A series connection refers to cases where two or more elements are in the form of a chain, with each of them connected to the other at only one point. Why are capacitors placed this way? How to do this correctly? What do you need to know? What features does series connection of capacitors have in practice? What is the result formula?
What do you need to know for a correct connection?
Alas, not everything here is as easy to do as it might seem. Many beginners think that if the schematic drawing says that an element of 49 microfarads is needed, then it is enough to simply take it and install it (or replace it with an equivalent one). But it is difficult to select the necessary parameters even in a professional workshop. And what to do if you don’t have the necessary elements? Let's say there is such a situation: you need a 100 microfarad capacitor, but there are several 47 microfarad capacitors. It is not always possible to install it. Go to the radio market for one capacitor? Not necessary. It will be enough to connect a couple of elements. There are two main methods: series and parallel connection of capacitors. That's the first one we'll talk about. But if we talk about the series connection of the coil and capacitor, then there are no special problems.
Why do they do this?
When such manipulations are carried out with them, the electric charges on the plates of individual elements will be equal: KE = K 1 = K 2 = K 3. KE - final capacitance, K - transmitting value of the capacitor. Why is that? When charges are supplied from the power source to the external plates, a value can be transferred to the internal plates, which is the value of the element with the smallest parameters. That is, if you take a 3 µF capacitor, and after it connect it to 1 µF, then the end result will be 1 µF. Of course, on the first one you can observe a value of 3 µF. But the second element will not be able to pass so much, and it will cut off everything that is larger than the required value, leaving a large capacitance on the original capacitor. Let's look at what needs to be calculated when connecting capacitors in series. Formula:
- OE - total capacity;
- N - voltage;
- KE - final capacity.
What else do you need to know to properly connect capacitors?
To begin with, do not forget that in addition to capacity, they also have a rated voltage. Why? When a series connection is made, the voltage is distributed inversely proportional to their capacitances between themselves. Therefore, it makes sense to use this approach only in cases where any capacitor can provide the minimum required operating parameters. If elements that have the same capacitance are used, the voltage between them will be divided equally. Also a word of caution regarding electrolytic capacitors: When working with them, always carefully monitor their polarity. Because if this factor is ignored, series connection of capacitors can give a number of undesirable effects. And it’s good if everything is limited only to the breakdown of these elements. Remember that capacitors store current, and if something goes wrong, depending on the circuit, a precedent may occur that will result in other components of the circuit failing.
Current in series connection
Because it only has one possible flow path, it will have the same value for all capacitors. In this case, the amount of accumulated charge has the same value everywhere. It doesn't depend on the capacity. Look at any diagram of a series connection of capacitors. The right facing of the first is connected to the left of the second and so on. If more than 1 element is used, then some of them will be isolated from the general circuit. Thus, the effective area of the plates becomes smaller and equals the parameters of the smallest capacitor. What physical phenomenon underlies this process? The fact is that as soon as a capacitor is filled with an electric charge, it stops passing current. And then it cannot flow throughout the entire chain. In this case, the remaining capacitors will also not be able to charge.
Voltage drop and total capacitance
Each element dissipates tension a little. Considering that the capacity is inversely proportional to it, the smaller it is, the greater the drop will be. As mentioned earlier, capacitors connected in series have the same electrical charge. Therefore, by dividing all expressions by the total value, you can get an equation that shows the entire capacity. This is where series and parallel connection of capacitors are very different.
Example #1
Let's use the formulas presented in the article and calculate several practical problems. So we have three capacitors. Their capacitance is: C1 = 25 µF, C2 = 30 µF and C3 = 20 µF. They are connected in series. It is necessary to find their total capacity. We use the corresponding equation 1/C: 1/C1 + 1/C2 + 1/C3 = 1/25 + 1/30 + 1/20 = 37/300. We convert to microfarads, and the total capacitance of the capacitor when connected in series (and the group in this case is considered as one element) is approximately 8.11 μF.
Example No. 2
Let's solve one more problem to consolidate our work. There are 100 capacitors. The capacity of each element is 2 μF. It is necessary to determine their total capacity. You need to multiply their number by the characteristic: 100*2=200 µF. So, the total capacitance of the capacitor when connected in series is 200 microfarads. As you can see, nothing complicated.
Conclusion
So, we have worked through the theoretical aspects, analyzed the formulas and features of the correct connection of capacitors (in series), and even solved several problems. I would like to remind readers not to lose sight of the influence of rated voltage. It is also desirable that elements of the same type be selected (mica, ceramic, metal-paper, film). Then series connection of capacitors can give us the greatest beneficial effect.
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 supplied to 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-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, which is indicated on the body of the part, cannot 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 compound
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.
Content:
Circuits in electrical engineering consist of electrical elements in which the methods of connecting capacitors can be different. You need to understand how to properly connect a capacitor. Individual sections of the circuit with connected capacitors can be replaced with one equivalent element. It will replace a series of capacitors, but a mandatory condition must be met: when the voltage supplied to the plates of an equivalent capacitor is equal to the voltage at the input and output of the group of capacitors being replaced, then the charge on the capacitor will be the same as on the group of capacitors. To understand the question of how to connect a capacitor in any circuit, let's consider the types of its connection.
Parallel connection of capacitors in a circuit
Parallel connection of capacitors is when all the plates are connected to the switching points of the circuit, forming a bank of capacitors.
The potential difference on the plates of the capacitance storage devices will be the same, since they are all charged from the same current source. In this case, each charging capacitor has its own charge with the same amount of energy supplied to them.
Parallel capacitors, a general parameter for the amount of charge of the resulting storage battery, are calculated as the sum of all the charges placed on each capacitor, because each capacitor charge does not depend on the charge of another capacitor included in the group of capacitors connected in parallel to the circuit.
When capacitors are connected in parallel, the capacitance is equal to:
From the presented formula we can conclude that the entire group of drives can be considered as one capacitor equivalent to them.
Capacitors connected in parallel have a voltage:
Series connection of capacitors in a circuit
When a series connection of capacitors is made in a circuit, it looks like a chain of capacitive storage devices, where the plate of the first and last capacitive storage device (capacitor) is connected to a current source.
Series connection of a capacitor:
When capacitors are connected in series, all devices in this section take the same amount of electricity, because the first and last plate of the storage devices are involved in the process, and plates 2, 3 and others up to N are charged through influence. For this reason, the charge of plate 2 of the capacitance storage device is equal in value to the charge of plate 1, but has the opposite sign. The charge of drive plate 3 is equal to the charge value of plate 2, but also with the opposite sign; all subsequent drives have a similar charge system.
Formula for finding charge on a capacitor, capacitor connection diagram:
When capacitors are connected in series, the voltage on each capacitance storage device will be different, since different capacitances are involved in charging with the same amount of electrical energy. The dependence of capacitance on voltage is as follows: the smaller it is, the greater the voltage must be applied to the drive plates to charge it. And the inverse value: the higher the storage capacity, the less voltage is required to charge it. We can conclude that the capacitance of series-connected drives matters for the voltage on the plates - the lower it is, the more voltage is required, and also high-capacity drives require less voltage.
The main difference between the series connection of capacitance storage devices is that electricity flows in only one direction, which means that in each capacitance storage device of the stacked battery the current will be the same. This type of capacitor connections ensures uniform energy storage regardless of the storage capacity.
A group of capacitance storage devices can also be considered in the diagram as an equivalent storage device, the plates of which are supplied with a voltage determined by the formula:
The charge of the common (equivalent) storage device of a group of capacitive storage devices in a serial connection is equal to:
The general value of the capacitance of series-connected capacitors corresponds to the expression:
Mixed inclusion of capacitive storage devices in a circuit
The parallel and series connection of capacitors in one of the sections of the circuit circuit is called a mixed connection by specialists.
Section of the circuit of mixed-connected capacity storage devices:
The mixed connection of capacitors in the circuit is calculated in a certain order, which can be represented as follows:
- the circuit is divided into sections that are easy to calculate; this is a series and parallel connection of capacitors;
- we calculate the equivalent capacitance for a group of capacitors connected in series in a parallel connection section;
- we find the equivalent capacity in a parallel section;
- when the equivalent storage capacities are determined, it is recommended to redraw the diagram;
- The capacity of the resulting electrical energy storage devices after sequential switching on is calculated.
Capacitance storage devices (double-terminal networks) are connected in different ways to the circuit; this provides several advantages in solving electrical problems compared to traditional methods of connecting capacitors:
- Use for connecting electric motors and other equipment in workshops, in radio engineering devices.
- Simplifying the calculation of electrical circuit values. Installation is carried out in separate sections.
- The technical properties of all elements do not change when the current strength and magnetic field change; this is used to turn on different storage devices. It is characterized by a constant value of capacitance and voltage, and the charge is proportional to the potential.
Conclusion
Various types of inclusion of capacitors in a circuit are used to solve electrical problems, in particular, to obtain polar storage devices from several non-polar two-terminal networks. In this case, the solution would be to connect a group of single-pole capacitance storage devices using an anti-parallel method (triangle). In this circuit, minus is connected to minus, and plus is connected to plus. The storage capacity increases, and the operation of the two-terminal network changes.
The following entries are not displayed: serial parallel and mixed connection of capacitors, series and parallel connection of capacitors, and capacitance when connecting capacitors in parallel.
Capacitors, like resistors, can be connected in series or in parallel. Let's consider the connection of capacitors: what each of the circuits is used for, and their final characteristics.
This scheme is the most common. In it, the capacitor plates are connected to each other, forming an equivalent capacitance equal to the sum of the connected capacitances.
When connecting electrolytic capacitors in parallel, it is necessary that the terminals of the same polarity be connected to each other.
The peculiarity of this connection is equal voltage across all connected capacitors. The rated voltage of a group of parallel-connected capacitors is equal to the operating voltage of the group capacitor for which it is minimal.
The currents flow through the capacitors of the group are different: a larger current will flow through a capacitor with a larger capacitance.
In practice, a parallel connection is used to obtain a capacitance of the required size when it falls outside the range produced by industry or does not fit into a standard series of capacitors. In power factor control systems (cos ϕ), the change in capacitance occurs due to the automatic connection or disconnection of capacitors in parallel.
In a series connection, the capacitor plates are connected to each other, forming a chain. The outer plates are connected to the source, and the same current flows through all capacitors of the group.
The equivalent capacitance of capacitors connected in series is limited to the smallest capacitance in the group. This is explained by the fact that as soon as it is fully charged, the current will stop. You can calculate the total capacitance of two series-connected capacitors using the formula
But the use of a serial connection to obtain non-standard capacitance ratings is not as common as a parallel one.
In a series connection, the power supply voltage is distributed among the capacitors of the group. This allows you to get a bank of capacitors designed for higher voltage than the rated voltage of its components. So, blocks that can withstand high voltages are made from cheap and small capacitors.
Another area of application for series connection of capacitors is related to the redistribution of voltages between them. If the capacitances are the same, the voltage is divided in half; if not, the voltage on a capacitor with a larger capacitance is greater. A device operating on this principle is called capacitive voltage divider.
Mixed connection of capacitors
Such circuits exist, but in special-purpose devices that require high accuracy in obtaining the capacitance value, as well as for their precise adjustment.
To achieve the required capacitance or for voltages exceeding the rated voltage, capacitors can be connected in series or in parallel. Any complex connection consists of several combinations of serial and parallel connections.
In series connection, the capacitors are connected in such a way that only the first and last capacitor are connected to the emf/current source of one of their plates. The charge is the same on all plates, but the outer ones are charged from the source, and the inner ones are formed only due to the separation of charges that previously neutralized each other. In this case, the charge of the capacitors in the battery is less than if each capacitor were connected separately. Consequently, the total capacity of the capacitor bank is less.
The voltages in this section of the circuit are related as follows:
Knowing that the capacitor voltage can be represented in terms of charge and capacitance, we write:
Reducing the expression by Q, we get the familiar formula:
Where does the equivalent capacity of a bank of capacitors connected in series come from:
When capacitors are connected in parallel, the voltage on the plates is the same, but the charges are different.
The amount of total charge received by the capacitors is equal to the sum of the charges of all parallel connected capacitors. In the case of a battery of two capacitors:
Since the capacitor charge
And the voltages on each capacitor are equal, we obtain the following expression for the equivalent capacitance of two parallel-connected capacitors
Example 1
What is the resulting capacitance of 4 capacitors connected in series and in parallel, if it is known that C 1 = 10 µF, C 2 = 2 µF, C 3 = 5 µF, and C 4 = 1 µF?
With a series connection, the total capacitance is:
With a parallel connection, the total capacitance is:
Example 2
Determine the resulting capacitance of a group of capacitors connected in series-parallel, if it is known that C 1 = 7 µF, C 2 = 2 µF, C 3 = 1 µF.
