Series connection diagram formula. Serial and parallel connection
All electrical circuits use resistors, which are elements with exactly set value resistance. Thanks to the specific qualities of these devices, it becomes possible to adjust the voltage and current in any part of the circuit. These properties underlie the work of almost all electronic devices and equipment. So, the voltage when connecting resistors in parallel and in series will be different. Therefore, each type of connection can only be used under certain conditions, so that one or another electrical circuit can fully perform its functions.
Series voltage
In a series connection, two or more resistors are connected into a common circuit in such a way that each of them has contact with another device at only one point. In other words, the end of the first resistor is connected to the beginning of the second, and the end of the second to the beginning of the third, etc.
A feature of this circuit is that the same value passes through all connected resistors electric current. As the number of elements in the section of the circuit under consideration increases, the flow of electric current becomes more and more difficult. This occurs due to an increase in the total resistance of the resistors when they are connected in series. This property reflected by the formula: Rtot = R 1 + R 2.
The voltage distribution, in accordance with Ohm's law, is carried out for each resistor according to the formula: V Rn = I Rn x R n. Thus, as the resistance of the resistor increases, the voltage dropped across it also increases.
Parallel voltage
In a parallel connection, resistors are included in the electrical circuit in such a way that all resistance elements are connected to each other by both contacts at once. One point representing electrical unit, can connect several resistors simultaneously.
This connection involves the flow of a separate current in each resistor. The strength of this current is inversely proportional. As a result, there is an increase in the overall conductivity of a given section of the circuit, with a general decrease in resistance. In the case of parallel connection of resistors with different resistances, the value of the total resistance in this section will always be lower than the smallest resistance of a single resistor.
In the diagram shown, the voltage between points A and B represents not only the total voltage for the entire section, but also the voltage supplied to each individual resistor. Thus, in case of parallel connection, the voltage applied to all resistors will be the same.
As a result, the voltage between parallel and series connections will be different in each case. Thanks to this property, there is a real opportunity to adjust this value at any part of the chain.
Parallel connection electrical elements(conductors, resistances, capacitances, inductances) - this is a connection in which the connected elements of the circuit have two common connection points.
Another definition: resistances are connected in parallel if they are connected to the same pair of nodes.
Graphic designation of parallel connection diagram
The figure below shows a parallel connection diagram of resistances R1, R2, R3, R4. From the diagram it can be seen that all these four resistances have two common points (connection points).
In electrical engineering, it is common, but not strictly required, to draw wires horizontally and vertically. Therefore, the same diagram can be depicted as in the figure below. It is too parallel connection the same resistances.
Formula for calculating parallel connection of resistances
In a parallel connection, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of all parallel-connected resistances. Equivalent conductance is equal to the sum of all parallel connected conductances of the electrical circuit.
For the above circuit, the equivalent resistance can be calculated using the formula:
In the particular case when connecting two resistances in parallel:
The equivalent circuit resistance is determined by the formula:
In the case of connecting “n” identical resistances, the equivalent resistance can be calculated using the private formula:
Formulas for private calculations follow from the main formula.
Formula for calculating parallel connection of capacitors (capacitors)
When connecting capacitors (capacitors) in parallel, the equivalent capacitance is equal to the sum of the parallel connected capacitances:
Formula for calculating parallel connection of inductances
When connecting inductors in parallel, the equivalent inductance is calculated in the same way as the equivalent resistance in a parallel connection:
It is necessary to note that the formula does not take into account mutual inductances.
Example of collapsing parallel resistance
For the site electrical circuit it is necessary to find a parallel connection of resistances and convert them to one.
From the diagram it can be seen that only R2 and R4 are connected in parallel. R3 is not parallel, because one end is connected to E1. R1 - one end is connected to R5, and not to the node. R5 - one end is connected to R1, and not to the node. We can also say that the series connection of resistances R1 and R5 is connected in parallel with R2 and R4.
Parallel current
When resistances are connected in parallel, the current through each resistance is generally different. The amount of current is inversely proportional to the amount of resistance.
Parallel voltage
With a parallel connection, the potential difference between the nodes connecting the elements of the circuit is the same for all elements.
Application of parallel connection
1. Resistances of certain values are manufactured in industry. Sometimes it is necessary to obtain a resistance value outside of these series. To do this, you can connect several resistors in parallel. The equivalent resistance will always be less than the largest resistance rating.
2. Current divider.
Content:The flow of current in an electrical circuit is carried out through conductors, in the direction from the source to the consumers. Most of these circuits use copper wires and electrical receivers in a given quantity, having different resistances. Depending on the tasks performed, electrical circuits use serial and parallel connections of conductors. In some cases, both types of connections can be used, then this option will be called mixed. Each circuit has its own characteristics and differences, so they must be taken into account in advance when designing circuits, repairing and servicing electrical equipment.
Series connection of conductors
In electrical engineering great importance has a serial and parallel connection of conductors in an electrical circuit. Among them, a series connection scheme of conductors is often used, which assumes the same connection of consumers. In this case, inclusion in the circuit is performed one after another in order of priority. That is, the beginning of one consumer is connected to the end of another using wires, without any branches.
The properties of such an electrical circuit can be considered using the example of sections of a circuit with two loads. The current, voltage and resistance on each of them should be designated respectively as I1, U1, R1 and I2, U2, R2. As a result, relations were obtained that express the relationship between quantities as follows: I = I1 = I2, U = U1 + U2, R = R1 + R2. The data obtained are confirmed in practice by taking measurements with an ammeter and a voltmeter of the corresponding sections.
Thus, serial connection conductors have the following individual features:
- The current strength in all parts of the circuit will be the same.
- The total voltage of the circuit is the sum of the voltages in each section.
- The total resistance includes the resistance of each individual conductor.
These ratios are suitable for any number of conductors connected in series. The total resistance value is always higher than the resistance of any individual conductor. This is due to an increase in their total length when connected in series, which also leads to an increase in resistance.
If you connect identical elements in series n, you get R = n x R1, where R is total resistance, R1 is the resistance of one element, and n is the number of elements. Voltage U, on the contrary, is divided into equal parts, each of which is n times less general meaning. For example, if 10 lamps of the same power are connected in series to a network with a voltage of 220 volts, then the voltage in any of them will be: U1 = U/10 = 22 volts.
Conductors connected in series have a characteristic distinctive feature. If at least one of them fails during operation, the current flow stops in the entire circuit. The most striking example is when one burned out light bulb in series circuit, leads to failure of the entire system. To identify a burnt out light bulb, you will need to check the entire garland.
Parallel connection of conductors
In electrical networks, conductors can be connected different ways: series, parallel and combined. Among them, a parallel connection is an option when the conductors at the starting and ending points are connected to each other. Thus, the beginnings and ends of the loads are connected together, and the loads themselves are located parallel to each other. An electrical circuit may contain two, three or more conductors connected in parallel.
If we consider a series and parallel connection, the current strength in the latter can be studied using the following circuit. Take two incandescent lamps that have the same resistance and are connected in parallel. For control, each light bulb is connected to its own. In addition, another ammeter is used to monitor the total current in the circuit. The test circuit is supplemented by a power source and a key.
After closing the key, you need to monitor the readings of the measuring instruments. The ammeter on lamp No. 1 will show the current I1, and on lamp No. 2 the current I2. The general ammeter shows the current value equal to the sum of the currents of individual, parallel-connected circuits: I = I1 + I2. Unlike a series connection, if one of the bulbs burns out, the other will function normally. Therefore, in home electrical networks it is used parallel connection devices.
Using the same circuit, you can set the value of the equivalent resistance. For this purpose, a voltmeter is added to the electrical circuit. This allows you to measure the voltage in a parallel connection, while the current remains the same. There are also crossing points for the conductors connecting both lamps.
As a result of measurements, the total voltage for a parallel connection will be: U = U1 = U2. After this, you can calculate the equivalent resistance, which conditionally replaces all the elements in a given circuit. With a parallel connection, in accordance with Ohm's law I = U/R, the following formula is obtained: U/R = U1/R1 + U2/R2, in which R is the equivalent resistance, R1 and R2 are the resistances of both bulbs, U = U1 = U2 is the voltage value shown by the voltmeter.
One should also take into account the fact that the currents in each circuit add up to the total current strength of the entire circuit. In its final form, the formula reflecting the equivalent resistance will look like this: 1/R = 1/R1 + 1/R2. As the number of elements in such chains increases, the number of terms in the formula also increases. The difference in basic parameters distinguishes current sources from each other, allowing them to be used in various electrical circuits.
A parallel connection of conductors is characterized by a fairly low equivalent resistance value, so the current strength will be relatively high. This factor should be taken into account when plugging in a large number of electrical appliances. In this case, the current increases significantly, leading to overheating of cable lines and subsequent fires.
Laws of series and parallel connection of conductors
These laws concerning both types of conductor connections have been partially discussed earlier.
For a clearer understanding and perception in a practical sense, series and parallel connection of conductors, formulas should be considered in a certain sequence:
- A series connection assumes the same current in each conductor: I = I1 = I2.
- Parallel and series connection of conductors is explained in each case differently. For example, with a series connection, the voltages on all conductors will be equal to each other: U1 = IR1, U2 = IR2. In addition, with a series connection, the voltage is the sum of the voltages of each conductor: U = U1 + U2 = I(R1 + R2) = IR.
- Impedance a circuit when connected in series consists of the sum of the resistances of all individual conductors, regardless of their number.
- With a parallel connection, the voltage of the entire circuit is equal to the voltage on each of the conductors: U1 = U2 = U.
- The total current measured in the entire circuit is equal to the sum of the currents flowing through all conductors connected in parallel: I = I1 + I2.
In order to more effectively design electrical networks, you need to have a good knowledge of the series and parallel connection of conductors and its laws, finding the most rational practical application for them.
Mixed connection of conductors
Electrical networks typically use serial parallel and mixed connections of conductors designed for specific operating conditions. However, most often preference is given to the third option, which is a set of combinations consisting of various types connections.
In such mixed circuits, serial and parallel connection of conductors is actively used, the pros and cons of which must be taken into account when designing electrical networks. These connections consist not only of individual resistors, but also rather complex sections that include many elements.
The mixed connection is calculated according to the known properties of series and parallel connections. The calculation method consists of breaking the circuit down into simpler components, which are calculated separately and then summed up with each other.
In the previous summary, it was established that the current strength in a conductor depends on the voltage at its ends. If you change the conductors in an experiment, leaving the voltage on them unchanged, then you can show that when constant voltage at the ends of the conductor, the current strength is inversely proportional to its resistance. Combining the dependence of current on voltage and its dependence on conductor resistance, we can write: I = U/R . This law, established experimentally, is called Ohm's law(for a section of chain).
Ohm's law for a circuit section: The current strength in a conductor is directly proportional to the voltage applied to its ends and inversely proportional to the resistance of the conductor. First of all, the law is always true for solid and liquid metal conductors. And also for some other substances (usually solid or liquid).
Consumers of electrical energy (light bulbs, resistors, etc.) can be connected to each other in different ways in an electrical circuit. Dva main types of conductor connections : serial and parallel. And there are also two more connections that are rare: mixed and bridge.
Series connection of conductors
When connecting conductors in series, the end of one conductor will connect to the beginning of another conductor, and its end to the beginning of a third, etc. For example, connecting light bulbs in Christmas tree garland. When the conductors are connected in series, current passes through all the bulbs. In this case, the same charge passes through the cross section of each conductor per unit time. That is, the charge does not accumulate in any part of the conductor.
Therefore, when connecting conductors in series The current strength in any part of the circuit is the same:I 1 = I 2 = I .
The total resistance of series-connected conductors is equal to the sum of their resistances: R1 + R2 = R . Because when conductors are connected in series, their total length increases. It is greater than the length of each individual conductor, and the resistance of the conductors increases accordingly.
According to Ohm's law, the voltage on each conductor is equal to: U 1 = I* R 1 ,U 2 = I*R 2 . In this case, the total voltage is equal to U = I( R1+ R 2) . Since the current strength in all conductors is the same, and the total resistance is equal to the sum of the resistances of the conductors, then the total voltage on series-connected conductors is equal to the sum of the voltages on each conductor: U = U 1 + U 2 .
From the above equalities it follows that a series connection of conductors is used if the voltage for which the electrical energy consumers are designed is less than the total voltage in the circuit.
For series connection of conductors, the following laws apply: :
1) the current strength in all conductors is the same; 2) the voltage across the entire connection is equal to the sum of the voltages on the individual conductors; 3) the resistance of the entire connection is equal to the sum of the resistances of the individual conductors.
Parallel connection of conductors
Example parallel connection conductors serve to connect electrical energy consumers in the apartment. So, light bulbs, kettle, iron, etc. are switched on in parallel.
When connecting conductors in parallel, all conductors at one end are connected to one point in the circuit. And the second end to another point in the chain. A voltmeter connected to these points will show the voltage on both conductor 1 and conductor 2. In this case, the voltage at the ends of all parallel-connected conductors is the same: U 1 = U 2 = U .
When conductors are connected in parallel, the electrical circuit branches out. Therefore, part of the total charge passes through one conductor, and part through the other. Therefore, when connecting conductors in parallel, the current strength in the unbranched part of the circuit is equal to the sum of the current strength in the individual conductors: I = I 1 + I 2 .
According to Ohm's law I = U/R, I 1 = U 1 /R 1, I 2 = U 2 /R 2 . This implies: U/R = U 1 /R 1 + U 2 /R 2, U = U 1 = U 2, 1/R = 1/R 1 + 1/R 2 The reciprocal of the total resistance of parallel-connected conductors is equal to the sum of the reciprocals of the resistance of each conductor.
When conductors are connected in parallel, their total resistance is less than the resistance of each conductor. Indeed, if two conductors having the same resistance are connected in parallel G, then their total resistance is equal to: R = g/2. This is explained by the fact that when connecting conductors in parallel, their cross-sectional area increases. As a result, resistance decreases.
From the above formulas it is clear why electrical energy consumers are connected in parallel. They are all designed for a certain identical voltage, which in apartments is 220 V. Knowing the resistance of each consumer, you can calculate the current strength in each of them. And also the correspondence of the total current strength to the maximum permissible current strength.
For parallel connection of conductors, the following laws apply:
1) the voltage on all conductors is the same; 2) the current strength at the junction of the conductors is equal to the sum of the currents in the individual conductors; 3) the reciprocal value of the resistance of the entire connection is equal to the sum of the reciprocal values of the resistance of individual conductors.
Parallel and series connection of conductors are methods of switching an electrical circuit. Electrical circuits of any complexity can be represented using these abstractions.
Definitions
There are two ways to connect conductors; it becomes possible to simplify the calculation of a circuit of arbitrary complexity:
- The end of the previous conductor is connected directly to the beginning of the next one - the connection is called serial. A chain is formed. To turn on the next link, you need electrical diagram break it by inserting a new conductor there.
- The beginnings of the conductors are connected by one point, the ends by another, the connection is called parallel. A ligament is usually called a branch. Each individual conductor forms a branch. Common points are called electrical network nodes.
In practice, a mixed connection of conductors is more common, some are connected in series, some in parallel. You need to break the chain into simple segments and solve the problem for each separately. An arbitrarily complex electrical circuit can be described by a parallel, series connection of conductors. This is how it is done in practice.
Using parallel and series connection of conductors
Terms applied to electrical circuits
Theory serves as the basis for the formation of solid knowledge; few people know how voltage (potential difference) differs from voltage drop. In physics terms, the internal circuit is the current source; the one located outside is called the external circuit. The demarcation helps to correctly describe the distribution of the field. The current does work. In the simplest case, heat generation follows the Joule-Lenz law. Charged particles, moving towards a lower potential, collide with the crystal lattice and release energy. The resistances heat up.
To ensure movement, it is necessary to maintain a potential difference at the ends of the conductor. This is called circuit section voltage. If you simply place a conductor in a field along the power lines, the current will flow and will be very short-lived. The process will end with the onset of equilibrium. The external field will be balanced own field charges, opposite direction. The current will stop. For the process to become continuous, an external force is needed.
The current source acts as such a drive for the movement of the electrical circuit. To maintain potential, work is done inside. Chemical reaction, as in a galvanic cell, mechanical forces - a hydroelectric power station generator. The charges inside the source move in the direction opposite to the field. The work of outside forces is being done on this. You can paraphrase the above formulations and say:
- The outer part of the circuit, where the charges move, carried away by the field.
- The interior of a circuit where charges move against the voltage.
The generator (current source) is equipped with two poles. The one with less potential is called negative, the other is called positive. When alternating current the poles continually change places. The direction of movement of charges is not constant. Current flows from the positive pole to the negative pole. The movement of positive charges goes in the direction of decreasing potential. According to this fact, the concept of potential drop is introduced:
The potential drop of a section of a circuit is the decrease in potential within the section. Formally, this is tension. For branches parallel circuit the same.
Voltage drop also means something else. The value characterizing heat losses is numerically equal to the product of the current and the active resistance of the section. Ohm's and Kirchhoff's laws, discussed below, are formulated for this case. In electric motors and transformers, the potential difference can differ significantly from the voltage drop. The latter characterizes losses on active resistance, while the first takes into account full time job current source.
When solving physical problems, for simplification, the motor can include an EMF, the direction of action of which is opposite to the effect of the power source. The fact of energy loss through the reactive part of the impedance is taken into account. School and university physics courses are distinguished by their isolation from reality. That is why students listen with open mouths about the phenomena taking place in electrical engineering. In the period preceding the era of the industrial revolution, the main laws were discovered; a scientist must combine the role of a theorist and a talented experimenter. The prefaces to Kirchhoff's works openly speak about this (Georg Ohm's works have not been translated into Russian). The teachers literally attracted people with additional lectures, flavored with visual, amazing experiments.
Ohm's and Kirchhoff's laws as applied to series and parallel connection of conductors
Ohm's and Kirchhoff's laws are used to solve real problems. The first deduced equality purely empirically - experimentally - the second began with a mathematical analysis of the problem, then tested his guesses with practice. Here is some information to help solve the problem:
Calculate the resistance of elements in series and parallel connection
Calculation algorithm real circuits simple Here are some points regarding the topic under consideration:
- When connected in series, the resistances are summed up; when connected in parallel, the conductivities are summed up:
- For resistors, the law is rewritten in unchanged form. With a parallel connection, the final resistance is equal to the product of the original ones divided by the total amount. In case of sequential, the denominations are summed up.
- Inductance stands out reactance(j*ω*L), behaves like a regular resistor. In terms of writing the formula, it is no different. The nuance, for any purely imaginary impedance, is that you need to multiply the result by the operator j, circular frequencyω (2*Pi*f). When the inductors are connected in series, the values are summed up; when inductors are connected in parallel, the reciprocal values are added up.
- The imaginary resistance of the capacitance is written as: -j/ω*С. It’s easy to notice: adding up the values of a series connection, we get a formula exactly as it was for resistors and inductances in a parallel connection. For capacitors the opposite is true. When connected in parallel, the values are added; when connected in series, the reciprocal values are added.
The theses can easily be extended to arbitrary cases. The voltage drop across two open silicon diodes is equal to the sum. In practice it is 1 volt, the exact value depends on the type of semiconductor element and characteristics. Power supplies are considered in a similar way: when connected in series, the ratings are added up. Parallel is often found in substations where transformers are placed side by side. The voltage will be the same (controlled by equipment), divided between the branches. The transformation coefficient is strictly equal, blocking the occurrence of negative effects.
Some people find it difficult: two batteries of different ratings are connected in parallel. The case is described by Kirchhoff's second law; physics cannot imagine any complexity. If the values of two sources are unequal, the arithmetic mean is taken, if we neglect internal resistance both. Otherwise, the Kirchhoff equations are solved for all contours. The unknown currents will be (three in total), the total number of which is equal to the number of equations. For complete understanding, a drawing has been provided.
An example of solving Kirchhoff's equations
Let's look at the image: according to the conditions of the problem, source E1 is stronger than E2. We take the direction of the currents in the circuit from common sense. But if they had entered it incorrectly, after solving the problem, one would have turned out with a negative sign. Then it was necessary to change direction. Obviously, current flows in the external circuit as shown in the figure. We compose the Kirchhoff equations for three circuits, this is what follows:
- The work of the first (strong) source is spent on creating a current in the external circuit, overcoming the weakness of the neighbor (current I2).
- The second source does not commit useful work under load, struggling with the first. There is no other way to say it.
Connecting batteries of different ratings in parallel is certainly harmful. What is observed at a substation when using transformers with different transmission ratios. Equalizing currents do no useful work. Different batteries connected in parallel will begin to function effectively when the strong one drops to the level of the weak one.