What is called serial and parallel connection. Electric circuit with series connection of elements
In electrical circuits, elements can be connected according to various schemes, including they have consistent and parallel connection.
Serial connection
With this connection, the conductors are connected to each other in series, that is, the beginning of one conductor will be connected to the end of the other. Main Feature of this connection is that all conductors belong to one wire, there are no branches. The same electric current will flow through each of the conductors. But the total voltage on the conductors will be equal to the combined voltages on each of them.
Consider a number of resistors connected in series. Since there are no branches, the amount of charge passing through one conductor will be equal to the amount of charge passing through the other conductor. The current strength on all conductors will be the same. This is the main feature of this connection.
This connection can be viewed differently. All resistors can be replaced with one equivalent resistor.
The current through the equivalent resistor will coincide with total current, flowing through all resistors. The equivalent total voltage will be the sum of the voltages across each resistor. This is the potential difference across the resistor.
If you use these rules and Ohm's law, which applies to each resistor, you can prove that the resistance of the equivalent common resistor will be equal to the sum of the resistances. The consequence of the first two rules will be the third rule.
Application
A serial connection is used when you need to purposefully turn on or off a device; the switch is connected to it via sequential circuit. For example, an electric bell will only ring when it is connected in series with a source and a button. According to the first rule, if there is no electric current on at least one of the conductors, then there will be no electric current on the other conductors. And vice versa, if there is current on at least one conductor, then it will be on all other conductors. A pocket flashlight also works, which has a button, a battery and a light bulb. All these elements must be connected in series, since the flashlight needs to shine when the button is pressed.
Sometimes a serial connection does not achieve the desired goals. For example, in an apartment where there are many chandeliers, light bulbs and other devices, you should not connect all the lamps and devices in series, since you never need to turn on the lights in each of the rooms of the apartment at the same time. For this purpose, serial and parallel connections are considered separately, and a parallel type of circuit is used to connect lighting fixtures in the apartment.
Parallel connection
In this type of circuit, all conductors are connected in parallel to each other. All the beginnings of the conductors are connected to one point, and all the ends are also connected together. Let's consider a number of homogeneous conductors (resistors) connected in a parallel circuit.
This type of connection is branched. Each branch contains one resistor. The electric current, having reached the branching point, is divided into each resistor and will be equal to the sum of the currents at all resistances. The voltage across all elements connected in parallel is the same.
All resistors can be replaced with one equivalent resistor. If you use Ohm's law, you can get an expression for resistance. If, with a series connection, the resistances were added, then with a parallel connection, the inverse values of them will be added, as written in the formula above.
Application
If we consider connections in domestic conditions, then in an apartment lighting lamps and chandeliers should be connected in parallel. If we connect them in series, then when one light bulb turns on, we turn on all the others. With a parallel connection, we can, by adding the corresponding switch to each of the branches, turn on the corresponding light bulb as desired. In this case, turning on one lamp in this way does not affect the other lamps.
All electric household devices in the apartment are connected in parallel to a network with a voltage of 220 V, and connected to the distribution panel. In other words, parallel connection is used when connection is required electrical devices independently of each other. Serial and parallel connections have their own characteristics. There are also mixed compounds.
Current work
The series and parallel connections discussed earlier were valid for voltage, resistance and current values being the fundamental ones. The work of the current is determined by the formula:
A = I x U x t, Where A– current work, t– flow time along the conductor.
To determine operation with a series connection circuit, it is necessary to replace the voltage in the original expression. We get:
A=I x (U1 + U2) x t
We open the brackets and find that in the entire diagram, the work is determined by the amount at each load.
We also consider a parallel connection circuit. We just change not the voltage, but the current. The result is:
A = A1+A2
Current power
When considering the formula for the power of a circuit section, it is again necessary to use the formula:
P=U x I
After similar reasoning, the result is that series and parallel connections can be determined by the following power formula:
P=P1 + P2
In other words, for any circuit, the total power is equal to the sum of all powers in the circuit. This can explain that it is not recommended to turn on several powerful electrical devices in an apartment at once, since the wiring may not withstand such power.
The influence of the connection diagram on the New Year's garland
After one lamp in a garland burns out, you can determine the type of connection diagram. If the circuit is sequential, then not a single light bulb will light up, since a burnt out light bulb breaks the common circuit. To find out which light bulb has burned out, you need to check everything. Next, replace faulty lamp, the garland will function.
When using a parallel connection circuit, the garland will continue to work even if one or more lamps have burned out, since the circuit is not completely broken, but only one small parallel section. To restore such a garland, it is enough to see which lamps are not lit and replace them.
Series and parallel connection for capacitors
With a series circuit, the following picture arises: charges from the positive pole of the power source go only to the outer plates of the outer capacitors. , located between them, transfer charge along the circuit. This explains the appearance of equal charges with different signs on all plates. Based on this, the charge of any capacitor connected in a series circuit can be expressed by the following formula:
q total = q1 = q2 = q3
To determine the voltage on any capacitor, you need the formula:
Where C is capacity. The total voltage is expressed by the same law that is suitable for resistances. Therefore, we obtain the capacity formula:
С= q/(U1 + U2 + U3)
To make this formula simpler, you can reverse the fractions and replace the ratio of the potential difference to the charge on the capacitor. As a result we get:
1/C= 1/C1 + 1/C2 + 1/C3
The parallel connection of capacitors is calculated a little differently.
The total charge is calculated as the sum of all charges accumulated on the plates of all capacitors. And the voltage value is also calculated according to general laws. In this regard, the formula for the total capacitance in a parallel connection circuit looks like this:
С= (q1 + q2 + q3)/U
This value is calculated as the sum of each device in the circuit:
C=C1 + C2 + C3
Mixed connection of conductors
In an electrical circuit, sections of a circuit can have both series and parallel connections, intertwined with each other. But all the laws discussed above for certain types of connections are still valid and are used in stages.
First you need to mentally decompose the diagram into separate parts. For a better representation, it is drawn on paper. Let's look at our example using the diagram shown above.
It is most convenient to depict it starting from the points B And IN. They are placed at some distance from each other and from the edge of the sheet of paper. From the left side to the point B one wire is connected, and two wires go off to the right. Dot IN on the contrary, it has two branches on the left, and one wire goes off after the point.
Next you need to depict the space between the points. Along the upper conductor there are 3 resistances with conditional meanings 2, 3, 4. A current with index 5 will flow from below. The first 3 resistors are connected in series in the circuit, and the fifth resistor is connected in parallel.
The remaining two resistances (the first and sixth) are connected in series with the section we are considering B-C. Therefore, we supplement the diagram with 2 rectangles on the sides of the selected points.
Now we use the formula for calculating resistance:
- The first formula for sequential type connections.
- Next, for the parallel circuit.
- And finally for the sequential circuit.
In a similar way, you can decompose any complex circuit, including connections not only of conductors in the form of resistances, but also of capacitors. To learn how to calculate using different types schemes, you need to practice in practice by completing several tasks.
Good day to all. In the last article, I looked at electrical circuits containing energy sources. But the basis of analysis and design electronic circuits Along with Ohm's law there are also laws of balance, called Kirchhoff's first law, and voltage balance in sections of the circuit, called Kirchhoff's second law, which we will consider in this article. But first, let’s find out how energy receivers are connected to each other and what the relationships are between currents, voltages, etc.
Receivers electrical energy can be connected with three different ways: series, parallel or mixed (series - parallel). First, let's consider a sequential connection method, in which the end of one receiver is connected to the beginning of the second receiver, and the end of the second receiver is connected to the beginning of the third, and so on. The figure below shows the series connection of energy receivers with their connection to the energy source
An example of serial connection of energy receivers.
IN in this case the circuit consists of three serial energy receivers with resistance R1, R2, R3 connected to an energy source with U. An electric current of force I flows through the circuit, that is, the voltage at each resistance will be equal to the product of the current and resistance
Thus, the voltage drop across series-connected resistances is proportional to the values of these resistances.
From the above, the rule of equivalent series resistance follows, which states that series-connected resistances can be represented by an equivalent series resistance, the value of which is equal to the sum of series-connected resistances. This dependence is represented by the following relations
where R is the equivalent series resistance.
Application of serial connection
The main purpose of series connection of power receivers is to provide the required voltage less than the voltage of the power source. One such application is voltage divider and potentiometer
Voltage divider (left) and potentiometer (right).
Series-connected resistors are used as voltage dividers, in this case R1 and R2, which divide the voltage of the energy source into two parts U1 and U2. Voltages U1 and U2 can be used to operate different energy receivers.
Quite often, an adjustable voltage divider is used, which is a variable resistor R. The total resistance is divided into two parts using a moving contact, and thus the voltage U2 at the energy receiver can be smoothly changed.
Another way to connect electrical energy receivers is a parallel connection, which is characterized by the fact that several energy successors are connected to the same nodes of the electrical circuit. An example of such a connection is shown in the figure below
An example of parallel connection of energy receivers.
Electrical circuit in the figure consists of three parallel branches with load resistances R1, R2 and R3. The circuit is connected to an energy source with a voltage U, an electric current with a force I flows through the circuit. Thus, a current flows through each branch equal to the ratio of the voltage to the resistance of each branch
Since all branches of the circuit are under the same voltage U, the currents of the energy receivers are inversely proportional to the resistances of these receivers, and therefore parallel connected energy receivers can be seen as one energy receiver with the corresponding equivalent resistance, according to the following expressions
Thus, with a parallel connection, the equivalent resistance is always less than the smallest of the parallel-connected resistances.
Mixed connection of energy receivers
The most widespread is a mixed connection of electrical energy receivers. This connection is a combination of series and parallel connected elements. There is no general formula for calculating this type of connection, so in each individual case it is necessary to highlight sections of the circuit where there is only one type of receiver connection - serial or parallel. Then, using the formulas of equivalent resistances, gradually simplify these fates and ultimately bring them to the simplest form with one resistance, while calculating currents and voltages according to Ohm’s law. The figure below shows an example of a mixed connection of energy receivers
An example of a mixed connection of energy receivers.
As an example, let's calculate currents and voltages in all sections of the circuit. First, let's determine the equivalent resistance of the circuit. Let us select two sections with parallel connection of energy receivers. These are R1||R2 and R3||R4||R5. Then their equivalent resistance will be of the form
As a result, we obtained a circuit of two serial energy receivers R 12 R 345 equivalent resistance and the current flowing through them will be
Then the voltage drop across sections will be
Then the currents flowing through each energy receiver will be
As I already mentioned, Kirchhoff’s laws, together with Ohm’s law, are fundamental in the analysis and calculations of electrical circuits. Ohm's law was discussed in detail in the two previous articles, now it is the turn for Kirchhoff's laws. There are only two of them, the first describes the relationship between currents in electrical circuits, and the second describes the relationship between EMF and voltage in the circuit. Let's start with the first one.
Kirchhoff's first law states that the algebraic sum of the currents in a node is equal to zero. This is described by the following expression
where ∑ denotes an algebraic sum.
The word “algebraic” means that the currents must be taken taking into account the sign, that is, the direction of inflow. Thus, all currents that flow into the node are assigned a positive sign, and those flowing out of the node are assigned a correspondingly negative sign. The figure below illustrates Kirchhoff's first law
Image of Kirchhoff's first law.
The figure shows a node into which current flows from the side of resistance R1, and current flows out from the side of resistances R2, R3, R4, then the current equation for this section of the circuit will have the form
Kirchhoff's first law applies not only to nodes, but also to any circuit or part of an electrical circuit. For example, when I talked about parallel connection of energy receivers, where the sum of the currents through R1, R2 and R3 is equal to the inflowing current I.
As mentioned above, Kirchhoff’s second law determines the relationship between EMF and voltages in a closed circuit and is as follows: the algebraic sum of the EMF in any circuit circuit is equal to the algebraic sum of the voltage drops across the elements of this circuit. Kirchhoff's second law is defined by the following expression
As an example, consider the following diagram below, containing some circuit
Diagram illustrating Kirchhoff's second law.
First you need to decide on the direction of traversing the contour. In principle, you can choose either clockwise or counterclockwise. I will choose the first option, that is, the elements will be counted in the following order E1R1R2R3E2, thus the equation according to Kirchhoff’s second law will look like this
Kirchhoff's second law does not only apply to circuits direct current, but also to chains alternating current and to nonlinear circuits.
In the next article I will look at the main methods of calculation complex circuits using Ohm's law and Kirchhoff's laws.
Theory is good, but without practical application these are just words.
Consistent This connection of resistors is called when the end of one conductor is connected to the beginning of another, etc. (Fig. 1). With a series connection, the current strength in any part of the electrical circuit is the same. This is explained by the fact that charges cannot accumulate in the nodes of the circuit. Their accumulation would lead to a change in the electric field strength, and consequently to a change in the current strength. That's why
\(~I = I_1 = I_2 .\)
Ammeter A measures the current strength in the circuit and has a small internal resistance (R A → 0).
Included voltmeters V 1 and V 2 measure voltage U 1 and U 2 on resistances R 1 and R 2. Voltmeter V measures what is supplied to the terminals Μ And N voltage U. Voltmeters show that when connected in series, the voltage U equal to the sum of the voltages in individual sections of the circuit:
\(~U = U_1 + U_2 . \qquad (1)\)
Applying Ohm's law for each section of the circuit, we obtain:
\(~U = IR; \ U_1 = IR_1; \ U_2 = IR_2 ,\)
Where R - total resistance series connected circuit. Substituting U, U 1 , U 2 into formula (1), we have
\(~IR = IR_1 + IR_2 \Rightarrow R = R_1 + R_2 .\)
n resistors connected in series is equal to the sum of the resistances of these resistors:
\(~R = R_1 + R_2 + \ldots R_n\) , or \(~R = \sum_(i=1)^n R_i .\)
If the resistances of individual resistors are equal to each other, i.e. R 1 = R 2 = ... = R n, then the total resistance of these resistors when connected in series n times the resistance of one resistor: R = nR 1 .
When resistors are connected in series, the relation \(~\frac(U_1)(U_2) = \frac(R_1)(R_2)\) is valid, i.e. The voltages across the resistors are directly proportional to the resistances.
Parallel This connection of resistors is called when some ends of all resistors are connected into one node, the other ends into another node (Fig. 2). A node is a point in a branched circuit where more than two conductors converge. When connecting resistors in parallel to points Μ And N voltmeter is connected. It shows that the voltages in individual sections of the circuit with resistances R 1 and R 2 are equal. This is explained by the fact that the work of the forces of a stationary electric field does not depend on the shape of the trajectory:
\(~U = U_1 = U_2 .\)
The ammeter shows that the current is I in the unbranched part of the circuit is equal to the sum of the currents I 1 and I 2 in parallel connected conductors R 1 and R 2:
\(~I = I_1 + I_2 . \qquad (2)\)
This also follows from the conservation law electric charge. Let's apply Ohm's law for individual areas circuit and the entire circuit with a common resistance R:
\(~I = \frac(U)(R) ; \ I_1 = \frac(U)(R_1) ; \ I_2 = \frac(U)(R_2) .\)
Substituting I, I 1 and I 2 into formula (2), we get:
\(~\frac(U)(R) = \frac(U)(R_1) + \frac(U)(R_2) \Rightarrow \frac(1)(R) = \frac(1)(R_1) + \ frac(1)(R_2) .\)
The reciprocal value of the resistance of a circuit consisting of n resistors connected in parallel is equal to the sum of the reciprocal values of the resistances of these resistors:
\(~\frac 1R = \sum_(i=1)^n \frac(1)(R_i) .\)
If everyone's resistance n resistors connected in parallel are identical and equal R 1 then \(~\frac 1R = \frac(n)(R_1)\) . Where does \(~R = \frac(R_1)(n)\) come from?
Resistance of a circuit consisting of n identical parallel connected resistors, in n times less than the resistance of each of them.
When connecting resistors in parallel, the following relation is valid: \(~\frac(I_1)(I_2) = \frac(R_2)(R_1)\), i.e. The strength of currents in the branches of a parallel-connected circuit is inversely proportional to the resistance of the branches.
Literature
Aksenovich L. A. Physics in secondary school: Theory. Tasks. Tests: Textbook. allowance for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyhavanne, 2004. - P. 257-259.
Content:All electrical circuits use resistors, which are elements with exactly set value resistance. Thanks to the specific qualities of these devices, it becomes possible to adjust the voltage and current in any part of the circuit. These properties underlie the work of almost all electronic devices and equipment. So, the voltage when connecting resistors in parallel and in series will be different. Therefore, each type of connection can only be used under certain conditions, so that one or another electrical diagram could fully perform its functions.
Series voltage
In a series connection, two or more resistors are connected into a common circuit in such a way that each of them has contact with another device at only one point. In other words, the end of the first resistor is connected to the beginning of the second, and the end of the second to the beginning of the third, etc.
A feature of this circuit is that the same value passes through all connected resistors electric current. As the number of elements in the section of the circuit under consideration increases, the flow of electric current becomes more and more difficult. This occurs due to an increase in the total resistance of the resistors when they are connected in series. This property reflected by the formula: Rtot = R 1 + R 2.
The voltage distribution, in accordance with Ohm's law, is carried out for each resistor according to the formula: V Rn = I Rn x R n. Thus, as the resistance of the resistor increases, the voltage dropped across it also increases.
Parallel voltage
In a parallel connection, resistors are included in the electrical circuit in such a way that all resistance elements are connected to each other by both contacts at once. One point, representing an electrical node, can connect several resistors simultaneously.
This connection involves the flow of a separate current in each resistor. The strength of this current is inversely proportional. As a result, there is an increase in the overall conductivity of a given section of the circuit, with a general decrease in resistance. In the case of parallel connection of resistors with different resistances, the value of the total resistance in this section will always be lower than the smallest resistance of a single resistor.
In the diagram shown, the voltage between points A and B represents not only the total voltage for the entire section, but also the voltage supplied to each individual resistor. Thus, in case of parallel connection, the voltage applied to all resistors will be the same.
As a result, the voltage between parallel and series connections will be different in each case. Thanks to this property, there is a real opportunity to adjust this value at any part of the chain.
Content:
As you know, the connection of any circuit element, regardless of its purpose, can be of two types - parallel connection and serial connection. A mixed, that is, series-parallel connection is also possible. It all depends on the purpose of the component and the function it performs. This means that resistors do not escape these rules. The series and parallel resistance of resistors is essentially the same as the parallel and series connection of light sources. IN parallel circuit The connection diagram implies input to all resistors from one point, and output from another. Let's try to figure out how a serial connection is made and how a parallel connection is made. And most importantly, what is the difference between such connections and in which cases is a serial and in which parallel connection necessary? It is also interesting to calculate such parameters as the total voltage and total resistance of the circuit in cases of series or parallel connection. Let's start with definitions and rules.
Connection methods and their features
The types of connections of consumers or elements play a very important role, because the characteristics of the entire circuit, the parameters of individual circuits, and the like depend on this. First, let's try to figure out the serial connection of elements to the circuit.
Serial connection
A serial connection is a connection where resistors (as well as other consumers or circuit elements) are connected one after another, with the output of the previous one connected to the input of the next one. This type of switching of elements gives an indicator equal to the sum of the resistances of these circuit elements. That is, if r1 = 4 Ohms, and r2 = 6 Ohms, then when they are connected in a series circuit, the total resistance will be 10 Ohms. If we add another 5 ohm resistor in series, adding these numbers will give 15 ohms - this will be the total resistance of the series circuit. That is, the total values are equal to the sum of all resistances. When calculating it for elements that are connected in series, no questions arise - everything is simple and clear. That is why there is no need to even dwell more seriously on this.
Completely different formulas and rules are used to calculate the total resistance of resistors at parallel connection, here it makes sense to dwell on it in more detail.
Parallel connection
A parallel connection is a connection in which all resistor inputs are combined at one point, and all outputs at the second. The main thing to understand here is that the total resistance with such a connection will always be lower than the same parameter of the resistor that has the smallest one.
It makes sense to analyze such a feature using an example, then it will be much easier to understand. There are two 16 ohm resistors, but only 8 ohms are required for proper installation of the circuit. In this case, when using both of them, when they are connected in parallel to the circuit, the required 8 ohms will be obtained. Let's try to understand by what formula calculations are possible. This parameter can be calculated as follows: 1/Rtotal = 1/R1+1/R2, and when adding elements, the sum can continue indefinitely.
Let's try another example. 2 resistors are connected in parallel, with a resistance of 4 and 10 ohms. Then the total will be 1/4 + 1/10, which will be equal to 1:(0.25 + 0.1) = 1:0.35 = 2.85 ohms. As you can see, although the resistors had significant resistance, when they were connected in parallel, the overall value became much lower.
You can also calculate the total resistance of four parallel-connected resistors, with a nominal value of 4, 5, 2 and 10 ohms. The calculations, according to the formula, will be as follows: 1/Rtotal = 1/4+1/5+1/2+1/10, which will be equal to 1:(0.25+0.2+0.5+0.1)=1/1.5 = 0.7 Ohm.
As for the current flowing through parallel-connected resistors, here it is necessary to refer to Kirchhoff’s law, which states “the current strength in a parallel connection leaving the circuit is equal to the current entering the circuit.” Therefore, here the laws of physics decide everything for us. In this case, the total current indicators are divided into values that are inversely proportional to resistance branches. To put it simply, the higher the resistance value, the smaller the currents will pass through this resistor, but in general, the input current will still be at the output. In a parallel connection, the voltage at the output also remains the same as at the input. The parallel connection diagram is shown below.
Series-parallel connection
A series-parallel connection is when a series connection circuit contains parallel resistances. In this case, the total series resistance will be equal to the sum of the individual common parallel ones. The calculation method is the same in the relevant cases.
Summarize
Summarizing all of the above, we can draw the following conclusions:
- When connecting resistors in series, no special formulas are required to calculate the total resistance. You just need to add up all the indicators of the resistors - the sum will be the total resistance.
- When connecting resistors in parallel, the total resistance is calculated using the formula 1/Rtot = 1/R1+1/R2…+Rn.
- The equivalent resistance in a parallel connection is always less than the minimum similar value of one of the resistors included in the circuit.
- The current, as well as the voltage, in a parallel connection remains unchanged, that is, the voltage in a series connection is the same at both the input and output.
- A serial-parallel connection during calculations is subject to the same laws.
In any case, whatever the connection, it is necessary to clearly calculate all the indicators of the elements, because the parameters play a very important role when installing circuits. And if you make a mistake in them, then either the circuit will not work, or its elements will simply burn out from overload. In fact, this rule applies to any circuit, even in electrical installations. After all, the cross-section of the wire is also selected based on power and voltage. And if you put a light bulb rated at 110 volts in a circuit with a voltage of 220, it’s easy to understand that it will burn out instantly. The same goes for radio electronics elements. Therefore, attentiveness and scrupulousness in calculations is the key proper operation scheme.