Many novice electronics enthusiasts in the process of assembling a homemade device have a question: “How to connect capacitors correctly?”
It would seem why this is necessary, because if the circuit diagram indicates that a 47 microfarad capacitor should be installed in a given place in the circuit, then we take it and install it. But, you must admit that in the workshop of even an avid electronics engineer there may not be a capacitor with the required rating!
A similar situation may arise when repairing any device. For example, you need an electrolytic capacitor with a capacity of 1000 microfarads, but you only have two or three at hand with a capacity of 470 microfarads. Set 470 microfarads instead of the required 1000? No, this is not always acceptable. So what should we do? Go to the radio market several tens of kilometers away and buy the missing part?
How to get out of this situation? You can connect several capacitors and as a result get the capacitance we need. In electronics, there are two ways to connect capacitors: parallel And sequential.
In reality it looks like this:
Parallel connection
Schematic diagram of parallel connection
Serial connection
Schematic diagram of serial connection
It is also possible to combine parallel and serial connections. But in practice you are unlikely to need this.
How to calculate the total capacitance of connected capacitors?
A few simple formulas will help us with this. Have no doubt, if you work in electronics, these simple formulas will help you out sooner or later.
Total capacitance of parallel connected capacitors:
C 1 – capacity of the first;
C 2 – capacity of the second;
C 3 – capacity of the third;
C N – capacity N th capacitor;
Ctot is the total capacity of the composite capacitor.
As you can see, when connecting the containers in parallel, you just need to fold them!
Attention! All calculations must be made in the same units. If we perform calculations in microfarads, then we need to indicate the capacitance C 1, C 2 in microfarads. The result will also be obtained in microfarads. This rule must be followed, otherwise mistakes cannot be avoided!
To avoid making mistakes when converting microfarads to picofarads, and nanofarads to microfarads, you need to know the abbreviated notation of numerical values. The table will also help you with this. It indicates the prefixes used for short notation and the factors with which you can recalculate. Read more about this.
The capacity of two series-connected capacitors can be calculated using another formula. It will be a little more complicated:
Attention! This formula is valid only for two capacitors! If there are more, then a different formula will be required. It is more confusing, and in reality it is not always useful.
Or the same thing, but more understandable:
If you carry out several calculations, you will see that with a series connection, the resulting capacitance will always be less than the smallest one included in this chain. What does this mean? This means that if you connect capacitors with a capacity of 5, 100 and 35 picofarads in series, the total capacitance will be less than 5.
If capacitors of the same capacity are used for a series connection, this cumbersome formula is magically simplified and takes the form:
Here, instead of a letter M set the number of capacitors, and C 1– its capacity.
It is also worth remembering a simple rule:
When two capacitors with the same capacitance are connected in series, the resulting capacitance will be half the capacitance of each of them.
Thus, if you connect two capacitors in series, each with a capacitance of 10 nanofarads, the resulting capacitance will be 5 nanofarads.
Let’s not waste words, but let’s check the capacitor by measuring the capacity, and in practice we will confirm the correctness of the formulas shown here.
Let's take two film capacitors. One is 15 nanofarads (0.015 µF), and the other is 10 nanofarads (0.01 µF). Let's connect them in series. Now let's take a multimeter Victor VC9805+ and measure the total capacitance of the two capacitors. This is what we get (see photo).
Measuring capacitance in series connection
The capacitance of the composite capacitor was 6 nanofarads (0.006 microfarads)
Now let's do the same thing, but for a parallel connection. Let's check the result using the same tester (see photo).
Capacitance measurement in parallel connection
As you can see, when connected in parallel, the capacitance of the two capacitors is added up and amounts to 25 nanofarads (0.025 μF).
What else do you need to know to properly connect capacitors?
Firstly, do not forget that there is another important parameter, such as the rated voltage.
When capacitors are connected in series, the voltage between them is distributed inversely proportional to their capacitances. Therefore, when connecting in series, it makes sense to use capacitors with a rated voltage equal to that of the capacitor, in place of which we are installing a composite one.
If capacitors with the same capacity are used, the voltage between them will be divided equally.
For electrolytic capacitors.
Series connection of electrolytes
Serial connection diagram
Also, do not forget about the rated voltage. In a parallel connection, each of the capacitors involved must have the same rated voltage as if we had placed one capacitor in the circuit. That is, if you need to install a capacitor with a rated voltage of 35 volts and a capacity of, for example, 200 microfarads in the circuit, then instead of it you can connect two capacitors in parallel with 100 microfarads and 35 volts. If at least one of them has a lower rated voltage (for example, 25 volts), it will soon fail.
It is advisable that for a composite capacitor, capacitors of the same type are selected (film, ceramic, mica, metal-paper). It would be best if they were taken from the same batch, since in this case the spread of parameters would be small.
Of course, a mixed (combined) connection is also possible, but it is not used in practice (I have not seen it). Calculating capacitance for a mixed connection usually falls to those who solve physics problems or pass exams :)
Those who are seriously interested in electronics definitely need to know how to correctly connect resistors and calculate their total resistance!
Fig.2 U=U 1 =U 2 =U 3
Total charge Q all capacitors
The total capacitance C, or the capacity of the battery, of capacitors connected in parallel is equal to the sum of the capacitances of these capacitors.
Connecting a capacitor in parallel to a group of other connected capacitors increases the total capacity of the bank of these capacitors. Therefore, parallel connection of capacitors is used to increase the capacitance.
4)If connected in parallel T identical capacitors with a capacity C´ each, then the total (equivalent) capacity of the battery of these capacitors can be determined by the expression
Series connection of capacitors
Fig.3
On the plates of series-connected capacitors connected to a direct current source with voltage U, charges of equal magnitude with opposite signs will appear.
The voltage on the capacitors is distributed inversely proportional to the capacitances of the capacitors:
The reciprocal of the total capacitance of series-connected capacitors is equal to the sum of the reciprocals of the capacitances of these capacitors.
When two capacitors are connected in series, their total capacitance is determined by the following expression:
If connected in series n identical capacitors with a capacity WITH each, then the total capacity of these capacitors:
From (14) it is clear that the more capacitors n connected in series, the lower their total capacity will be WITH, that is, connecting capacitors in series leads to a decrease in the total capacity of the capacitor bank.
In practice, it may turn out that the permissible operating voltage U p capacitor is less than the voltage to which the capacitor must be connected. If this capacitor is connected to such a voltage, it will fail, since the dielectric will be broken. If you connect several capacitors in series, the voltage will be distributed between them and the voltage on each capacitor will be less than its permissible operating voltage. U p . Hence, series connection of capacitors is used to ensure that the voltage on each capacitor does not exceed its operating voltageU p .
Mixed connection of capacitors
A mixed connection (series-parallel) of capacitors is used when it is necessary to increase the capacity and operating voltage of the capacitor bank.
Let's look at the mixed connection of capacitors using the examples below.
Capacitor Energy
Where Q - charge of the capacitor or capacitors to which voltage is applied U; WITH- electrical capacitance of a capacitor or bank of connected capacitors to which voltage is applied U.
Thus, capacitors serve to accumulate and store the electric field and its energy.
15. Defineconcepts three-rayed star and triangle of resistances. Write down the formulas for converting a three-ray star resistance into a triangle resistance and vice versa. Convert the circuit to two nodes (Figure 5)
Figure 5 - Electrical diagram
6.EXCHANGE DIAGRAMS
To facilitate the calculation, an equivalent circuit of the electrical circuit is drawn up, i.e., a circuit that displays the properties of the circuit under certain conditions.
The equivalent circuit shows all the elements whose influence on the calculation result cannot be neglected, and also indicates the electrical connections between them that are present in the circuit.
1. Replacement diagrams for electrical circuit elements
In calculation diagrams, the energy source can be represented by an EMF without internal resistance, if this resistance is small compared to the resistance of the receiver (Fig. 3.13.6).
the voltage at the source terminals at any current is equal to
EMF: U= E= const.
In some cases, the source of electrical energy in the design diagram is replaced by another (equivalent) circuit (Fig. 3.14, A), where instead of EMF E the source is characterized by its short circuit current I K, and instead of internal resistance, internal conductivity is introduced into the calculation g=1/ r.
The possibility of such a replacement can be proven by dividing equality (3.1) by r:
U/ r = E/ r- I,
Where U/ r = Io- a certain current equal to the ratio of the voltage at the source terminals to the internal resistance; E/ r = I K - source short circuit current;
Introducing new notations, we obtain the equality I K = Io + I, which is satisfied by the equivalent circuit in Fig. 3.14, A.
In this case, for any voltage at the terminals; source, its current remains equal to the short circuit current (Fig. 3.14.6):
A source with a constant current that does not depend on external resistance is called a current source.
The same source of electrical energy can be replaced in the design circuit by an EMF source or a current source.
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. 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:
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.
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. Diagram of parallel connection 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.
Content:In electronic and radio engineering circuits, parallel and series connections of capacitors have 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 previously provided for 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 compound
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.
