a battery, although with several limitations.

The ionistor 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, the ionistor is a non-polar device; the only thing that determines its polarity is charging at the manufacturer. To prevent this polarity from being confused in the future, it is indicated with a + sign.

The operating conditions of ionistors play a big role. At a temperature of 70˚C at a voltage of 0.8 of the rated voltage, the guaranteed durability is no more than 500 hours. If the device operates at a voltage of 0.6 of the nominal voltage, and the temperature does not exceed 40 degrees, then proper operation is possible for 40,000 hours or more.

The most common application of an ionistor is in backup power supplies. These are mainly memory chips or Digital Watch. In this case, the main parameter of the ionistor is low leakage current, its self-discharge.

Quite promising is the use of ionistors in conjunction with solar panels. This is also due to the non-criticality of the charge conditions and the practically unlimited number of charge-discharge cycles. Another valuable property is that the ionistor does not require maintenance.

So far I’ve managed to tell you how and where electrolytic capacitors work, mainly in DC circuits. The operation of capacitors in alternating current circuits will be discussed in another article -.