In every electrical circuit there is a resistor that has resistance to electric current. Resistors are of two types: fixed and variable. During the development of any electrical circuit and the repair of electronic products, it is often necessary to use a resistor with the required rating.
Although Resistors have different ratings, it may happen that it will not be possible to find the necessary one, or even no element at all can provide the required indicator.
The solution to this problem can be the use of serial and parallel connection. After reading this article, you will learn about the features of the calculation and selection of various resistance values.
Parallel connection: general information
Often, in the manufacture of a device, resistors are used that are connected in accordance with sequential circuit. The effect of using this assembly option is to increase the total resistance of the circuit. For this option connecting elements, the resistance they create is calculated as the sum of the ratings. If the assembly of parts is carried out according to a parallel scheme, then here need to calculate the resistance using the formulas below.
The parallel connection scheme is used in situations where the task is to reduce the total resistance, and, in addition, increase the power for a group of elements connected in parallel, which should be greater than when they are connected separately.
Resistance calculation
In the case of connecting parts to each other, using a parallel circuit to calculate the total resistance, the following formula will be used:
R(gen)=1/(1/R1+1/R2+1/R3+1/Rn).
- R1-R3 and Rn are resistors connected in parallel.
Moreover, if the circuit is created on the basis of only two elements, then the following formula should be used to determine the total nominal resistance:
R(total)=R1*R2/R1+R2.
- R(gen) - total resistance;
- R1 and R2 are resistors connected in parallel.
Video: Resistance Calculation Example
Universal calculation scheme
With regard to radio engineering, attention should be paid to one important rule: if the elements connected to each other in a parallel circuit have the same score, then to calculate the total nominal value, it is necessary to divide the total value by the number of connected nodes:
- R(total) - the total value of the resistance;
- R is the value of the resistor connected in parallel;
- n is the number of connected nodes.
Particular attention should be paid to the fact that the final resistance in the case of using a parallel connection will definitely be less compared to the rating of any element connected to the circuit.
Calculation example
For greater clarity, consider the following example: let's say we have three resistors, whose values are respectively 100, 150 and 30 ohms. If we use the first formula to determine the total face value, we get the following:
R(total)=1/(1/100+1/150+1/30)=
1 / (0.01 + 0.007 + 0.03) \u003d 1 / 0.047 \u003d 21.28 Ohm.
If you perform simple calculations, you can get the following: for a circuit that includes three parts, where the lowest resistance is 30 ohms, the resulting nominal value will be 21.28 ohms. This indicator will be less than the minimum value of the nominal value in the circuit by almost 30%.
Important nuances
Usually, for resistors, parallel connection is used when the task is to create a resistance of greater power. To solve it, resistors will be required, which should have equal resistance and power indicators. With this option you can determine the total power as follows: the power of one element must be multiplied with the total number of all resistors that make up the circuit, connected to each other in accordance with the parallel circuit.
Let's say if we use five resistors, whose nominal value is 100 ohms, and the power of each is 1 W, which are connected to each other in accordance with a parallel circuit, then the total resistance will be 20 ohms, and the power will be 5 watts.
If we take the same resistors, but connect them in accordance with the serial circuit, then the final power will be 5 W, and the total value will be 500 ohms.
Video: Correct connection of LEDs
The parallel circuit for connecting resistors is very much in demand for the reason that the task often arises of creating such a rating that cannot be achieved using a simple parallel connection. Wherein the procedure for calculating this parameter is rather complicated where different parameters must be taken into account.
Here, an important role is played not only by the number of connected elements, but also by the operating parameters of the resistors - first of all, resistance and power. If one of the connected elements has an unsuitable indicator, then this will not effectively solve the problem of creating the required denomination in the circuit.
), today we will talk about possible ways connections of resistors, in particular about serial connection and about parallel.
Let's start by looking at a circuit whose elements are connected. successively. And although we will consider only resistors as circuit elements in this article, the rules regarding voltages and currents for different connections will be valid for other elements. So, the first circuit that we will disassemble looks like this:
Here we have a classic case serial connection- two resistors connected in series. But let's not get ahead of ourselves and calculate the total resistance of the circuit, but first we will consider all voltages and currents. So, the first rule is that the currents flowing through all conductors in a series connection are equal to each other:
And to determine the total voltage in a series connection, the voltage across individual elements needs to be summarized:
At the same time, for voltages, resistances and currents in this circuit, the following relations are valid:
Then the following expression can be used to calculate the total voltage:
But for the total voltage, Ohm's law also holds:
Here, is the total resistance of the circuit, which, based on two formulas for the total voltage, is equal to:
Thus, when resistors are connected in series, the total resistance of the circuit will be equal to the sum of the resistances of all conductors.
For example for the following circuit:
The total resistance will be:
The number of elements does not matter, the rule by which we determine the total resistance will work in any case 🙂 And if all the resistances are equal in series connection (), then the total resistance of the circuit will be:
In this formula, it is equal to the number of elements in the chain.
We figured out the series connection of resistors, let's move on to parallel.
With a parallel connection, the voltages on the conductors are equal:
And for currents, the following expression is true:
That is, the total current branches into two components, and its value is equal to the sum of all components. Ohm's law:
Substitute these expressions in the formula for the total current:
And according to Ohm's law, the current:
Equate these expressions and get the formula for the total resistance of the circuit:
This formula can be written in a slightly different way:
Thus,when the conductors are connected in parallel, the reciprocal of the total resistance of the circuit is equal to the sum of the reciprocals of the resistances of the parallel-connected conductors.
A similar situation will be observed with a larger number of conductors connected in parallel:
In addition to parallel and series connections of resistors, there is also mixed connection. From the name it is already clear that with such a connection in the circuit there are resistors connected both in parallel and in series. Here is an example of such a circuit:
Let's calculate the total resistance of the circuit. Let's start with resistors and - they are connected in parallel. We can calculate the total resistance for these resistors and replace them in the circuit with a single resistor:
Parallel connection of resistors, along with series, is the main way to connect elements in an electrical circuit. In the second version, all elements are installed sequentially: the end of one element is connected to the beginning of the next. In such a circuit, the current strength on all elements is the same, and the voltage drop depends on the resistance of each element. There are two nodes in a serial connection. The beginnings of all elements are connected to one, and their ends to the second. Conventionally, for direct current, they can be designated as plus and minus, and for alternating current as phase and zero. Due to its properties, it is widely used in electrical diagrams, including those with a mixed connection. The properties are the same for permanent and alternating current.
Calculation of total resistance when resistors are connected in parallel
Unlike a series connection, where it is enough to add the value of each element to find the total resistance, for a parallel connection, the same will be true for conductivity. And since it is inversely proportional to the resistance, we get the formula presented together with the circuit in the following figure:
It is necessary to note one important feature of the calculation of the parallel connection of resistors: the total value will always be less than the smallest of them. For resistors, this is true for both direct and alternating current. Coils and capacitors have their own characteristics.
Current and voltage
When calculating the parallel resistance of resistors, you need to know how to calculate voltage and current. In this case, Ohm's law will help us, which determines the relationship between resistance, current and voltage.
Based on the first formulation of Kirchhoff's law, we obtain that the sum of the currents converging in one node is equal to zero. The direction is chosen according to the direction of current flow. Thus, the positive direction for the first node can be considered the incoming current from the power supply. And the outgoing from each resistor will be negative. For the second node, the picture is opposite. Based on the formulation of the law, we obtain that the total current is equal to the sum of the currents passing through each resistor connected in parallel.
The final voltage is determined by the second law of Kirchhoff. It is the same for each resistor and is equal to the total. This feature is used to connect sockets and lighting in apartments.
Calculation example
As a first example, we present the calculation of the resistance for parallel connection of identical resistors. The current flowing through them will be the same. An example of calculating resistance looks like this:
This example clearly shows that the total resistance is two times lower than each of them. This corresponds to the fact that the total current strength is twice as high as that of one. It also correlates well with a doubling of conductivity.
Second example
Consider an example of a parallel connection of three resistors. To calculate, we use the standard formula:
Similarly, circuits with a large number of resistors connected in parallel are calculated.
Mixed connection example
For a mixed compound, such as the one below, the calculation will be done in several steps.
To begin with, serial elements can be conditionally replaced by one resistor with a resistance equal to the sum of the two replaced. Further, the total resistance is considered in the same way as for the previous example. This method suitable for others complex schemes. Consistently simplifying the circuit, you can get the desired value.
For example, if two parallel resistors are connected instead of R3, you will first need to calculate their resistance, replacing them with an equivalent one. And then the same as in the example above.
Applying a Parallel Circuit
Parallel connection of resistors finds its application in many cases. Connecting in series increases the resistance, but in our case it will decrease. For example, an electrical circuit requires a resistance of 5 ohms, but there are only 10 ohm and higher resistors. From the first example, we know that you can get half the resistance value if you install two identical resistors in parallel with each other.
You can reduce the resistance even more, for example, if two pairs of resistors connected in parallel are connected in parallel relative to each other. You can reduce the resistance by a factor of two if the resistors have the same resistance. By combining with a serial connection, any value can be obtained.
The second example is the use of parallel connection for lighting and sockets in apartments. Thanks to this connection, the voltage on each element will not depend on their number and will be the same.
Another example of the use of parallel connection is the protective earthing of electrical equipment. For example, if a person touches metal case the device on which the breakdown occurs, you will get a parallel connection of it and the protective conductor. The first node will be the place of contact, and the second will be the zero point of the transformer. A different current will flow through the conductor and the person. The resistance value of the latter is taken as 1000 ohms, although the real value is often much higher. If there were no ground, all the current flowing in the circuit would go through the person, since he would be the only conductor.
Parallel connection can also be used for batteries. The voltage remains the same, but their capacitance doubles.
Outcome
When resistors are connected in parallel, the voltage across them will be the same, and the current will be equal to the sum of the currents flowing through each resistor. Conductivity will equal the sum of each. From this, an unusual formula for the total resistance of resistors is obtained.
When calculating the parallel connection of resistors, it must be taken into account that the final resistance will always be less than the smallest. This can also be explained by the summation of the conductance of the resistors. The latter will increase with the addition of new elements, and, accordingly, the conductivity will decrease.
used to increase resistance. Those. when resistors are connected in series, the total resistance equals the sum of the resistances of each resistor. For example, if resistors R1 and R2 are connected in series, their total resistance is calculated using the formula:R = R1 + R2 .
This is also true for more resistors connected in series:
R = R1 + R2 + R3 + R4 + ... + Rn .
Chain of resistors connected in series will always resist more than any resistor in this circuit.
When resistors are connected in series, a change in the resistance of any resistor from this circuit entails both a change in the resistance of the entire circuit and a change in the current strength in this circuit.
Parallel connection of resistors (formula)
It is necessary to reduce the total resistance and, as an option, to increase the power of several resistors compared to one.
Parallel resistance calculation
Parallel resistance calculation two resistors R1 and R2 connected in parallel is produced by the following formula:Parallel connection of three or more resistors requires a more complex formula to calculate the total resistance:
Resistance of parallel resistors
| 1 | = | 1 | + | 1 | + | 1 | + ... |
| R | R1 | R2 | R3 |
As you can see, calculate resistance of two parallel resistors much more convenient.
The resistance of resistors connected in parallel will always be less than that of any of these resistors.
Often used in cases where resistance with more power is needed. For this, as a rule, resistors with the same power and the same resistance are used. The total power, in this case, is calculated by multiplying the power of one resistor by the number of resistors connected in parallel.
For example: ten resistors with a nominal value of 1 KΩ and a power of 1 W each connected in parallel will have a total resistance of 100 Ω and a power of 10 W.
When connected in series, the power of the resistors also adds up. Those. in the same example, but with a series connection, the total resistance will be 10 kΩ and the power will be 10 watts.
When assembling independent circuits, novice radio amateurs are faced with the need to establish one or another resistance, the value of which is not in the standard series or on hand. Therefore, the desired impedance value is selected by parallel or series connection of elements. To correctly calculate the equivalent value, it is easiest to use a resistance calculator, but you can also do the calculations yourself using simple formulas.
Purpose and definition of impedance
Virtually none electronic device does not do without resistors in its circuit. Being passive elements, they have the main purpose - to limit the amount of current in the electrical circuit. In addition to current limiting, they serve as voltage dividers or shunts in measuring instruments.
Electrical resistance is a quantity that has a physical nature and characterizes the ability of a conductor to pass an electric current. The principle of operation of the resistor was described by the outstanding experimenter Ohm. Later, the unit of measurement of electrical resistance, Ohm, was named in his honor. The scientist, conducting a series of experiments, established the relationship between the current strength, voltage and resistance in the conductor. The result was a simple formula known as Ohm's law: I = U/R, where:
- I - current passing through the conductor, measured in amperes;
- U - voltage applied to the conductor, unit of measurement - Volt;
- R - conductor resistance, measured in ohms.
Later, devices used only as resistance elements in electrical circuits were called resistors. Such devices, in addition to the resistance value, are characterized by power, calculated according to the following formula: P \u003d I2 * R. The resulting value is measured in Watts.
In circuitry, both parallel and series connection of conductors are used. Depending on this, the value of the impedance of the circuit section also changes. Connection type, if not used for picking desired value, just characterizes the use of resistors in the first case as current limiters, and in the second - as voltage dividers.
In the diagrams, resistors are indicated in the form of a rectangle and signed with the Latin letter R. Next to it is the serial number and resistance value. For example, R23 1k means that resistor number 23 has a resistance of one kiloohm. The bars depicted inside the rectangle characterize the power dissipated on the conductor.
The fundamental law of conservation of energy says: energy does not disappear anywhere and does not appear from nowhere, but only changes form. Therefore, when the current is limited, part of the energy is transformed into heat. It is this part that is called the dissipation power of the resistor, i.e., such a value that the resistance can withstand without changing its parameters.
The resistor itself can have a different design and type.. For example, to be wire, ceramic, mica, etc. It is marked in three ways:
Therefore, seeing which resistors are installed in the circuit, it will not be difficult for even a novice radio amateur to calculate the total resistance, especially using an online calculator for parallel connection of resistors or series. If it is impossible to distinguish the marking on the case, its resistance can be measured with a multimeter. But experienced electrical engineers know that for accurate measurement you will need one resistance lead to disconnect from the circuit. This is due just to the type of connection of the conductor.
Parallel connection
It can be seen from the solution that if R1 is equal in value to R2, then the total resistance value is equal to half the value of one of the elements. Therefore, with the required rating equal to 6 ohms, this value will be: Rx = 2 * 6 = 12 ohms. To check the result, you should substitute the received answer into the formula: Re \u003d (R1 * R2) / (R1 + R2) \u003d (12 * 12) / (12 + 12) \u003d 6 Ohms.
Thus, the solution to the problem will be the parallel connection of two resistors with a resistance value of 12 ohms.
The task of finding the equivalent
Let there be a circuit with three resistors connected in parallel, and to simplify it, it is necessary to replace them with one element. Conductor ratings are: R1 = 320 Ohm, R2 = 10 Ohm, R3 = 1 kOhm. To solve the problem, the already known formula is used:
- 1/R = (1/R1) + (1/R2) + (1/R3);
- Req = (R1*R2*R3) / (R1+R2+R3).
Before substituting values in the formula, they will all need to be converted to the international system of units (SI). So, one kiloOhm is equal to 1000 Ohm, when substituting this value, the answer is: Re \u003d (320 * 1 * 1000) / (320 + 10 + 1000) \u003d 2406 Ohm or 2.4 kOhm, which just corresponds to the value from the standard series. This calculation method is used for any number of resistors connected in parallel.
Series connection
Using these rules, which are valid for any number of connected conductors in a circuit, the total impedance value for any kind of connection is determined. In order to determine the equivalent resistance value of a parallel-series connection, the circuit section is divided into small groups of parallel or series-connected resistors. Then an algorithm is used to help optimally calculate the value of the equivalent:
The total resistance of all nodes in the circuit with parallel connection of resistors is determined:
- When there are series-connected conductors in these nodes, their resistance is initially considered.
- Once the equivalent values are calculated, the circuit is simplified to a series string of equivalent resistors.
- The final value of the total resistance is found.
For example, there is a scheme in which it is necessary to define impedance circuit, while the resistance of the resistors R1=R3=R5=R6=3 ohms, and R2 =20 ohms and R4=24 ohms. The resistances R3, R4, and R5 are connected in series, so the total impedance in this section of the circuit is: Rb1 = R3 + R4 + R5 = 30 ohms.
After replacing R3, R4, R5 with Rb1, the resistor R3 will be connected in parallel with this resistance. Therefore, the impedance in this section will be equal to:
Rb2 \u003d (R2 * Rb1) / (R3 + Rb1) \u003d (20 * 30) / (20 + 30) \u003d 12 Ohm.
Resistors R1 and R6 are connected in series with Rb2, which means that the equivalent of the entire circuit is: Rekv = Rb1 + Rb2 + R6 = 3 + 12 + 3 = 18 ohms.
So, step by step, the equivalent value of any complexity of the circuit is calculated. With many conductors included in electrical circuit, it is easy to make mistakes in the calculations, so all operations are performed carefully or online calculators are used.
Online calculation on the calculator
Many web pages have been created that allow you to find the resistance of parallel resistors in a few seconds, using formulas for calculating a parallel connection in their computational algorithms. Such calculators are quite useful for radio amateur designers or electronic equipment specialists in case of difficulty in choosing the required resistor value to replace it in the circuit of an electronic device.
The appearance of online applications may differ from each other, but the principle of operation is the same. It is also important in the work of programs that the algorithms for calculating them use different accuracy in rounding the result, so the answer in some programs may differ slightly when compared.
The application itself is usually a cell in which the value of the values \u200b\u200bof resistors in the international system of measurements is entered. After all the fields are filled in, the "Calculate" button is pressed and the answer is obtained in the cell opposite. The answer is calculated in ohms. In some applications, functionality can be extended, these are features such as automatic translation values of resistors to the SI system, displaying the nearest standard value of resistance from the nominal series, close to the received answer.
A reverse transition can also be a useful function, when an equivalent resistance is entered, and the combination of conductor ratings for parallel connection is given in response.
Thus, calculation using online calculators helps to solve the problem not only quickly, but also accurately, which is often used not only by radio amateurs, but also by professionals.
