Methods for connecting capacitors in an electrical circuit. Capacitor connection diagrams: parallel, series Capacitor connection calculator

Content:

In electronic and radio engineering circuits, parallel and series connection of capacitors has become widespread. In the first case, the connection is carried out without any common nodes, and in the second option, all elements are combined into two nodes and are not connected to other nodes, unless this is provided for in advance by the circuit.

Serial connection

In a series connection, two or more capacitors are connected into a common circuit in such a way that each previous capacitor is connected to the next one at only one common point. The current (i) charging a series circuit of capacitors will have the same value for each element, since it passes only along the only possible path. This position is confirmed by the formula: i = i c1 = i c2 = i c3 = i c4.

Due to the same amount of current flowing through capacitors in series, the amount of charge stored by each will be the same, regardless of capacitance. This becomes possible because the charge coming from the plate of the previous capacitor accumulates on the plate of the subsequent circuit element. Therefore, the amount of charge on series-connected capacitors will look like this: Q total = Q 1 = Q 2 = Q 3.

If we consider three capacitors C 1, C 2 and C 3 connected in a series circuit, it turns out that the middle capacitor C 2 at constant current is electrically isolated from the general circuit. Ultimately, the effective area of the plates will be reduced to the area of the capacitor plates with the most minimal dimensions. Complete filling of the plates with an electric charge makes it impossible for further current to pass through it. As a result, the flow of current stops in the entire circuit, and accordingly, the charging of all other capacitors stops.

The total distance between the plates in a series connection is the sum of the distances between the plates of each element. As a result of connection in a series circuit, a single large capacitor is formed, the area of the plates of which corresponds to the plates of the element with a minimum capacitance. The distance between the plates turns out to be equal to the sum of all the distances available in the chain.

The voltage drop across each capacitor will be different depending on the capacitance. This position is determined by the formula: C = Q/V, in which the capacitance is inversely proportional to the voltage. Thus, as the capacitor's capacitance decreases, a higher voltage drops across it. The total capacitance of all capacitors is calculated by the formula: 1/C total = 1/C 1 + 1/C 2 + 1/C 3.

The main feature of such a circuit is the passage of electrical energy in only one direction. Therefore, the current value in each capacitor will be the same. Each drive in a series circuit stores an equal amount of energy, regardless of capacity. That is, the capacity can be reproduced due to the energy present in the neighboring storage device.

Online calculator for calculating the capacitance of capacitors connected in series in an electrical circuit.

Mixed connection

Parallel connection of capacitors

A parallel connection is considered to be one in which the capacitors are connected to each other by two contacts. Thus, several elements can be connected at once at one point.

This type of connection allows you to form a single capacitor with large dimensions, the area of the plates of which will be equal to the sum of the areas of the plates of each individual capacitor. Due to the fact that it is in direct proportion to the area of the plates, the total capacitance is the total number of all capacitances of the capacitors connected in parallel. That is, C total = C 1 + C 2 + C 3.

Since the potential difference occurs only at two points, the same voltage will drop across all capacitors connected in parallel. The current strength in each of them will be different, depending on the capacitance and voltage value. Thus, serial and parallel connections used in various circuits make it possible to adjust various parameters in certain areas. Due to this, the necessary results of the operation of the entire system as a whole are obtained.

Many radio amateurs, especially those starting to design electrical circuits for the first time, have a question: how should a capacitor of the required capacity be connected? When, for example, a capacitor with a capacity of 470 μF is needed in some place in the circuit, and such an element is available, then there will be no problem. But when you need to install a 1000 μF capacitor, and there are only elements of unsuitable capacitance, circuits of several capacitors connected together come to the rescue. The elements can be connected using parallel and series connection of capacitors individually or using a combined principle.

Serial connection diagram

When a series connection of capacitors is used, the charge of each part is equivalent. Only the outer plates are connected to the source; the others are charged by redistributing electric charges between them. All capacitors store a similar amount of charge on their plates. This is explained by the fact that each subsequent element receives a charge from the neighboring one. As a result, the equation is valid:

q = q1 = q2 = q3 = …

It is known that when resistor elements are connected in series, their resistances are summed up, but the capacitance of a capacitor included in such an electrical circuit is calculated differently.

The voltage drop across an individual capacitor element depends on its capacitance. If there are three capacitor elements in a series electrical circuit, an expression for the voltage is drawn up U based on Kirchhoff's law:

U = U1 + U2 + U3,

in this case U= q/C, U1 = q/C1, U2 = q/C2, U3 = q/C3.

Substituting the voltage values into both sides of the equation, we get:

q/C = q/C1 + q/C2 + q/C3.

Since the electric charge q is the same quantity, all parts of the resulting expression can be divided by it.

The resulting formula for capacitor capacities is:

1/C = 1/C1 + 1/C2 + 1/C3.

Important! If capacitors are connected in a series circuit, the reciprocal of the resulting capacitance is equal to the set of reciprocal values of individual capacitances.

Example.Three capacitor elements are connected in a series circuit and have capacitances: C1 = 0.05 µF, C2 = 0.2 µF, C3 = 0.4 µF.Calculate the total capacitance value:

1/C = 1/0.05 + 1/0.2 + 1/0.4 = 27.5;
C = 1/27.5 = 0.036 µF.

Important! When capacitor elements are connected in a series circuit, the total capacitance value does not exceed the smallest capacitance of the individual element.

If the chain consists of only two components, the formula is rewritten as follows:

C = (C1 x C2)/(C1 + C2).

In the case of creating a circuit of two capacitors with identical capacitance value:

C = (C x C)/(2 x C) = C/2.

Series-connected capacitors have a reactance that depends on the frequency of the flowing current. The voltage across each capacitor drops due to the presence of this resistance, so a capacitive voltage divider is created based on such a circuit.

Formula for capacitive voltage divider:

U1 = U x C/C1, U2 = U x C/C2, where:

U – circuit supply voltage;
U1, U2 – voltage drop across each element;
C – final capacity of the circuit;
C1, C2 – capacitive indicators of single elements.

Calculation of voltage drops across capacitors

For example, there is a 12 V AC network and two alternative electrical circuits for connecting series capacitor elements:

the first is for connecting one capacitor C1 = 0.1 µF, another C2 = 0.5 µF;
the second – C1 = C2 = 400 nF.

First option

The final capacitance of the electrical circuit C = (C1 x C2)/(C1 + C2) = 0.1 x 0.5/(0.1 + 0.5) = 0.083 μF;
Voltage drop across one capacitor: U1 = U x C/C1 = 12 x 0.083/0.1 = 9.9 V
On the second capacitor: U2 = U x C/C2 = 12 x 0.083/0.5 = 1.992 V.

Second option

Resulting capacitance C = 400 x 400/(400 + 400) = 200 nF;
Voltage drop U1 = U2 = 12 x 200/400 = 6 V.

According to calculations, we can conclude that if capacitors of equal capacitances are connected, the voltage is divided equally on both elements, and when the capacitance values differ, then the voltage on the capacitor with a smaller capacitance value increases, and vice versa.

Parallel and combined connection

Connecting capacitors in parallel is represented by a different equation. To determine the total capacitance value, you simply need to find the totality of all quantities separately:

C = C1 + C2 + C3 + ...

The voltage will be applied identically to each element. Therefore, to enhance the capacitance, it is necessary to connect several parts in parallel.

If the connections are mixed, series-parallel, then equivalent or simplified electrical circuits are used for such circuits. Each region of the circuit is calculated separately, and then, representing them as calculated capacitances, they are combined into a simple circuit.

Features of replacing capacitors

For example, there is a 12 V AC mains supply and two alternative groups of series capacitor elements.

Capacitors are connected in a series circuit to increase the voltage at which they remain operational, but their total capacitance drops in accordance with the formula for calculating it.

A mixed connection of capacitors is often used to create the desired capacitance value and increase the voltage that the parts can withstand.

You can give an option on how to connect several components to achieve the desired parameters. If an 80 µF capacitor element is required at 50 V, but only 40 µF capacitors are available at 25 V, the following combination must be formed:

Connect two 40 µF/25 V capacitors in series for a total of 20 µF/50 V;
Now the parallel connection of capacitors comes into play. A pair of capacitor groups connected in series, created in the first stage, are connected in parallel, the result is 40 µF / 50 V;
Connect the two finally assembled groups in parallel, resulting in 80 µF/50 V.

Important! In order to amplify the voltage of capacitors, it is possible to combine them into a series circuit. An increase in the total capacitive value is achieved by parallel connection.

Things to consider when creating a daisy chain:

When connecting capacitors, the best option is to take elements with slightly different or identical parameters, due to the large difference in discharge voltages;
To balance the leakage currents, an equalizing resistance is connected to each capacitor element (in parallel).

Inclusion in a series circuit must always occur in compliance with the “plus” and “minus” of the capacitors. If they are connected by poles of the same name, then such a combination already loses its polarization. In this case, the capacitance of the created group will be equal to half the capacitance value of one of the parts. Such capacitors can be used as starting capacitors on electric motors.

Video

1 mF = 0.001 F. 1 µF = 0.000001 = 10⁻⁶ F. 1 nF = 0.000000001 = 10⁻⁹ F. 1 pF = 0.000000000001 = 10⁻¹² F.

According to Kirchhoff's second rule, the voltage drop V₁, V₂ and V₃ across each capacitor in a group of three capacitors connected in series is generally different and the total potential difference V equal to their sum:

By definition of capacity and taking into account that the charge Q a group of series-connected capacitors is common to all capacitors, the equivalent capacitance C eq of all three capacitors connected in series is given by

For a group of n equivalent capacitance of capacitors connected in series C eq is equal to the reciprocal of the sum of the reciprocals of the capacitances of individual capacitors:

This formula is for C eq and is used for calculations in this calculator. For example, the total capacitance of three capacitors of 10, 15 and 20 μF connected in series will be equal to 4.62 μF:

If there are only two capacitors, then their total capacity is determined by the formula

If available n capacitors connected in series with a capacitance C, their equivalent capacity is

Note that to calculate the total capacitance of several capacitors connected in series, the same formula is used as for calculating the total resistance of resistors connected in parallel.

Note also that the total capacitance of a group of any number of capacitors connected in series will always be less than the capacitance of the smallest capacitor, and adding capacitors to a group always results in a decrease in capacitance.

The voltage drop across each capacitor in a group of series-connected capacitors deserves special mention. If all capacitors in a group have the same rated capacitance, the voltage drop across them will likely be different, since the capacitors will actually have different capacitances and different leakage current. The capacitor with the smallest capacitance will have the largest voltage drop and will thus be the weakest link in the circuit.

To obtain a more uniform voltage distribution, equalizing resistors are included in parallel with the capacitors. These resistors act as voltage dividers, reducing the voltage spread across the individual capacitors. But even with these resistors, you should still choose capacitors with a large operating voltage margin for series connection.

If several capacitors connected in parallel, potential difference V on a group of capacitors is equal to the potential difference between the connecting wires of the group. Total charge Q is divided between the capacitors and if their capacitances are different, then the charges on the individual capacitors Q₁, Q₂ and Q₃ will also be different. The total charge is defined as

Almost any electronic board uses capacitors, and they are also installed in power circuits. In order for a component to perform its functions, it must have certain characteristics. Sometimes a situation arises when a necessary element is not on sale or its price is unreasonably high.

You can get out of this situation by using several elements, and the necessary characteristics are obtained by using parallel and series connections of capacitors to each other.

A little theory

A capacitor is a passive electronic component, with a variable or constant capacitance value, which is designed to accumulate charge and energy from an electric field.

When choosing these electronic components, we are guided by two main characteristics:

The symbol for a non-polar permanent capacitor in the diagram is shown in Fig. 1, a. For a polar electronic component, a positive terminal is additionally noted - Fig. 1, b.

Methods for connecting capacitors

Composing banks of capacitors allows you to change the total capacity or operating voltage. For this, the following connection methods can be used:

sequential;
parallel;
mixed.

Serial connection

The series connection of capacitors is shown in Fig. 1, c. This connection is used mainly to increase the operating voltage. The fact is that the dielectrics of each element are located one behind the other, so with this connection the voltages add up.

Total capacity elements connected in series can be calculated using the formula, which for three components will have the form shown in Fig. 1, e.

After transformation into a more familiar form for us, the formula will take the form of Fig. 1, f.

If the components connected in series have the same capacities, then the calculation is greatly simplified. In this case, the total value can be determined by dividing the value of one element by their number. For example, if you need to determine what the capacitance is when two 100 μF capacitors are connected in series, then this value can be calculated by dividing 100 μF by two, that is, the total capacitance is 50 μF.

Simplify as much as possible calculations of series connected components, allows the use of online calculators, which can be found on the Internet without any problems.

Parallel connection

Parallel connection of capacitors is shown in Fig. 1, g. With this connection, the operating voltage does not change, and the capacitances are added. Therefore, to obtain high-capacity batteries, parallel connection of capacitors is used. You don’t need a calculator to calculate the total capacity, since the formula has the simplest form:

C sum = C 1 + C 2 + C 3.

When assembling a battery to start three-phase asynchronous electric motors, a parallel connection of electrolytic capacitors is often used. This is due to the large capacity of this type of element and the short startup time of the electric motor. This mode of operation of electrolytic components is acceptable, but you should choose those elements whose rated voltage is at least twice the mains voltage.

Mixed inclusion

Mixed connection of capacitors - a combination of parallel and serial connections.

Schematically, such a chain may look different. As an example, consider the diagram shown in Fig. 1, d. The battery consists of six elements, of which C1, C2, C3 are connected in parallel, and C4, C5, C6 are connected in series.

The operating voltage can be determined by adding the rated voltages C4, C5, C6 and the voltage of one of the parallel-connected capacitors. If parallel-connected elements have different rated voltages, then the smaller of the three is taken for calculation.

To determine the total capacity, the circuit is divided into sections with the same connection of elements, calculations are made for these sections, after which the total value is determined.

For our scheme, the sequence of calculations is as follows:

We determine the capacity of parallel connected elements and denote it C 1-3.
We calculate the capacity of series-connected elements C 4-6.
At this stage, you can draw a simplified equivalent circuit, in which, instead of six elements, two are depicted - C 1-3 and C 4-6. These circuit elements are connected in series. It remains to calculate such a connection and we will get the desired one.

In life, detailed knowledge about mixed connections can only be useful to radio amateurs.

Almost all electrical circuits include capacitive elements. The connection of capacitors to each other is carried out according to the diagrams. They must be known both during calculations and during installation.

Serial connection

A capacitor, or colloquially “capacitance”, is a part that no electrical or electronic board can do without. Even in modern gadgets it is present, albeit in a modified form.

Let us remember what this radio element is. This is a store of electrical charges and energy, 2 conductive plates, between which a dielectric is located. When a DC source is applied to the plates, current will briefly flow through the device and it will charge to the source voltage. Its capacity is used to solve technical problems.

The word itself originated long before the device was invented. The term appeared back when people believed that electricity was something like a liquid, and it could be filled with some kind of vessel. In relation to the capacitor, it is unsuccessful, because implies that the device can only accommodate a finite amount of electricity. Although this is not true, the term has remained unchanged.

The larger the plates and the smaller the distance between them, the greater the capacitance of the capacitor. If its plates are connected to any conductor, then a rapid discharge will occur through this conductor.

In coordinated telephone exchanges, with the help of this feature, signals are exchanged between devices. The length of the pulses required for commands, such as: “line connection”, “subscriber answer”, “hang up”, is regulated by the capacitance of the capacitors installed in the circuit.

The unit of measurement for capacitance is 1 Farad. Because Since this is a large value, they use microfarads, picofarads and nanofarads (μF, pF, nF).

In practice, by making a series connection, you can increase the applied voltage. In this case, the applied voltage is received by the 2 outer plates of the assembled system, and the plates located inside are charged using charge distribution. Such methods are resorted to when the necessary elements are not at hand, but there are parts of other voltage ratings.

A section that has 2 capacitors connected in series, rated for 125 V, can be connected to 250 V power.

If for direct current the capacitor is an obstacle due to its dielectric gap, then with alternating current everything is different. For currents of different frequencies, like coils and resistors, the resistance of the capacitor will change. It passes high-frequency currents well, but creates a barrier for their low-frequency counterparts.

Radio amateurs have a way - through a capacitance of 220-500 pF, instead of an antenna, a lighting network with a voltage of 220 V is connected to the radio receiver. It will filter out a current with a frequency of 50 Hz, and allow high-frequency currents to pass through. This capacitor resistance can be easily calculated using the formula for capacitance: RC = 1/6*f*C.

Rc – capacitance, Ohm;
f – current frequency, Hz;
C is the capacitance of this capacitor, F;
6 is the number 2π rounded to the nearest integer.

But not only the applied voltage to the circuit can be changed using a similar connection circuit. This is how capacitance changes are achieved in series connections. To make it easier to remember, we came up with a hint that the total capacitance value obtained when choosing such a circuit is always less than the smaller of the two included in the chain.

If you connect 2 parts of the same capacity in this way, then their total value will be half that of each of them. Calculations for series capacitor connections can be made using the formula below:

Commun = C1*C2/C1+C2,

Let C1=110 pF, and C2=220 pF, then Total = 110×220/110+220 = 73 pF.

Do not forget about the simplicity and ease of installation, as well as ensuring high-quality operation of the assembled device or equipment. In series connections, tanks must have 1 manufacturer. And if the parts of the entire chain are from the same production batch, then there will be no problems with the operation of the created chain.

Parallel connection

Electric charge storage devices of constant capacity are distinguished:

ceramic;
paper;
mica;
metal and paper;
electrolytic capacitors.

They are divided into 2 groups: low-voltage and high-voltage. They are used in rectifier filters, for communication between low-frequency sections of circuits, in power supplies for various devices, etc.

Variable capacitors also exist. They found their purpose in tunable oscillating circuits of television and radio receivers. The capacity is adjusted by changing the position of the plates relative to each other.

Let's consider the connection of capacitors when their terminals are connected in pairs. This connection is suitable for 2 or more elements designed for the same voltage. The rated voltage indicated on the body of the part must not be exceeded. Otherwise, dielectric breakdown will occur and the element will fail. But in a circuit where there is a voltage less than the rated voltage, a capacitor can be connected.

By connecting capacitors in parallel, you can increase the total capacity. Some devices require a large accumulation of electrical charge. There are not enough existing denominations; we have to make parallels and use what is at hand. Determining the total amount of the resulting compound is simple. To do this, you simply need to add up the values of all the elements used.

To calculate the capacitances of capacitors, the formula looks like:

Commun = C1+C2, where C1 and C2 are the capacity of the corresponding elements.

If C1 = 20 pF and C2 = 30 pF, then Ct = 50 pF. There can be an nth number of parts in parallel.

In practice, such a connection is used in special devices used in energy systems and in substations. They are installed knowing how to connect capacitors to increase capacity into entire blocks of batteries.

In order to maintain reactive power balance both in power supply installations and in energy consumer installations, there is a need to include reactive power compensating devices (RPCs). To reduce losses and regulate voltage in networks, when calculating the device, it is necessary to know the values of the reactance of the capacitors used in the installation.

It happens that it becomes necessary to calculate the voltage on the capacitors using the formula. In this case, we will proceed from the fact that C = q/U, i.e. charge to voltage ratio. And if the charge value is q and the capacity is C, we can get the desired number by substituting the values. It looks like:

Mixed connection

When calculating a chain that is a set of combinations discussed above, do this. First, we look for capacitors in a complex circuit that are connected to each other either in parallel or in series. Replacing them with an equivalent element, we get a simpler circuit. Then, in the new circuit, we carry out the same manipulations with sections of the circuit. We simplify until only a parallel or serial connection remains. We have already learned how to calculate them in this article.

Parallel-series connection is used to increase the capacitance, battery or to ensure that the applied voltage does not exceed the operating voltage of the capacitor.