Parallel resistance online. Parallel connection of resistors: formula for calculating total resistance. It follows from it

Connecting in different ways allows you to obtain the required resistance value and one equivalent resistor. There are three ways to connect resistors - series, parallel and mixed.

Series connection of resistors

Series connection of resistors involves the use of two or more radio-electronic elements. The end of the previous element is connected to the beginning of the next one and so on. When connected in series, the resistance and power dissipation of all resistors are added up.
Consider the following example. Let's connect four resistors in series, each with R = 1 kOhm and power dissipation P = 0.25 W .

Rtotal = R1 + R2 + R3 + R4 = 1 kOhm + 1 kOhm + 1 kOhm + 1 kOhm = 4 kOhm.

Ptot = P1 + P2 + P3 + P4 = 0.25 W + 0.25 W + 0.25 W + 0.25 W = 1 W.

Thus, we obtain one equivalent or common resistor having the following parameters:
Rtotal = 4 kOhm; Ptotal = 1 W .

In a series circuit, the electric current flows of the same magnitude, so electrons along the entire path inevitably encounter all obstacles in the form of resistance. With each obstacle, the number of free charges decreases, which leads to a decrease in the strength of the electric current.

When resistors are connected in parallel, the number of paths for moving free charges, that is, electrons, from one section of the path to another increases. Therefore, when resistors are connected in parallel, their total (total, equivalent) resistance is always lower than the lowest resistance of all resistors.

The reciprocal of resistance is called conductivity. Conductivity is measured in Siemens [Sm] and is denoted by a capital letter G .

G = 1/R = 1/Ohm = cm

Therefore, when performing various calculations in electrical circuits that have a parallel connection, conductivity is used.

If the resistances of all parallel-connected resistors are equal, then to determine the total Rtot enough R one of them divided by their total number:

If R1 = R2 = R3 = R4 = R , That

Rtotal = R/4.

For example, each of the four resistors has R = 10 kOhm , Then

Rtotal = 10 kOhm/4 = 2.5 kOhm .

The dissipation powers are summed up in the same way as in a series connection.

Mixed connection of resistors

Mixed resistor connections are combinations of series and parallel connections. In principle, even the most complex electrical circuit, consisting of power supplies, diodes, and other radio-electronic elements, at a specific moment in time can be replaced by resistors and voltage sources, the parameters of which change with each subsequent moment in time. For example, let's draw a diagram that has several connections.

Resistors are widely used in electrical engineering and electronics. They are mainly used for regulation of current and voltage circuits. Main parameters: electrical resistance (R) measured in Ohms, power (W), stability and accuracy of their parameters during operation. You can remember many more of its parameters - after all, this is an ordinary industrial product.

Serial connection

A series connection is a connection in which each subsequent resistor is connected to the previous one, forming an unbroken circuit without branches. The current I=I1=I2 in such a circuit will be the same at each point. On the contrary, the voltage U1, U2 at its different points will be different, and the work of charge transfer through the entire circuit consists of the work of charge transfer in each of the resistors, U=U1+U2. According to Ohm's law, voltage U is equal to current times resistance, and the previous expression can be written as follows:

where R is the total resistance of the circuit. That is, simply put, there is a voltage drop at the connection points of the resistors and the more connected elements, the greater the voltage drop occurs

It follows that
, the total value of such a connection is determined by summing the resistances in series. Our reasoning is valid for any number of chain sections connected in series.

Parallel connection

Let's combine the beginnings of several resistors (point A). At another point (B) we will connect all their ends. As a result, we get a section of the circuit, which is called a parallel connection and consists of a certain number of branches parallel to each other (in our case, resistors). In this case, the electric current between points A and B will be distributed along each of these branches.

The voltages on all resistors will be the same: U=U1=U2=U3, their ends are points A and B.

The charges passing through each resistor per unit time add up to forming a charge passing through the entire block. Therefore, the total current through the circuit shown in the figure is I=I1+I2+I3.

Now, using Ohm's law, the last equality is transformed to this form:

U/R=U/R1+U/R2+U/R3.

It follows that for the equivalent resistance R the following is true:

1/R=1/R1+1/R2+1/R3

or after transforming the formula we can get another entry like this:
.

The more resistors (or other parts of an electrical circuit that have some resistance) are connected in a parallel circuit, the more paths for current flow are created, and the lower the overall resistance of the circuit.

It should be noted that the reciprocal of resistance is called conductivity. We can say that when sections of a circuit are connected in parallel, the conductivities of these sections are added up, and when connected in series, their resistances are added up.

Examples of using

It is clear that with a series connection, a break in the circuit in one place leads to the fact that the current stops flowing throughout the entire circuit. For example, a Christmas tree garland stops shining if just one light bulb burns out, this is bad.

But the series connection of light bulbs in a garland makes it possible to use a large number of small light bulbs, each of which is designed for mains voltage (220 V) divided by the number of light bulbs.

Series connection of resistors using the example of 3 light bulbs and EMF

But when a safety device is connected in series, its operation (break of the fuse link) allows you to de-energize the entire electrical circuit located after it and ensure the required level of safety, and this is good. The switch in the power supply network of the electrical appliance is also connected in series.

Parallel connection is also widely used. For example, a chandelier - all the bulbs are connected in parallel and are under the same voltage. If one lamp burns out, it’s not a big deal, the rest won’t go out, they remain under the same voltage.

Parallel connection of resistors using the example of 3 light bulbs and a generator

When it is necessary to increase the ability of a circuit to dissipate the thermal power released when current flows, both series and parallel combinations of resistors are widely used. For both series and parallel methods of connecting a certain number of resistors of the same value, the total power is equal to the product of the number of resistors and the power of one resistor.

Mixed connection of resistors

A mixed compound is also often used. If, for example, it is necessary to obtain a resistance of a certain value, but it is not available, you can use one of the methods described above or use a mixed connection.

From here, we can derive a formula that will give us the required value:

Rtot.=(R1*R2/R1+R2)+R3

In our era of the development of electronics and various technical devices, all complexities are based on simple laws, which are discussed superficially on this site and I think that they will help you successfully apply them in your life. If, for example, we take a Christmas tree garland, then the light bulbs are connected one after another, i.e. Roughly speaking, this is a separate resistance.

Not long ago, garlands began to be connected in a mixed way. In general, in total, all these examples with resistors are taken conditionally, i.e. any resistance element can be a current passing through the element with a voltage drop and heat generation.

Content:

All known types of conductors have certain properties, including electrical resistance. This quality has found its application in resistors, which are circuit elements with a precisely set resistance. They allow you to adjust current and voltage with high precision in circuits. All such resistances have their own individual qualities. For example, the power for parallel and series connection of resistors will be different. Therefore, in practice, various calculation methods are often used, thanks to which it is possible to obtain accurate results.

Properties and technical characteristics of resistors

As already noted, resistors in electrical circuits and circuits perform a regulatory function. For this purpose, Ohm's law is used, expressed by the formula: I = U/R. Thus, with a decrease in resistance, a noticeable increase in current occurs. And, conversely, the higher the resistance, the lower the current. Due to this property, resistors are widely used in electrical engineering. On this basis, current dividers are created that are used in the designs of electrical devices.

In addition to the current regulation function, resistors are used in voltage divider circuits. In this case, Ohm's law will look slightly different: U = I x R. This means that as the resistance increases, the voltage increases. The entire operation of devices designed to divide voltage is based on this principle. For current dividers, a parallel connection of resistors is used, and for a serial connection.

In the diagrams, resistors are displayed in the form of a rectangle measuring 10x4 mm. The symbol R is used for designation, which can be supplemented with the power value of a given element. For power above 2 W, the designation is made using Roman numerals. The corresponding inscription is placed on the diagram near the resistor icon. Power is also included in the composition applied to the element body. The units of resistance are ohm (1 ohm), kilohm (1000 ohm) and megaohm (1,000,000 ohm). The range of resistors ranges from fractions of an ohm to several hundred megaohms. Modern technologies make it possible to produce these elements with fairly accurate resistance values.

An important parameter of a resistor is the resistance deviation. It is measured as a percentage of the nominal value. The standard series of deviations represents values ​​in the form: + 20, + 10, + 5, + 2, + 1% and so on up to the value + 0,001%.

The power of the resistor is of great importance. An electric current passes through each of them during operation, causing heating. If the permissible power dissipation value exceeds the norm, this will lead to failure of the resistor. It should be taken into account that during the heating process the resistance of the element changes. Therefore, if devices operate over wide temperature ranges, a special value called the temperature coefficient of resistance is used.

To connect resistors in circuits, three different connection methods are used - parallel, series and mixed. Each method has individual qualities, which allows these elements to be used for a variety of purposes.

Power in series connection

When resistors are connected in series, electric current passes through each resistance in turn. The current value at any point in the circuit will be the same. This fact is determined using Ohm's law. If you add up all the resistances shown in the diagram, you get the following result: R = 200+100+51+39 = 390 Ohms.

Considering the voltage in the circuit is 100 V, the current will be I = U/R = 100/390 = 0.256 A. Based on the data obtained, the power of the resistors in series connection can be calculated using the following formula: P = I 2 x R = 0.256 2 x 390 = 25.55 W.

• P 1 = I 2 x R 1 = 0.256 2 x 200 = 13.11 W;
• P 2 = I 2 x R 2 = 0.256 2 x 100 = 6.55 W;
• P 3 = I 2 x R 3 = 0.256 2 x 51 = 3.34 W;
• P 4 = I 2 x R 4 = 0.256 2 x 39 = 2.55 W.

If we add up the received power, then the total P will be: P = 13.11 + 6.55 + 3.34 + 2.55 = 25.55 W.

Power with parallel connection

With a parallel connection, all the beginnings of the resistors are connected to one node of the circuit, and the ends to another. In this case, the current branches out and it begins to flow through each element. According to Ohm's law, the current will be inversely proportional to all connected resistances, and the voltage value across all resistors will be the same.

Before calculating the current, it is necessary to calculate the admittance of all resistors using the following formula:

• 1/R = 1/R 1 +1/R 2 +1/R 3 +1/R 4 = 1/200+1/100+1/51+1/39 = 0.005+0.01+0.0196+ 0.0256 = 0.06024 1/Ohm.
• Since resistance is a quantity inversely proportional to conductivity, its value will be: R = 1/0.06024 = 16.6 Ohms.
• Using a voltage value of 100 V, Ohm's law calculates the current: I = U/R = 100 x 0.06024 = 6.024 A.
• Knowing the current strength, the power of resistors connected in parallel is determined as follows: P = I 2 x R = 6.024 2 x 16.6 = 602.3 W.
• The current strength for each resistor is calculated using the formulas: I 1 = U/R 1 = 100/200 = 0.5A; I 2 = U/R 2 = 100/100 = 1A; I 3 = U/R 3 = 100/51 = 1.96A; I 4 = U/R 4 = 100/39 = 2.56A. Using these resistances as an example, a pattern can be seen that as the resistance decreases, the current increases.

There is another formula that allows you to calculate the power when resistors are connected in parallel: P 1 = U 2 / R 1 = 100 2 / 200 = 50 W; P 2 = U 2 /R 2 = 100 2 /100 = 100 W; P 3 = U 2 /R 3 = 100 2 /51 = 195.9 W; P 4 = U 2 / R 4 = 100 2 / 39 = 256.4 W. By adding up the powers of individual resistors, you get their total power: P = P 1 + P 2 + P 3 + P 4 = 50 + 100 + 195.9 + 256.4 = 602.3 W.

Thus, the power for series and parallel connection of resistors is determined in different ways, with the help of which the most accurate results can be obtained.

Not a single operation in electronics or electrical engineering is complete without calculating resistance. In this case, only the section of the circuit in which the mixed connection of resistors is located is considered. Engineers and physicists need to understand exactly how calculations occur in such schemes. In total, there are several types of connections that are used in circuits of varying complexity.

Serial connection

There are such methods of connecting resistors: serial, parallel and combined. When connected in series, the end of the first resistor is connected to the beginning of the second, and part of it to the third. This is how they work with all components. That is, all components of the chain follow each other. One common electric current will pass through them in such a connection. For such schemes, physicists use a formula in which between points A and B there is only one path for charged electrons to flow.

The resistance to flowing electricity depends on the number of connected resistors. The more components, the higher it is. It is calculated using the formula: R total = R1+R2+…+Rn, where:

• R total is the sum of all resistances;
• R1 - first resistor;
• R2 - second component;
• Rn is the last component in the chain.

Parallel connection

Parallel connection implies connecting the beginning of the resistors to one point, and ends to the other. The components themselves are located at the same distance from each other, and their number is not limited. Electricity flows through each component separately, choosing one of several paths.

Because there are multiple components and current paths in the circuit, the resistance is much lower than with a series connection. That is, the total amount of counteraction decreases in proportion to the increase in the number of components. The formula for determining the total amount of resistance to electricity is: 1/R total = 1/R1+1/R2+…+1/Rn.

In calculations, the total resistance should always be less than any of the components of the circuit. The way to calculate the sum of opposition for a circuit of two resistors is slightly different: 1/R total = (R1 x R2)/(R1+R2). If the components in the system have the same resistance values, then the total number will be equal to half of one of the components.

Mixed option

In a mixed connection of resistances, a serial and parallel connection circuit is combined. In this case, several components are connected in one way, and others in another, but they are all included in one circuit. In physics, this connection method is called series-parallel.

To calculate the amount of resistance to electricity, the circuit must be divided into small sections in which the resistors are connected in the same way. Then calculations are carried out according to the algorithm:

• in a circuit with parallel connected components, calculate the equivalent resistance;
• after this, the opposition is calculated in the series-connected sections of the circuit;
• the visual illustration needs to be redrawn, usually a circuit with resistors connected in series is obtained;
• calculate the resistance in the new circuit using one of two formulas.

An example will help you better understand the calculation methods. If there are only five components in a circuit, they may be arranged differently. The beginning of the first resistor is connected to point A, the end to B. A separate circuit with a combined connection comes from it. The second and third components are on a serial line, the fourth component is parallel to them. The last resistor comes from the end point of this circuit - G.

At first calculate the sum of the resistance of the serial section of the internal circuit: R2+R3. After this, the circuit is redrawn so that the second and third components are connected into one. As a result, the internal circuit is connected in parallel. Now its opposition is calculated: (R2.3xR4)/(R2.3+R4). You can draw the resulting circuit a second time.

The circuit will have three resistors connected in series. Moreover, the average includes the parameters of the second, third and fourth components.

Now you can find out the total amount of resistance. To do this, add up the resistance to electricity indicators of the first, fifth and other components. The formula will look like: R1+(R2.3xR4)/(R2.3+R4)+R5. You can immediately substitute all the parameters of the components into it.

In practice, serial and parallel connection methods are rarely used, because the circuits in devices are usually complex. Therefore, resistors in circuits are often connected in a combined way. Resistance in such cases is calculated step by step.

If you immediately put numbers into a general formula, you can make mistakes and get incorrect results. This may adversely affect the operation of the electrical appliance.

Content:

A resistor is a device that has a stable, stable resistance value. This allows you to adjust parameters in any part of the electrical circuit. There are various types of connections, including mixed connections of resistors. The use of one or another method in a particular circuit directly affects the voltage drop and current distribution in the circuit. The mixed connection option consists of serial and parallel connection of active resistances. Therefore, you need to consider these two types of connections first to understand how other circuits work.

Serial connection

A sequential connection diagram involves the arrangement of resistors in the circuit in such a way that the end of the first element is connected to the beginning of the second, and the end of the second to the beginning of the third, etc. That is, all resistors follow each other in turn. The current strength in a series connection will be the same in each element. In the form of a formula, it looks like this: I total = I 1 = I 2, where I total is the total current of the circuit, I 1 and I 2 correspond to the currents of the 1st and 2nd resistor.

In accordance with Ohm's law, the voltage of the power source will be equal to the sum of the voltage drops across each resistor: U total = U 1 + U 2 = I 1 r 1 + I 2 r 2, in which U total is the voltage of the electricity source or the network itself; U 1 and U 2 - the value of the voltage drops across the 1st and 2nd resistors; r 1 and r 2 - resistances of the 1st and 2nd resistors. Since the currents in any section of the circuit have the same value, the formula takes the form: Utot = I(r 1 + r 2).

Thus, we can conclude that with a series circuit of resistors, the electric current flowing through each of them is equal to the total current value in the entire circuit. The voltage across each resistor will be different, but their total sum will be a value equal to the total voltage of the entire electrical circuit. The total resistance of the circuit will also be equal to the sum of the resistances of each resistor included in this circuit.

Parameters of the circuit in parallel connection

A parallel connection is the connection of the initial outputs of two or more resistors at a single point, and the ends of the same elements at another common point. Thus, each resistor is actually connected directly to the power source.

As a result, it will be the same as the overall circuit voltage: U total = U 1 = U 2. In turn, the value of the currents will be different on each resistor, their distribution becomes directly proportional to the resistance of these resistors. That is, as the resistance increases, the current decreases, and the total current becomes equal to the sum of the currents passing through each element. The formula for this position is as follows: I total = I 1 + I 2.

To calculate the total resistance, the formula is used: . It is used when there are only two resistances in the circuit. In cases where three or more resistances are connected in the circuit, another formula is used:

Thus, the value of the total resistance of the electrical circuit will be less than the minimum resistance of one of the resistors connected in parallel to this circuit. Each element receives a voltage that is the same as the voltage of the electricity source. The current distribution will be directly proportional. The value of the total resistance of resistors connected in parallel should not exceed the minimum resistance of any element.

Mixed resistor connection diagram

A mixed connection circuit has the properties of resistor circuits. In this case, the elements are partially connected in series, and the other part is connected in parallel. In the presented diagram, resistors R 1 and R 2 are connected in series, and resistor R 3 is connected in parallel with them. In turn, resistor R 4 is connected in series with the previous group of resistors R 1, R 2 and R 3.

Calculating the resistance for such a circuit is fraught with certain difficulties. In order to perform calculations correctly, the conversion method is used. It consists in the sequential transformation of a complex chain into a simple chain in several stages.

If we again use the presented circuit as an example, then at the very beginning the resistance R 12 of resistors R 1 and R 2 connected in series is determined: R 12 = R 1 + R 2. Next, you need to determine the resistance of resistors R 123 connected in parallel using the following formula: R 123 = R 12 R 3 / (R 12 + R 3) = (R 1 + R 2) R 3 / (R 1 + R 2 + R 3). At the last stage, the equivalent resistance of the entire circuit is calculated by summing the obtained data R 123 and the resistance R 4 connected in series with it: R eq = R 123 + R 4 = (R 1 + R 2) R 3 / (R 1 + R 2 + R 3) + R 4.

In conclusion, it should be noted that a mixed connection of resistors has the positive and negative qualities of a series and parallel connection. This property is successfully used in practice in electrical circuits.