Calculator connecting resistors online. Parallel compound of resistors

Each electrical circuit has a resistor having resistance electric Toku.. Resistors are two types: constant and variables. During the development of any electrical circuit and repair of electronic products, it is often necessary to apply a resistor with a necessary face value.

Although various denominations are provided for resistors.It may happen that it will not be possible to find the necessary or any element in general will not be able to provide the desired indicator.

By solving this problem, the use of a sequential and parallel compound can be the use of a sequential and parallel connection. After reading this article, you will learn about the peculiarities of the calculation and selection of various resistance denominations.

Parallel compound: general information

Often, during the manufacture of any device, resistors are used, which are connected in accordance with the sequential scheme. The effect of the application of this embodiment is reduced to an increase in the total chain resistance. For this option Connections of the elements created by them resistance is calculated as the sum of the denominations. If the assembly of parts is performed on a parallel scheme, then here it will be necessary to calculate resistanceUsing the formulas described below.

The parallel compound scheme resorts in a situation where there is a task to reduce the total resistance, and, in addition to this, increasing the power for a group of elements connected via a parallel diagram, which must be greater than when they are separately connected.

Calculation of resistance

In the case of connecting parts with each other, using a parallel scheme to calculate the total resistance, the following formula will be used:

R (total) \u003d 1 / (1 / R1 + 1 / R2 + 1 / R3 + 1 / Rn).

R1-R3 and Rn are resistors connected by parallel diagram.

Moreover, if the chain is created on the basis of only two elements, then such a formula should be used to determine the total nominal resistance:

R (total) \u003d R1 * R2 / R1 + R2.

R (total) - total resistance;
R1 and R2 are resistors connected via a parallel diagram.

Video: An example of resistance calculation

Universal calculation scheme

For radio engineering, attention should be paid to one important rule: if the elements are connected to each other along a parallel scheme have the same indicator, To calculate the total nominal value, it is necessary to divide the number of connected nodes to the number of connected nodes:

R (total) - the total resistance value;
R is the value of the resistor connected via a parallel scheme;
n - the number of connected nodes.

Special attention should be paid to the fact that the final resistance indicator in the case of using a parallel connection scheme be sure to be less Compared to the face value of any element connected to the chain.

Example of calculation

For greater clarity, you can consider the following example: let's say, we have three resistors whose rates are respectively 100, 150 and 30 ohms. If you use the first formula to determine the total nominal value, we will receive the following:

R (total) \u003d 1 / (1/100 + 1/150 + 1/30) \u003d

1 / (0.01 + 0.007 + 0.03) \u003d 1 / 0.047 \u003d 21.28.

If you perform simple calculations, then you can obtain the following: for a chain, including three parts, where the smallest resistance indicator is 30 ohms, the resultant value of the nominal will be 21.28 ohms. This indicator will be less minimum meaning Nominal in the chain is almost 30%.

Important nuances

Usually, the parallel compound is used for resistors when it is necessary for the task of creating the resistance of greater power. It will require resistors to solve it, which must have equal resistance and power indicators. With this option it is possible to determine the overall power as follows.: The power of one element must be multiplied with the total number of all resistors from which the chain is connected to each other in accordance with the parallel scheme.

Let's say if we are used by five resistors whose rating is 100 ohms, and each power is equal to 1 W, which are attached to each other in accordance with the parallel diagram, the total resistance rate will be equal to 20 ohms, and the power will be 5 W.

If you take the same resistors, but connect them in accordance with the sequential scheme, then the final power will be 5 W, and the total value will be equal to 500 ohms.

Video: Proper LED connection

The parallel diagram of connecting resistors is very in demand for the reason that it often arises the task of creating a nominal value that cannot be achieved using a simple parallel compound. Wherein the procedure for calculating this parameter is quite sufficientwhere you need to consider different parameters.

Here, an important role is assigned not only to the number of connected elements, but also the working parameters of the resistors - first of all, resistance and power. If one of the connected elements will have an inappropriate indicator, it will not effectively solve the problem to create the required nominal in the chain.

Parallel compound of resistors - One of the two types of electrical connections, when both outputs of one resistor are connected to the corresponding conclusions of another resistor or resistors. Often or in parallel in order to create more complex electronic circuits.

The parallel connection circuit is shown in the figure below. With parallel compound of resistors, the voltage on all resistors will be the same, and the current flowing through them will be proportional to their resistance:

Formula of parallel compound resistors

The overall resistance of several resistors connected in parallel is determined by the following formula:

The current flowing through a separately taken resistor, according to, can be found by the formula:

Parallel compound of resistors - calculation

Example №1

When developing the device, it was necessary to establish a resistor with an 8 ohm resistance. If we review the entire nominal number of standard resistor values, we will see that the resistor with the resistance of 8 ohms in it is not.

The way out of this situation will be the use of two parallel connected resistors. The equivalent resistance value for two resistors connected in parallel is calculated as follows:

This equation shows that if R1 is R2, the resistance R is half the resistance of one of two resistors. At r \u003d 8 ohms, R1 and R2 should, therefore, have a value of 2 × 8 \u003d 16 ohms.
Now we will check, calculating the overall resistance of two resistors:

Thus, we obtained the necessary resistance of 8 ohms, connecting parallel to the two resistors of 16 ohms.

Example of calculation No. 2.

Find the total resistance R from the three parallel to the connected resistors:

The general resistance R is calculated by the formula:

This calculation method can be used to calculate any number of individual resistance connected in parallel.

One important momentIt is necessary to remember when calculating parallel to the connected resistors - this is that the overall resistance will always be less than the value of the smallest resistance in this combination.

How to calculate complex compound schemes of resistors

More complex compounds of resistors can be calculated by systematic grouping of resistors. Figure below, it is necessary to calculate the total chain resistance consisting of three resistors:

For ease of calculation, first grouped resistors over a parallel and sequential type of compound.
Resistors R2 and R3 are connected sequentially (group 2). They, in turn, are connected in parallel with the resistor R1 (group 1).

The sequential compound of the group 2 resistors is calculated as the sum of resistance R2 and R3:

As a result, we simplify the scheme in the form of two parallel resistors. Now the overall resistance of the whole scheme can be calculated as follows:

Calculation of more complex compounds of resistors can be performed using the laws of Kirchhoff.

The current flowing into the circuit parallel to the connected resistors

The total current I flowing in the circuit parallel resistors is equal to the sum of individual currents occurring in all parallel branches, and the current in a separate branch does not have to be equal to the current in the neighboring branches.

Despite the parallel connection, the same voltage is applied to each resistor. And since the magnitude of the resistance in the parallel chain can be different, then the value of the flowing current through each resistor will also differ (by defining the Ohm law).

Consider this on the example of two parallel connected resistors. The current that flows through each of the resistors (I1 and I2) will differ from each other since resistance resistors R1 and R2 are not equal.
However, we know that the current that enters the chain at the point "A" should exit the chain at the point "B".

The first Kirchhoff rule says: "The total current coming out of the circuit is equal to the circuit."

Thus, the flowing current in the chain can be defined as:

Then, using the Ohm law, you can calculate the current that flows through each resistor:

The current flowing into R1 \u003d U ÷ R1 \u003d 12 ÷ 22 kΩ \u003d 0.545 mA

The current flowing into R 2 \u003d U ÷ R2 \u003d 12 ÷ 47 com \u003d 0.255 mA

Thus, the total current will be equal to:

I \u003d 0.545 mA + 0.255 mA \u003d 0.8 mA

It can also be checked using the Ohm Law:

I \u003d u ÷ r \u003d 12 V ÷ 15 kΩ \u003d 0.8 mA (the same)

where 15kom is the overall resistance of two parallel connected resistors (22 com and 47 com)

And at the end, I would like to note that most modern resistors are marked with colored stripes and it can be found for it.

Parallel Connection Resistors - Online Calculator

To quickly calculate the overall resistance of two or more resistors connected in parallel, you can use the following online calculator:

Summarize

When two or more resistors are connected so that both outputs of one resistor are connected to the corresponding conclusions of another resistor or resistors, they say that they are interconnected in parallel. The voltage on each resistor inside the parallel combination is the same, but currents flowing through them may differ from each other, depending on the resistance of each resistor.

Equivalent or impedance A parallel combination will always be less than the minimum resistance of the resistor incoming in a parallel connection.

1 Mom \u003d 0.001 ohms. 1 com \u003d 1 000 \u003d 10³ Ohm. 1 MOM \u003d 1 000 000 \u003d 10 Ω.

The equivalent resistance R EQ group parallel to the connected resistors is the value of the inverse amount of the values, inversely proportional to the resistance of these resistors.

In other words, conductivity G. Parallel to the connected resistors is equal to the amount of conductors of these resistors:

This formula for R EQ is used in this calculator for calculations. For example, the total resistance of three resistors 10, 15 and 20 ohms connected in parallel, equal to 4.62 ohms:

If only two resistors are connected in parallel, the formula is simplified:

If available n. connected parallel to the same resistors R.then their equivalent resistance will be equal

It should be noted that the general resistance of the group from any number of connected parallel resistors will always be less than the smallest resistance of the resistor in the group and the addition of a new resistor will always lead to a decrease in equivalent resistance.

We also note that all resistors connected in parallel are under the same voltage. However, currents flowing through individual resistors differ and depend on their resistance. The total current through a group of resistors is equal to the sum of currents in separate resistors.

When connecting several resistors in parallel, you should always consider their tolerances and dispel power.

Examples of applying parallel compound resistors

One example of a parallel compound of resistors is a shunt in the device for measuring currents that are too high in order to be directly measured by the device intended for measuring small currents or stresses. To measure the current parallel to the galvanometer or electronic device measuring the voltage, a resistor is connected with a very small precisely known resistance made of material with stable characteristics. This resistor is called Shunts. The measured current flows through the shunt. As a result, it falls on it small tensionwhich is measured by a voltmeter. Since the voltage drop is proportional to the current flowing through the shunt with a known and accurate resistance, the voltmeter connected parallel to the shunt can be chased directly in the current units (amperes).

Parallel and serial schemes are often used to obtain accurate resistance or if there is no resistor with the required resistance or it is too expensive if it is purchased in small quantities for mass production. For example, if the device contains many resistors for 20 kΩ and only one resistor is required 10 com. Of course, it is easy to find a resistor on 10 com. However, for mass production, it is sometimes better to put two resistors on 20 kΩ in parallel to get the necessary 10 com. This will reduce costs pCBbecause it will be reduced wholesale price Components, as well as the cost of installation, as the number of elements sizes will be reduced, which must be installed on the board of the component installation machine.

We check the justice of the formulas shown here on a simple experiment.

Take two resistors MLT-2 on the 3 and 47 Oh. and connect them successively. Then I measure the overall resistance of the resulting circuit with a digital multimeter. As we see, it is equal to the sum of the resistance of the resistors included in this chain.

Measurement of general resistance with a sequential connection

Now connect our resistors in parallel and measure their overall resistance.

Measurement of resistance with parallel connection

As we see, the resulting resistance (2.9 Ohms) is less than the smaller (3 ohms) included in the chain. From here, it follows another well-known rule that can be applied in practice:

With parallel compound of resistors, the total chain resistance will be less than the smallest resistance incoming in this chain.

What else to take into account when connecting resistors?

Firstly, before Their nominal power is taken into account. For example, we need to find a replacement resistor on 100 Oh. and power 1 W.. Take two resistors of 50 ohms each and connect them successively. What power of scattering should these two resistors be calculated?

Since through consistently, the connected resistors flow the same permanent current (let's say 0.1 A.), and the resistance of each of them is equal 50 Ohm., then the dispersion capacity of each of them should be at least 0.5 W.. As a result, each of them will be separated by 0.5 W. Power. In the amount it will be the same 1 W..

This example is rude enough. Therefore, if there are doubts, it is worth taking resistors with a reserve in power.

Read more about the dispersion capacity of the resistor, read.

Secondly, when connected it is worth using the same type of resistors, for example, a series of MLT. Of course, there is nothing wrong with to take different. This is only a recommendation.

Parallel compound of resistors, along with consistent, is the main way to connect elements in electrical chain. In the second embodiment, all items are set sequentially: the end of one element is connected to the beginning of the following. In such a scheme, the current force on all elements is the same, and the voltage drop depends on the resistance of each element. There are two nodes in the serial connection. The beginning of all elements are connected to one, and their ends them. Conditionally for DC, you can designate them as plus and minus, and for variable as a phase and zero. Thanks to its peculiarities finding widespread use in electrical circuits, Including with a mixed connection. Properties are the same for constant and alternating current.

Calculation of general resistance with parallel compound of resistors

Unlike a serial connection, where to find a general resistance, it suffices to fold the value of each element, for a parallel, the same will be fair for conductivity. And since it is inversely proportional to the resistance, we obtain the formula shown along with the scheme in the following figure:

It is necessary to note one important feature of the calculation of the parallel connection of the resistors: the total value will always be less than the smallest of them. The resistors are fair both for permanent and alternating current. Coils and capacitors have their own characteristics.

Current and voltage

When calculating parallel resistance of resistance, you need to know how to calculate the voltage and current strength. In this case, the law of Oma will help us, which determines the relationship between the resistance, current and voltage.

Based on the first formulation of the Law of Kirchhoff, we obtain that the sum of currents converging in one node is zero. The direction is chosen in terms of current flow. Thus, the positive direction for the first node can be considered an incoming current from the power supply. And negative will be departing from each resistor. For the second node, the picture is the opposite. Based on the wording of the law, we obtain that the total current is equal to the amount of currents passing through each parallel to the connected resistor.

The final voltage is determined by the second law of Kirchoff. It is equally for each resistor and equally common. This feature is used to connect sockets and lighting in apartments.

Example of calculation

As a first example, we present the calculation of the resistance with a parallel connection of the same resistors. The strength flowing through them will be the same. An example of calculating the resistance looks like this:

According to this example, it is perfect that the overall resistance is two times lower than each of them. This corresponds to the fact that the total current is twice as much as one. And also well correlates with increasing conductivity by two times.

The second example

Consider an example of a parallel connection of three resistors. To calculate, use the standard formula:

Similarly, schemes with a large number of parallel to the connected resistors are calculated.

An example of a mixed compound

For a mixed connection, for example, presented below, the calculation will be made in several stages.

For starters, serial elements can be replaced by a single resistor with a resistance equal to the sum of two replaced. Next, the general resistance is considered in the same way as for the previous example. This method Suitable for other more complex schemes. A consistently simplifying scheme, you can get the necessary value.

For example, if instead of the R3 resistor, two parallel will be connected, you will need to first calculate their resistance, replacing them equivalent. And then the same as in the example above.

Application of parallel diagram

Parallel compound of resistors finds its application in many cases. Sequential connection increases resistance, and for our case it will decrease. For example, for the electrical circuit, resistance is required in 5 ohms, but there are only resistors for 10 ohms and above. From the first example, we know that you can get two times the smaller resistance value if you install two identical resistors in parallel to each other.

The resistance can be reduced even more, for example, if two pairs of parallel to the connected resistors are connected in parallel relative to each other. You can reduce the resistance even twice if the resistors have the same resistance. Combining with a serial connection, you can get any value.

The second example is the use of a parallel connection for lighting and sockets in apartments. Thanks to this connection, the voltage on each element will not depend on their quantity and will be the same.

Another example of using a parallel connection is a protective grounding of electrical equipment. For example, if a person touches the metal body of the device to which the breakdown will occur, the parallel connection of it and the protective conductor will be. The first node will be a touch, and the second zero point of the transformer. According to the conductor and man will flow a different current. The magnitude of the resistance of the latter is taken for 1000 ohms, although the real meaning is often much more. If there were no grounding, the entire current flowing in the scheme would go through a person, since he would be the only conductor.

A parallel connection can be used for batteries. The voltage remains the same, but their container increases twice.

Outcome

When the resistors are connected in parallel, the voltage on them will be the same, and the current is equal to the amount of each resistor. The conductivity will be leveling the sum of each. From this, it turns out an unusual formula for the total resistance of the resistors.

It is necessary to take into account when calculating the parallel compound of resistors, the final resistance will always be smaller than the smallest. It can also be explained by summing the conductivity of the resistors. The latter will increase when adding new elements, respectively, the conductivity will decrease.