Parallel connection of current and voltage resistors. Conductor current in parallel and series connection

Parallel connections of resistors, the calculation formula for which is derived from Ohm's law and Kirchhoff's rules, are the most common type of inclusion of elements in an electrical circuit. When connecting conductors in parallel, two or more elements are connected by their contacts on both sides, respectively. Connecting them to general scheme carried out precisely by these nodal points.

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General form

Features of inclusion

Conductors connected in this way are often part of complex chains that, in addition, contain a series connection of individual sections.

The following features are typical for such inclusion:

• The total voltage in each of the branches will have the same value;
• Flowing in any of the resistances electricity always inversely proportional to the value of their denomination.

In the particular case when all resistors connected in parallel have the same nominal values, the “individual” currents flowing through them will also be equal to each other.

Calculation

The resistances of a number of conductive elements connected in parallel are determined using a well-known form of calculation, which involves the addition of their conductivities (the reciprocal of the resistance values).

The current flowing in each of the individual conductors in accordance with Ohm's law can be found by the formula:

I= U/R (one of the resistors).

After familiarizing yourself with general principles for calculating the elements of complex chains, you can go to specific examples solving problems of this class.

Typical Connections

Example No. 1

Often, in order to solve the problem facing the designer, it is necessary to ultimately obtain a specific resistance by combining several elements. When considering the simplest version of such a solution, let’s assume that the total resistance of a chain of several elements should be 8 Ohms. This example requires separate consideration for the simple reason that in the standard series of resistances there is no nominal value of 8 Ohms (there are only 7.5 and 8.2 Ohms).

The solution to this simplest task can be obtained by connecting two identical elements with resistances of 16 Ohms each (such ratings exist in the resistive series). According to the formula given above, the total resistance of the chain in this case is calculated very simply.

It follows from it:

16x16/32=8 (Ohm), that is, exactly as much as was required.

So comparatively in a simple way it is possible to solve the problem of forming a total resistance equal to 8 Ohms.

Example No. 2

As another typical example of the formation of the required resistance, we can consider the construction of a circuit consisting of 3 resistors.

The total R value of such a connection can be calculated using the formula for series and parallel connections in conductors.

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In accordance with the nominal values ​​​​indicated in the picture, the total resistance of the chain will be equal to:

1/R = 1/200+1/220+1/470 = 0.0117;

R=1/0.0117 = 85.67 Ohm.

As a result, we find the total resistance of the entire chain obtained by connecting three elements in parallel with nominal values ​​of 200, 240 and 470 Ohms.

Important! This method is also applicable when calculating any number conductors or consumers connected in parallel.

It should also be noted that with this method of connecting elements of different sizes, the total resistance will be less than that of the smallest value.

Calculation of combined circuits

The considered method can also be used when calculating the resistance of more complex or combined circuits consisting of a whole set of components. They are sometimes called mixed, since both methods are used at once when forming chains. A mixed connection of resistors is shown in the figure below.

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Mixed scheme

To simplify the calculation, we first divide all resistors according to the type of connection into two independent groups. One of them is a serial connection, and the second is a parallel type connection.

From the above diagram it can be seen that elements R2 and R3 are connected in series (they are combined into group 2), which, in turn, is connected in parallel with resistor R1, which belongs to group 1.

A sequential connection is a connection of circuit elements in which the same current I occurs in all elements included in the circuit (Fig. 1.4).

Based on Kirchhoff’s second law (1.5), the total voltage U of the entire circuit is equal to the sum of the voltages in individual sections:

U = U 1 + U 2 + U 3 or IR eq = IR 1 + IR 2 + IR 3,

whence follows

R eq = R 1 + R 2 + R 3.

Thus, when serial connection elements of the circuit, the total equivalent resistance of the circuit is equal to the arithmetic sum of the resistances of the individual sections. Consequently, a circuit with any number of series-connected resistances can be replaced by a simple circuit with one equivalent resistance R eq (Fig. 1.5). After this, the calculation of the circuit is reduced to determining the current I of the entire circuit according to Ohm’s law

and using the above formulas, calculate the voltage drop U 1 , U 2 , U 3 in the corresponding sections of the electrical circuit (Fig. 1.4).

The disadvantage of sequential connection of elements is that if at least one element fails, the operation of all other elements of the circuit stops.

Electric circuit with parallel connection of elements

A parallel connection is a connection in which all consumers of electrical energy included in the circuit are under the same voltage (Fig. 1.6).

In this case, they are connected to two circuit nodes a and b, and based on Kirchhoff’s first law, we can write that the total current I of the entire circuit is equal to the algebraic sum of the currents of the individual branches:

I = I 1 + I 2 + I 3, i.e.

whence it follows that

.

In the case when two resistances R 1 and R 2 are connected in parallel, they are replaced by one equivalent resistance

.

From relation (1.6), it follows that the equivalent conductivity of the circuit is equal to the arithmetic sum of the conductivities of the individual branches:

g eq = g 1 + g 2 + g 3.

As the number of parallel-connected consumers increases, the conductivity of the circuit g eq increases, and vice versa, the total resistance R eq decreases.

Voltages in an electrical circuit with resistances connected in parallel (Fig. 1.6)

U = IR eq = I 1 R 1 = I 2 R 2 = I 3 R 3.

It follows that

those. The current in the circuit is distributed between parallel branches in inverse proportion to their resistance.

According to a parallel-connected circuit, consumers of any power, designed for the same voltage, operate in nominal mode. Moreover, turning on or off one or more consumers does not affect the operation of the others. Therefore, this circuit is the main circuit for connecting consumers to a source of electrical energy.

Electric circuit with a mixed connection of elements

A mixed connection is a connection in which the circuit contains groups of parallel and series-connected resistances.

For the circuit shown in Fig. 1.7, the calculation of equivalent resistance begins from the end of the circuit. To simplify the calculations, we assume that all resistances in this circuit are the same: R 1 =R 2 =R 3 =R 4 =R 5 =R. Resistances R 4 and R 5 are connected in parallel, then the resistance of the circuit section cd is equal to:

.

In this case, the original circuit (Fig. 1.7) can be represented in the following form (Fig. 1.8):

In the diagram (Fig. 1.8), resistance R 3 and R cd are connected in series, and then the resistance of the circuit section ad is equal to:

.

Then the diagram (Fig. 1.8) can be presented in an abbreviated version (Fig. 1.9):

In the diagram (Fig. 1.9) the resistance R 2 and R ad are connected in parallel, then the resistance of the circuit section ab is equal to

.

The circuit (Fig. 1.9) can be represented in a simplified version (Fig. 1.10), where resistances R 1 and R ab are connected in series.

Then the equivalent resistance of the original circuit (Fig. 1.7) will be equal to:

As a result of the transformations, the original circuit (Fig. 1.7) is presented in the form of a circuit (Fig. 1.11) with one resistance R eq. Calculation of currents and voltages for all elements of the circuit can be made according to Ohm's and Kirchhoff's laws.

LINEAR CIRCUITS OF SINGLE-PHASE SINEUSOIDAL CURRENT.

Obtaining sinusoidal EMF. . Basic characteristics of sinusoidal current

The main advantage of sinusoidal currents is that they allow the most economical production, transmission, distribution and use of electrical energy. The feasibility of their use is due to the fact that the efficiency of generators, electric motors, transformers and power lines in this case is the highest.

To obtain sinusoidally varying currents in linear circuits, it is necessary that e. d.s. also changed according to a sinusoidal law. Let us consider the process of occurrence of sinusoidal EMF. The simplest sinusoidal EMF generator can be a rectangular coil (frame), uniformly rotating in a uniform magnetic field with angular velocity ω (Fig. 2.1, b).

Magnetic flux passing through the coil as the coil rotates abcd induces (induces) in it based on the law of electromagnetic induction EMF e . The load is connected to the generator using brushes 1 , pressed against two slip rings 2 , which in turn are connected to the coil. Coil induced value abcd e. d.s. at each moment of time is proportional to the magnetic induction IN, the size of the active part of the coil l = ab + dc and the normal component of the speed of its movement relative to the field vn:

e = Blvn (2.1)

Where IN And l- constant values, a vn- a variable depending on the angle α. Expressing the speed v n through the linear speed of the coil v, we get

e = Blv·sinα (2.2)

In expression (2.2) the product Blv= const. Therefore, e. d.s. induced in a coil rotating in a magnetic field is a sinusoidal function of the angle α .

If the angle α = π/2, then the product Blv in formula (2.2) there is a maximum (amplitude) value of the induced e. d.s. E m = Blv. Therefore, expression (2.2) can be written in the form

e = Emsinα (2.3)

Because α is the angle of rotation in time t, then, expressing it in terms of angular velocity ω , we can write α = ωt, and rewrite formula (2.3) in the form

e = Emsinωt (2.4)

Where e- instantaneous value e. d.s. in a reel; α = ωt- phase characterizing the value of e. d.s. V this moment time.

It should be noted that instant e. d.s. over an infinitesimal period of time can be considered a constant value, therefore for instantaneous values ​​of e. d.s. e, voltage And and currents i laws are fair direct current.

Sinusoidal quantities can be represented graphically by sinusoids and rotating vectors. When depicting them as sinusoids, instantaneous values ​​of quantities are plotted on the ordinate on a certain scale, and time is plotted on the abscissa. If a sinusoidal quantity is represented by rotating vectors, then the length of the vector on the scale reflects the amplitude of the sinusoid, the angle formed with the positive direction of the abscissa axis at the initial time is equal to the initial phase, and the rotation speed of the vector is equal to the angular frequency. Instantaneous values ​​of sinusoidal quantities are projections of the rotating vector onto the ordinate axis. It should be noted that the positive direction of rotation of the radius vector is considered to be the direction of rotation counterclockwise. In Fig. 2.2 graphs of instantaneous e values ​​are plotted. d.s. e And e".

If the number of pairs of magnet poles p ≠ 1, then in one revolution of the coil (see Fig. 2.1) occurs p full cycles of change e. d.s. If the angular frequency of the coil (rotor) n revolutions per minute, then the period will decrease by pn once. Then the frequency e. d.s., i.e. the number of periods per second,

f = Pn / 60

From Fig. 2.2 it is clear that ωТ = 2π, where

ω = 2π / T = 2πf (2.5)

Size ω , proportional to the frequency f and equal to the angular velocity of rotation of the radius vector, is called the angular frequency. Angular frequency is expressed in radians per second (rad/s) or 1/s.

Graphically depicted in Fig. 2.2 e. d.s. e And e" can be described by expressions

e = Emsinωt; e" = E"msin(ωt + ψe") .

Here ωt And ωt + ψe"- phases characterizing the values ​​of e. d.s. e And e" at a given point in time; ψ e"- the initial phase that determines the value of e. d.s. e" at t = 0. For e. d.s. e the initial phase is zero ( ψ e = 0 ). Corner ψ always counted from the zero value of the sinusoidal value when it passes from negative to positive values ​​to the origin (t = 0). In this case, the positive initial phase ψ (Fig. 2.2) are laid to the left of the origin (towards negative values ωt), and the negative phase - to the right.

If two or more sinusoidal quantities that change with the same frequency do not have the same sinusoidal origins in time, then they are shifted relative to each other in phase, i.e., they are out of phase.

Angle difference φ , equal to the difference in the initial phases, is called the phase shift angle. Phase shift between sinusoidal quantities of the same name, for example between two e. d.s. or two currents, denote α . The phase shift angle between the current and voltage sinusoids or their maximum vectors is denoted by the letter φ (Fig. 2.3).

When for sinusoidal quantities the phase difference is equal to ±π , then they are opposite in phase, but if the phase difference is equal ±π/2, then they are said to be in quadrature. If the initial phases are the same for sinusoidal quantities of the same frequency, this means that they are in phase.

Sinusoidal voltage and current, the graphs of which are presented in Fig. 2.3 are described as follows:

u = Umsin(ω t+ψ u) ; i = Imsin(ω t+ψ i) , (2.6)

and the phase angle between current and voltage (see Fig. 2.3) in this case φ = ψ u - ψ i.

Equations (2.6) can be written differently:

u = Umsin(ωt + ψi + φ) ; i = Imsin(ωt + ψu - φ) ,

because the ψ u = ψ i + φ And ψ i = ψ u - φ .

From these expressions it follows that the voltage leads the current in phase by an angle φ (or the current is out of phase with the voltage by an angle φ ).

Forms of representation of sinusoidal electrical quantities.

Any sinusoidally varying electrical quantity (current, voltage, emf) can be presented in analytical, graphical and complex forms.

1). Analytical presentation form

I = I m sin( ω·t + ψ i), u = U m sin( ω·t + ψ u), e = E m sin( ω·t + ψ e),

Where I, u, e– instantaneous value of sinusoidal current, voltage, EMF, i.e. values ​​at the considered moment in time;

I m , U m , E m– amplitudes of sinusoidal current, voltage, EMF;

(ω·t + ψ ) – phase angle, phase; ω = 2·π/ T– angular frequency, characterizing the rate of phase change;

ψ i, ψ u, ψ e – the initial phases of current, voltage, EMF are counted from the point of transition of the sinusoidal function through zero to a positive value before the start of time counting ( t= 0). The initial phase can have both positive and negative meanings.

Graphs of instantaneous current and voltage values ​​are shown in Fig. 2.3

The initial phase of the voltage is shifted to the left from the origin and is positive ψ u > 0, the initial phase of the current is shifted to the right from the origin and is negative ψ i< 0. Алгебраическая величина, равная разности начальных фаз двух синусоид, называется сдвигом фаз φ . Phase shift between voltage and current

φ = ψ u – ψ i = ψ u – (- ψ i) = ψ u+ ψ i.

The use of an analytical form for calculating circuits is cumbersome and inconvenient.

In practice, one has to deal not with instantaneous values ​​of sinusoidal quantities, but with actual ones. All calculations are carried out for effective values; the rating data of various electrical devices indicate effective values ​​(current, voltage), most electrical measuring instruments show effective values. RMS current is the equivalent of direct current, which at the same time generates the same amount of heat in the resistor as alternating current. Effective value is related to the amplitude simple relation

2). Vector the form of representation of a sinusoidal electrical quantity is a vector rotating in a Cartesian coordinate system with a beginning at point 0, the length of which is equal to the amplitude of the sinusoidal quantity, the angle relative to the x axis is its initial phase, and the rotation frequency is ω = 2πf. The projection of a given vector onto the y-axis at any time determines the instantaneous value of the quantity under consideration.

Rice. 2.4

A set of vectors depicting sinusoidal functions is called a vector diagram, Fig. 2.4

3). Complex The presentation of sinusoidal electrical quantities combines the clarity of vector diagrams with accurate analytical calculations of circuits.

Rice. 2.5

We depict current and voltage as vectors on the complex plane, Fig. 2.5 The abscissa axis is called the axis of real numbers and is designated +1 , the ordinate axis is called the axis of imaginary numbers and is denoted +j. (In some textbooks, the real number axis is denoted Re, and the axis of imaginary ones is Im). Let's consider the vectors U And I at a point in time t= 0. Each of these vectors corresponds to a complex number, which can be represented in three forms:

A). Algebraic

U = U’+ jU"

I = I’ – jI",

Where U", U", I", I" – projections of vectors on the axes of real and imaginary numbers.

b). Indicative

Where U, I– modules (lengths) of vectors; e– the base of the natural logarithm; rotation factors, since multiplication by them corresponds to rotation of the vectors relative to the positive direction of the real axis by an angle equal to the initial phase.

V). Trigonometric

U = U·(cos ψ u+ j sin ψ u)

I = I·(cos ψ i – j sin ψ i).

When solving problems, they mainly use the algebraic form (for addition and subtraction operations) and the exponential form (for multiplication and division operations). The connection between them is established by Euler's formula

e jψ = cos ψ + j sin ψ .

Unbranched electrical circuits

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 series circuit. That is general values 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 in this case when you use both of them, when they are connected in parallel to the circuit, you will get the required 8 ohms. 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 general series resistance will be equal to the sum of 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:

1. 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.
2. When connecting resistors in parallel, the total resistance is calculated using the formula 1/Rtot = 1/R1+1/R2…+Rn.
3. The equivalent resistance in a parallel connection is always less than the minimum similar value of one of the resistors included in the circuit.
4. 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.
5. 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.

Series and parallel connection of conductors are the main types of conductor connections encountered in practice. Since electrical circuits, as a rule, do not consist of homogeneous conductors of the same cross-section. How to find the resistance of a circuit if the resistances of its individual parts are known.

Let's consider two typical cases. The first of these is when two or more resistive conductors are connected in series. In series means that the end of the first conductor is connected to the beginning of the second, and so on. With this connection of the conductors, the current strength in each of them will be the same. But the voltage on each of them will be different.

Figure 1 - serial connection of conductors

The voltage drop across the resistances can be determined based on Ohm's law.

Formula 1 - Voltage drop across resistance

The sum of these voltages will be equal to the total voltage applied to the circuit. The voltage on the conductors will be distributed in proportion to their resistance. That is, you can write it down.

Formula 2 - the relationship between resistance and voltage

The total resistance of the circuit will be equal to the sum of all resistances connected in series.

Formula 3 - calculation of the total resistance when connected in parallel

The second case is when the resistances in the circuit are connected in parallel to each other. That is, there are two nodes in the circuit and all conductors with resistance are connected to these nodes. In such a circuit, the currents in all branches are generally not equal to each other. But the sum of all currents in the circuit after the branching will be equal to the current before the branching.

Figure 2 - Parallel connection of conductors

Formula 4 - relationship between currents in parallel branches

The current strength in each of the branched circuits also obeys Ohm's law. The voltage on all conductors will be the same. But the current strength will be separated. In a circuit consisting of parallel-connected conductors, the currents are distributed in proportion to the resistances.

Formula 5 - Distribution of currents in parallel branches

To find impedance circuit in this case, it is necessary to add the reciprocal values ​​of the resistance, that is, the conductivity.

Formula 6 - Resistance of parallel-connected conductors

There is also a simplified formula for the special case when two identical resistances are connected in parallel.

The current in an electrical circuit passes through conductors from the voltage source to the load, that is, to lamps and devices. In most cases, copper wires are used as conductors. The circuit may contain several elements with different resistances. In an instrument circuit, conductors can be connected in parallel or in series, and there can also be mixed types.

A circuit element with resistance is called a resistor, voltage of this element is the potential difference between the ends of the resistor. Parallel and series electrical connections of conductors are characterized by a single operating principle, according to which the current flows from plus to minus, and the potential decreases accordingly. In electrical circuits, the wiring resistance is taken as 0, since it is negligibly low.

A parallel connection assumes that the elements of the circuit are connected to the source in parallel and are turned on simultaneously. Series connection means that the resistance conductors are connected in strict sequence one after another.

When calculating, the idealization method is used, which greatly simplifies understanding. In fact, in electrical circuits the potential gradually decreases as it moves through the wiring and elements that are included in a parallel or series connection.

Series connection of conductors

The serial connection scheme means that they are switched on in a certain sequence, one after the other. Moreover, the current strength in all of them is equal. These elements create a total stress in the area. Charges do not accumulate in the nodes of the electrical circuit, since otherwise a change in voltage and current would be observed. At constant voltage The current is determined by the value of the circuit resistance, so in a series circuit the resistance changes if one load changes.

The disadvantage of this scheme is the fact that if one element fails, the others also lose the ability to function, since the circuit is broken. An example would be a garland that does not work if one bulb burns out. This is key difference from a parallel connection in which the elements can function separately.

The sequential circuit assumes that, due to the single-level connection of the conductors, their resistance is equal at any point in the network. The total resistance is equal to the sum of the voltage reduction individual elements networks.

At this type connections, the beginning of one conductor is connected to the end of another. Key Feature connection is that all conductors are on one wire without branches, and one electric current flows through each of them. However, the total voltage is equal to the sum of the voltages on each. You can also look at the connection from another point of view - all conductors are replaced by one equivalent resistor, and the current on it coincides with the total current that passes through all resistors. The equivalent cumulative voltage is the sum of the voltage values ​​across each resistor. This is how the potential difference across the resistor appears.

Using a serial connection is useful when you need to specifically turn on and off specific device. For example, an electric bell can ring only when there is a connection to a voltage source and a button. The first rule states that if there is no current on at least one of the elements of the circuit, then there will be no current on the rest. Accordingly, if there is current in one conductor, it is also in the others. Another example would be a battery-powered flashlight, which only lights up if there is a battery, a working light bulb, and a button pressed.

In some cases, a sequential circuit is not practical. In an apartment where the lighting system consists of many lamps, sconces, chandeliers, there is no need to organize a scheme of this type, since there is no need to turn the lighting on and off in all rooms at the same time. For this purpose, it is better to use a parallel connection in order to be able to turn on the light in individual rooms.

Parallel connection of conductors

In a parallel circuit, the conductors are a set of resistors, some ends of which are assembled into one node, and the other ends into a second node. It is assumed that the voltage in the parallel type of connection is the same in all sections of the circuit. Parallel sections of the electrical circuit are called branches and pass between two connecting nodes; they have the same voltage. This voltage is equal to the value on each conductor. The sum of the inverse indicators of the resistances of the branches is also the inverse with respect to the resistance of an individual section of the circuit of the parallel circuit.

For parallel and series connections, the system for calculating the resistance of individual conductors is different. In the case of a parallel circuit, the current flows through the branches, which increases the conductivity of the circuit and reduces the total resistance. When several resistors with similar values ​​are connected in parallel, the total resistance of such an electrical circuit will be less than one resistor a number of times equal to .

Each branch has one resistor, and the electric current, when it reaches the branching point, is divided and diverges to each resistor, its final value is equal to the sum of the currents at all resistances. All resistors are replaced with one equivalent resistor. Applying Ohm's law, the value of resistance becomes clear - in a parallel circuit, the values ​​inverse to the resistances on the resistors are summed up.

With this circuit, the current value is inversely proportional to the resistance value. The currents in the resistors are not interconnected, so if one of them is turned off, this will in no way affect the others. For this reason, this circuit is used in many devices.

When considering the possibilities of using a parallel circuit in everyday life, it is advisable to note the apartment lighting system. All lamps and chandeliers must be connected in parallel; in this case, turning one of them on and off does not in any way affect the operation of the remaining lamps. Thus, by adding a switch for each light bulb in a branch of the circuit, you can turn the corresponding light on and off as needed. All other lamps operate independently.

All electrical appliances are connected in parallel into an electrical network with a voltage of 220 V, then they are connected to. That is, all devices are connected regardless of the connection of other devices.

Laws of series and parallel connection of conductors

For a detailed understanding in practice of both types of connections, we present formulas explaining the laws of these types of connections. Power calculations for parallel and series connections are different.

In a series circuit, there is the same current in all conductors:

According to Ohm's law, these types of conductor connections in different cases are explained differently. So, in the case of a series circuit, the voltages are equal to each other:

U1 = IR1, U2 = IR2.

In addition, the total voltage is equal to the sum of the voltages of the individual conductors:

U = U1 + U2 = I(R1 + R2) = IR.

The total resistance of the electrical circuit is calculated as the sum active resistances all conductors, regardless of their number.

In the case of a parallel circuit, the total voltage of the circuit is similar to the voltage of the individual elements:

And the total strength of the electric current is calculated as the sum of the currents that exist in all conductors located in parallel:

To ensure maximum efficiency electrical networks, it is necessary to understand the essence of both types of connections and apply them expediently, using the laws and calculating the rationality of practical implementation.

Mixed connection of conductors

Consistent and parallel circuit Resistance connections can be combined in one circuit if necessary. For example, it is possible to connect parallel resistors according to a sequential or group of them, this type is considered combined or mixed.

In this case, the total resistance is calculated by summing the values ​​for the parallel connection in the system and for the series connection. First, it is necessary to calculate the equivalent resistances of resistors in a series circuit, and then the elements of a parallel circuit. Serial connection is considered a priority, and circuits of such combined type often used in household appliances and devices.

So, by considering the types of conductor connections in electrical circuits and based on the laws of their functioning, you can fully understand the essence of the organization of circuits of most household electrical appliances. For parallel and series connections, the calculation of resistance and current is different. Knowing the principles of calculation and formulas, you can competently use each type of circuit organization to connect elements in the best possible way and with maximum efficiency.