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 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:
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:
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:
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:
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, capacitance when connecting capacitors in parallel.
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 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.
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 This is a large value, then 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.
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.
Electric charge storage devices of constant capacity are distinguished:
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 oscillatory 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. In some devices it is necessary to ensure a large accumulation of electrical charge. The existing denominations are not enough; 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:
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: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.
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.
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.
Can be connected to each other in various ways. In all cases, it is possible to find the capacitance of some equivalent capacitor, which can replace a series of interconnected capacitors.
For an equivalent capacitor, the following condition is met: if the voltage supplied to the plates of an equivalent capacitor is equal to the voltage supplied to the outer terminals of a group of capacitors, then the equivalent capacitor will accumulate the same charge as the group of capacitors.
Parallel connection of capacitors
In Fig. Figure 1 shows a parallel connection of several capacitors. In this case, the voltages supplied to the individual capacitors are the same: U1 = U2 = U3 = U. The charges on the plates of the individual capacitors: Q1 = C1U, Q 2 = C 2U, Q 3 = C 3U, and the charge received from the source Q = Q1 + Q2 + Q3.
Rice. 1. Parallel connection diagram of capacitors
Total capacitance of an equivalent capacitor:
C = Q / U = (Q1 + Q2 + Q3) / U = C1 + C2 + C3,
that is, when capacitors are connected in parallel, the total capacitance is equal to the sum of the capacitances of the individual capacitors.
Rice. 2. Methods for connecting capacitors
Series connection of capacitors
When capacitors are connected in series (Fig. 3), the electric charges on the plates of individual capacitors are equal in magnitude: Q1 = Q2 = Q3 = Q
Indeed, from the power source, charges are supplied only to the outer plates of the chain of capacitors, and on the interconnected internal plates of adjacent capacitors, only a transfer of the same magnitude of charge from one plate to another occurs (electrostatic induction is observed), therefore equal amounts appear on them. and opposite electric charges.
Rice. 3. Series connection diagram of capacitors
The voltages between the plates of individual capacitors when connected in series depend on the capacitances of the individual capacitors: U1 = Q/C1, U1 = Q/C 2, U1 = Q/C 3, and the total voltage U = U1 + U2 + U3
The total capacitance of an equivalent (equivalent) capacitor is C = Q / U = Q / (U1 + U2 + U3), i.e., when capacitors are connected in series, the reciprocal of the total capacitance is equal to the sum of the reciprocals of the capacitances of the individual capacitors.
The formulas for equivalent capacitances are similar to the formulas for equivalent conductivities.
Example 1. Three capacitors, the capacitances of which C1 = 20 μF, C2 = 25 μF and C3 = 30 μF, are connected in series; it is necessary to determine the total capacitance.
The total capacitance is determined from the expression 1/C = 1/C1 + 1/C2 + 1/C3 = 1/20 + 1/25 + 1/30 = 37/300, from which C = 8.11 μF.
Example 2. 100 capacitors with a capacity of each 2 μF are connected in parallel. Determine the total capacity. Total capacitance C = 100 Sc = 200 microfarads.
