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.
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 capacitance 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
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 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.
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 No. 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 are selected (mica, ceramic, metal-paper, film). Then series connection of capacitors can give us the greatest beneficial effect.
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