Serial circuit diagram. Parallel connection of conductors

Let's check the validity of the formulas shown here using a simple experiment.

Let's take two resistors MLT-2 on 3 And 47 Ohm and connect them in series. Then we measure the total resistance of the resulting circuit with a digital multimeter. As we can see, it is equal to the sum of the resistances of the resistors included in this chain.

Measuring total resistance in series connection

Now let's connect our resistors in parallel and measure their total resistance.

Resistance measurement in parallel connection

As you can see, the resulting resistance (2.9 Ohms) is less than the smallest (3 Ohms) included in the chain. This leads to another well-known rule that can be applied in practice:

When resistors are connected in parallel, the total resistance of the circuit will be less than the smallest resistance included in this circuit.

What else needs to be considered when connecting resistors?

Firstly, Necessarily their rated power is taken into account. For example, we need to select a replacement resistor for 100 Ohm and power 1 W. Let's take two resistors of 50 ohms each and connect them in series. How much power dissipation should these two resistors be rated for?

Since the same direct current flows through series-connected resistors (for example 0.1 A), and the resistance of each of them is equal 50 ohm, then the dissipation power of each of them must be at least 0.5 W. As a result, on each of them there will be 0.5 W power. In total this will be the same 1 W.

This example is quite crude. Therefore, if in doubt, you should take resistors with a power reserve.

Read more about resistor power dissipation.

Secondly, when connecting, you should use resistors of the same type, for example, the MLT series. Of course, there is nothing wrong with taking different ones. This is just a recommendation.

Conductor resistance. Parallel and series connection of conductors.

Electrical resistance- a physical quantity that characterizes the properties of a conductor to prevent the passage of electric current and is equal to the ratio of the voltage at the ends of the conductor to the strength of the current flowing through it. Resistance for alternating current circuits and for alternating electromagnetic fields is described by the concepts of impedance and characteristic impedance. Resistance (resistor) is also called a radio component designed to introduce active resistance into electrical circuits.

Resistance (often symbolized by the letter R or r) is considered, within certain limits, a constant value for a given conductor; it can be calculated as

R- resistance;

U- electrical potential difference (voltage) at the ends of the conductor;

I- the strength of the current flowing between the ends of the conductor under the influence of a potential difference.

For serial connection conductors (Fig. 1.9.1), the current strength in all conductors is the same:

According to Ohm's law, voltage U 1 and U 2 on the conductors are equal

In a series connection, the total resistance of the circuit is equal to the sum of the resistances of the individual conductors.

This result is valid for any number of conductors connected in series.

In parallel connection (Fig. 1.9.2) voltage U 1 and U 2 on both conductors are the same:

This result follows from the fact that at current branching points (nodes A And B) charges cannot accumulate in a DC circuit. For example, to the node A in time Δ t charge is leaking IΔ t, and the charge flows away from the node at the same time I 1Δ t + I 2Δ t. Hence, I = I 1 + I 2 .

Writing based on Ohm's law

When connecting conductors in parallel, the reciprocal of the total resistance of the circuit is equal to the sum of the reciprocals of the resistances of parallel-connected conductors.

This result is valid for any number of conductors connected in parallel.

Formulas for series and parallel connection of conductors allow in many cases to calculate the resistance of a complex circuit consisting of many resistors. In Fig. 1.9.3 shows an example of such a complex circuit and indicates the sequence of calculations.

It should be noted that not all complex circuits consisting of conductors with different resistances can be calculated using formulas for series and parallel connections. In Fig. 1.9.4 shows an example of an electrical circuit that cannot be calculated using the above method.

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. Their connection to the general circuit is 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;
• The electric current flowing in any of the resistances is always inversely proportional to the value of their nominal value.

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 becoming familiar with the general principles of calculating the elements of complex chains, you can move on to specific examples of 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 problem 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.

In this relatively 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 an arbitrary number of 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.

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 a parallel circuit, the connection diagram involves 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 when connected in parallel, so 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 the resistance of the branch. 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:

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 to the correct operation of the circuit.

In electrical circuits, elements can be connected in various ways, including serial and parallel connections.

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. The 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 across the equivalent resistor will be the same as the 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 in a series 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 electrical 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 it is necessary to connect 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 the 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:

С=С1 + С2 + С3

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 compounds 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 comes off after the point.

Next you need to depict the space between the points. Along the upper conductor there are 3 resistances with conventional values ​​2, 3, 4. From below there will be a current with index 5. The first 3 resistances 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 a series connection.
• Next, for the parallel circuit.
• And finally for the sequential circuit.

In a similar way, any complex circuit can be decomposed into separate circuits, including connections of not only conductors in the form of resistances, but also capacitors. To learn how to use calculation techniques for different types of schemes, you need to practice in practice by completing several tasks.