Types of connection of conductors formulas. Parallel and series connection of conductors. Laws for parallel connection of conductors
In electrical circuits, elements can be connected according to various circuits, including sequential and parallel connection.
Serial connection
With this connection, the conductors are connected to each other in series, that is, the beginning of one conductor will be connected to the end of the other. The main feature of this connection is that all conductors belong to one wire, there are no branches. The same electric current will flow through each of the conductors. But the total voltage on the conductors will be equal to the combined voltages on each of them.
Consider a number of resistors connected in series. Since there are no branches, the amount of charge passing through one conductor will be equal to the amount of charge passing through the other conductor. The current strength on all conductors will be the same. This is the main feature of this connection.
This connection can be viewed differently. All resistors can be replaced with one equivalent resistor.
The current across the equivalent resistor will be the same as the total current flowing through all resistors. The equivalent total voltage will be the sum of the voltages across each resistor. This is the potential difference across the resistor.
If you use these rules and Ohm's law, which applies to each resistor, you can prove that the resistance of the equivalent common resistor will be equal to the sum of the resistances. The consequence of the first two rules will be the third rule.
Application
A serial connection is used when you need to purposefully turn on or off a device; the switch is connected to it in a series circuit. For example, an electric bell will only ring when it is connected in series with a source and a button. According to the first rule, if there is no electric current on at least one of the conductors, then there will be no electric current on the other conductors. And vice versa, if there is current on at least one conductor, then it will be on all other conductors. A pocket flashlight also works, which has a button, a battery and a light bulb. All these elements must be connected in series, since the flashlight needs to shine when the button is pressed.
Sometimes a serial connection does not achieve the desired goals. For example, in an apartment where there are many chandeliers, light bulbs and other devices, you should not connect all the lamps and devices in series, since you never need to turn on the lights in each of the rooms of the apartment at the same time. For this purpose, serial and parallel connections are considered separately, and they are used to connect lighting fixtures in the apartment. parallel view scheme.
Parallel connection
In this type of circuit, all conductors are connected in parallel to each other. All the beginnings of the conductors are connected to one point, and all the ends are also connected together. Let's consider a number of homogeneous conductors (resistors) connected in a parallel circuit.
This type of connection is branched. Each branch contains one resistor. Electricity, having reached the branching point, is divided into each resistor, and will be equal to the sum of the currents at all resistances. The voltage across all elements connected in parallel is the same.
All resistors can be replaced with one equivalent resistor. If you use Ohm's law, you can get an expression for resistance. If, with a series connection, the resistances were added, then with a parallel connection, the inverse values of them will be added, as written in the formula above.
Application
If we consider connections in domestic conditions, then in an apartment lighting lamps and chandeliers should be connected in parallel. If we connect them in series, then when one light bulb turns on, we turn on all the others. With a parallel connection, we can, by adding the corresponding switch to each of the branches, turn on the corresponding light bulb as desired. In this case, turning on one lamp in this way does not affect the other lamps.
All electrical household devices in the apartment are connected in parallel to a network with a voltage of 220 V, and connected to the distribution panel. In other words, parallel connection is used when it is necessary to connect electrical devices independently of each other. Serial and parallel connections have their own characteristics. There are also mixed compounds.
Current work
The series and parallel connections discussed earlier were valid for voltage, resistance and current values being the fundamental ones. The work of the current is determined by the formula:
A = I x U x t, Where A– current work, t– flow time along the conductor.
To determine operation with a series connection circuit, it is necessary to replace the voltage in the original expression. We get:
A=I x (U1 + U2) x t
We open the brackets and find that in the entire diagram, the work is determined by the amount at each load.
We also consider a parallel connection circuit. We just change not the voltage, but the current. The result is:
A = A1+A2
Current power
When considering the formula for the power of a circuit section, it is again necessary to use the formula:
P=U x I
After similar reasoning, the result is that series and parallel connections can be determined by the following power formula:
P=P1 + P2
In other words, for any circuit, the total power is equal to the sum of all powers in the circuit. This can explain that it is not recommended to turn on several powerful electrical devices in an apartment at once, since the wiring may not withstand such power.
The influence of the connection diagram on the New Year's garland
After one lamp in a garland burns out, you can determine the type of connection diagram. If the circuit is sequential, then not a single light bulb will light up, since a burnt out light bulb breaks the common circuit. To find out which light bulb has burned out, you need to check everything. Next, replace the faulty lamp, the garland will function.
When using a parallel connection circuit, the garland will continue to work even if one or more lamps have burned out, since the circuit is not completely broken, but only one small parallel section. To restore such a garland, it is enough to see which lamps are not lit and replace them.
Series and parallel connection for capacitors
With a series circuit, the following picture arises: charges from the positive pole of the power source go only to the outer plates of the outer capacitors. , located between them, transfer charge along the circuit. This explains the appearance on all plates of equal charges with different signs. Based on this, the charge of any capacitor connected in a series circuit can be expressed by the following formula:
q total = q1 = q2 = q3
To determine the voltage on any capacitor, you need the formula:
Where C is capacity. The total voltage is expressed by the same law that is suitable for resistances. Therefore, we obtain the capacity formula:
С= q/(U1 + U2 + U3)
To make this formula simpler, you can reverse the fractions and replace the ratio of the potential difference to the charge on the capacitor. As a result we get:
1/C= 1/C1 + 1/C2 + 1/C3
The parallel connection of capacitors is calculated a little differently.
The total charge is calculated as the sum of all charges accumulated on the plates of all capacitors. And the voltage value is also calculated according to general laws. In this regard, the formula for the total capacitance in a parallel connection circuit looks like this:
С= (q1 + q2 + q3)/U
This value is calculated as the sum of each device in the circuit:
C=C1 + C2 + C3
Mixed connection of conductors
In an electrical circuit, sections of a circuit can have both series and parallel connections, intertwined with each other. But all the laws discussed above for individual species connections are still valid and are used in stages.
First you need to mentally decompose the diagram into separate parts. For a better representation, it is drawn on paper. Let's look at our example using the diagram shown above.
It is most convenient to depict it starting from the points B And IN. They are placed at some distance from each other and from the edge of the sheet of paper. From the left side to the point B one wire is connected, and two wires go off to the right. Dot IN on the contrary, it has two branches on the left, and one wire goes off after the point.
Next you need to depict the space between the points. Along the upper conductor there are 3 resistances with conventional values 2, 3, 4. From below there will be a current with index 5. The first 3 resistances are connected in series in the circuit, and the fifth resistor is connected in parallel.
The remaining two resistances (the first and sixth) are connected in series with the section we are considering B-C. Therefore, we supplement the diagram with 2 rectangles on the sides of the selected points.
Now we use the formula for calculating resistance:
- The first formula for a series connection.
- Next, for the parallel circuit.
- And finally for the sequential circuit.
In a similar way, any complex circuit can be decomposed into separate circuits, including connections of not only conductors in the form of resistances, but also capacitors. To learn how to calculate using different types schemes, you need to practice in practice by completing several tasks.
Topics of the Unified State Examination codifier: parallel and series connection of conductors, mixed connection of conductors.
There are two main ways to connect conductors to each other - this is sequential And parallel connections. Various combinations of serial and parallel connections result in mixed connection of conductors.
We'll be exploring the properties of these compounds, but first we'll need some background information.
We call a conductor with resistance resistor and depicted as follows (Fig. 1):
Rice. 1. Resistor
Resistor voltage is the potential difference of a stationary electric field between the ends of the resistor. Between which ends exactly? In general, this is not important, but it is usually convenient to match the potential difference with the direction of the current.
The current in the circuit flows from the “plus” of the source to the “minus”. In this direction, the potential of the stationary field decreases. Let us remind you again why this is so.
Let a positive charge move along the circuit from point to point, passing through a resistor (Fig. 2):
Rice. 2.
The stationary field does positive work in this case.
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Therefore, we calculate the voltage across the resistor as the potential difference in the direction of the current: .
The resistance of the lead wires is usually negligible; on electrical diagrams it is considered equal to zero. From Ohm's law it then follows that the potential does not change along the wire: after all, if and , then . (Fig. 3):
Rice. 3.
Thus, when considering electrical circuits, we use an idealization that greatly simplifies their study. Namely, we believe that the potential of a stationary field changes only when passing through individual elements of the circuit, and along each connecting wire remains unchanged. In real circuits, the potential decreases monotonically when moving from the positive terminal of the source to the negative.
Serial connection
For serial connection conductors, the end of each conductor is connected to the beginning of the next conductor.
Let's consider two resistors and connected in series and connected to a constant voltage source (Fig. 4). Recall that the positive terminal of the source is indicated by a longer line, so the current in this circuit flows clockwise.
Rice. 4. Serial connection
Let us formulate the basic properties of a serial connection and illustrate them with this simple example.
1. When the conductors are connected in series, the current strength in them is the same.
In fact, the same charge will pass through any cross section of any conductor in one second. After all, charges do not accumulate anywhere, they do not leave the circuit outside and do not enter the circuit from the outside.
2. The voltage in a section consisting of series-connected conductors is equal to the sum of the voltages on each conductor.
Indeed, the voltage in the area is the work of the field to transfer a unit charge from point to point; voltage in a section is the work of the field to transfer a unit charge from point to point. Added up, these two works will give the field work to transfer a unit charge from point to point, that is, the voltage throughout the entire section:
It is also possible more formally, without any verbal explanations:
3. The resistance of a section consisting of series-connected conductors is equal to the sum of the resistances of each conductor.
Let be the resistance of the section. According to Ohm's law we have:
which is what was required.
You can give an intuitive explanation of the rule for adding resistances using one particular example. Let two conductors of the same substance and with the same cross-sectional area be connected in series, but with different lengths and.
The resistances of the conductors are equal:
These two conductors form a single conductor with length and resistance
But this, we repeat, is only special example. The resistances will also add up in the most general case - if the materials of the conductors and their cross sections are also different.
The proof of this is given using Ohm's law as shown above.
Our proofs of the properties of a series connection, given for two conductors, can be transferred without significant changes to the case of an arbitrary number of conductors.
Parallel connection
At parallel connection conductors, their beginnings are connected to one point in the circuit, and their ends to another point.
Again we consider two resistors, this time connected in parallel (Fig. 5).
Rice. 5. Parallel connection
Resistors are connected to two points: and. These points are called nodes or branching points chains. Parallel sections are also called branches; the section from to (in the direction of current) is called unbranched part chains.
Now let’s formulate the properties of a parallel connection and prove them for the case of two resistors shown above.
1. The voltage on each branch is the same and equal to the voltage on the unbranched part of the circuit.
In fact, both voltages across the resistors are equal to the potential difference between the connection points:
This fact serves as the most clear manifestation of the potentiality of a stationary electric field of moving charges.
2. The current strength in the unbranched part of the circuit is equal to the sum of the current strengths in each branch.
Let, for example, suppose that a charge arrives at a point from an unbranched section over a period of time. During the same time, charge leaves the point to the resistor, and charge leaves the resistor.
It's clear that . Otherwise, a charge would accumulate at a point, changing the potential of a given point, which is impossible (after all, the current is constant, the field of moving charges is stationary, and the potential of each point in the circuit does not change with time). Then we have:
which is what was required.
3. The reciprocal value of the resistance of a section of a parallel connection is equal to the sum of the reciprocal values of the resistances of the branches.
Let be the resistance of the branched section. The voltage on the section is equal to ; the current flowing through this section is equal to . That's why:
Reducing by , we get:
(1)
which is what was required.
As in the case of a series connection, this rule can be explained using a particular example without resorting to Ohm's law.
Let conductors from the same substance with the same lengths, but different cross sections And . Then this connection can be considered as a conductor of the same length, but with a cross-sectional area. We have:
The above proofs of the properties of a parallel connection can be transferred without significant changes to the case of any number of conductors.
From relation (1) you can find:
(2)
Unfortunately, in the general case of parallel-connected conductors, a compact analogue of formula (2) does not work, and one has to be content with the relation
(3)
Nevertheless, one useful conclusion can be drawn from formula (3). Namely, let the resistances of all resistors be the same and equal. Then:
We see that the resistance of a section of parallel-connected identical conductors is several times less than the resistance of one conductor.
Mixed compound
Mixed connection conductors, as the name suggests, can be a set of any combinations of serial and parallel connections, and these connections can include both individual resistors and more complex composite sections.
The calculation of a mixed connection is based on the already known properties of serial and parallel connections. There is nothing new here: you just need to carefully divide this circuit into simpler sections connected in series or in parallel.
Let's consider an example of a mixed connection of conductors (Fig. 6).
Rice. 6. Mixed compound
Let V, Om, Om, Om, Om, Om. Let's find the current strength in the circuit and in each of the resistors.
Our circuit consists of two sections connected in series and . Section resistance:
Ohm.
The section is a parallel connection: two resistors connected in series and connected in parallel to a resistor. Then:
Ohm.
Circuit resistance:
Ohm.
Now we find the current strength in the circuit:
To find the current in each resistor, let's calculate the voltage in both sections:
(Note in passing that the sum of these voltages is equal to V, i.e., the voltage in the circuit, as it should be with a series connection.)
Both resistors are energized, so:
(In total we have A, as it should be with a parallel connection.)
The current strength in the resistors is the same, since they are connected in series:
Therefore, current A flows through the resistor.
When solving problems, it is customary to transform the circuit so that it is as simple as possible. To do this, equivalent transformations are used. Equivalent are those transformations of a part of an electrical circuit circuit in which the currents and voltages in the non-transformed part remain unchanged.
There are four main types of conductor connections: series, parallel, mixed and bridge.
Serial connection
Serial connection- this is a connection in which the current strength throughout the entire circuit is the same. A striking example of a series connection is an old Christmas tree garland. There the light bulbs are connected in series, one after another. Now imagine one light bulb burns out, the circuit is broken and the rest of the light bulbs go out. The failure of one element leads to the shutdown of all the others; this is a significant disadvantage of a serial connection.
When connected in series, the resistances of the elements are summed up.
Parallel connection
Parallel connection- this is a connection in which the voltage at the ends of the circuit section is the same. Parallel connection is the most common, mainly because all the elements are under the same voltage, the current is distributed differently and when one of the elements exits, all the others continue to work.
In a parallel connection, the equivalent resistance is found as:
In the case of two parallel connected resistors 
In the case of three resistors connected in parallel:
Mixed compound
Mixed compound– a connection, which is a collection of serial and parallel connections. To find the equivalent resistance, you need to “collapse” the circuit by alternately transforming parallel and serial sections of the circuit.
First, let's find the equivalent resistance for the parallel section of the circuit, and then add to it the remaining resistance R 3 . It should be understood that after the conversion, the equivalent resistance R 1 R 2 and resistor R 3 are connected in series.
So, that leaves the most interesting and most complex connection of conductors.
Bridge circuit
The bridge connection diagram is shown in the figure below.
In order to collapse the bridge circuit, one of the bridge triangles is replaced with an equivalent star.
And find the resistances R 1, R 2 and R 3.
Individual conductors of an electrical circuit can be connected to each other in series, parallel and mixed. In this case, series and conductors are the main types of connections, and this is their totality.
A series connection of conductors is such a connection when the end of the first conductor is connected to the beginning of the second, the end of the second conductor is connected to the beginning of the third, and so on (Figure 1).
U 1 = I × r 1 = 4 × 2 = 8 V.
Voltmeter V 1 included between points A And b, will show 8 V.
In resistance r 2 there is also a voltage drop:
U 2 = I × r 2 = 4 × 3 = 12 V.
Voltmeter V 2 included between points V And G, will show 12 V.
Voltage drop in resistance r 3:
U 3 = I × r 3 = 4 × 5 = 20 V.
Voltmeter V 3 included between points d And e, will show 20 V.
If a voltmeter is connected at one end to a point A, the other end to the point G, then it will show the potential difference between these points, equal to the sum of the voltage drops in the resistances r 1 and r 2 (8 + 12 = 20 V).
So the voltmeter V, measuring the voltage at the terminals of the circuit and connected between the points A And e, will show the potential difference between these points or the sum of the voltage drops in the resistances r 1 , r 2 and r 3 .
This shows that the sum of the voltage drops in individual sections of the electrical circuit is equal to the voltage at the circuit terminals.
Since in a series connection the circuit current is the same in all sections, the voltage drop is proportional to the resistance of a given section.
Example 2. Three resistances of 10, 15 and 20 ohms are connected in series, as shown in Figure 3. The current in the circuit is 5 A. Determine the voltage drop across each resistance.
U 1 = I × r 1 = 5 ×10 = 50 V,
U 2 = I × r 2 = 5 ×15 = 75 V,
U 3 = I × r 3 = 5 ×20 = 100 V.
Figure 3. Example 2
The total voltage of the circuit is equal to the sum of the voltage drops in individual sections of the circuit:
U = U 1 + U 2 + U 3 = 50 + 75 + 100 = 225 V.
A parallel connection of conductors is a connection when the beginnings of all conductors are connected to one point, and the ends of the conductors to another point (Figure 4). The beginning of the circuit is connected to one pole of the voltage source, and the end of the circuit is connected to the other pole.
The figure shows that when conductors are connected in parallel, there are several paths for current to pass. Current flowing to branch point A, spreads further over three resistances and equal to the sum currents leaving this point:
I = I 1 + I 2 + I 3 .
If the currents arriving at the branching point are considered positive, and the currents leaving are negative, then for the branching point we can write:
that is, the algebraic sum of currents for any nodal point in the circuit is always equal to zero. This relationship connecting the currents at any branch point in the circuit is called. The definition of Kirchhoff's first law can be expressed in another formulation, namely: the sum of currents flowing into a node of an electrical circuit is equal to the sum of currents flowing out of this node.
Video 2. Kirchhoff's first law
Usually, when calculating electrical circuits, the direction of the currents in the branches connected to any branch point is unknown. Therefore, in order to be able to write down the equation of Kirchhoff’s first law, before starting to calculate the circuit, it is necessary to arbitrarily select the so-called positive directions of currents in all its branches and designate them with arrows on the diagram.
g = g 1 + g 2 + g 3 .
Thus, with a parallel connection, it is not the resistance that increases, but the conductivity.
Example 3. Determine the total resistance of three parallel-connected resistances if r 1 = 2 Ohm, r 2 = 3 Ohm, r 3 = 4 ohms.
Example 4. Five resistances of 20, 30, 15, 40 and 60 Ohms are connected in parallel to the network. Determine the total resistance:
It should be noted that when calculating the total resistance of a branch, it is always less than the smallest resistance included in the branch.
If the resistances connected in parallel are equal to each other, then the total resistance r circuit is equal to the resistance of one branch r 1 divided by the number of branches n:
Example 5. Determine the total resistance of four parallel-connected resistances of 20 ohms each:
To check, let's try to find the branching resistance using the formula:
As you can see, the answer is the same.
Example 6. Let it be necessary to determine the currents in each branch when they are connected in parallel, shown in Figure 5, A.
Let's find the total resistance of the circuit:
Now we can depict all the branches in a simplified manner as one resistance (Figure 5, b).
Voltage drop between points A And B will:
U = I × r= 22 × 1.09 = 24 V.
Returning again to Figure 5, we see that all three resistances will be energized at 24 V, since they are connected between the points A And B.
Considering the first branch of the branching with resistance r 1, we see that the voltage in this section is 24 V, the resistance of the section is 2 Ohms. According to Ohm's law for a section of a circuit, the current in this section will be:
Second branch current
Third branch current
Let's check using Kirchhoff's first law
I = I 1 + I 2 + I 3 = 12 + 6 + 4 = 22 A.
Therefore, the problem was solved correctly.
Let's pay attention to how the currents are distributed in the branches of our parallel connection.
First branch: r 1 = 2 Ohm, I 1 = 12 A.
Second branch: r 2 = 4 Ohm, I 2 = 6 A.
Third branch: r 3 = 6 Ohm, I 3 = 4 A.
As you can see, the resistance of the first branch is two times less than the resistance of the second branch, and the current of the first branch is twice the current of the second branch. The resistance of the third branch is three times greater than the resistance of the first branch, and the current of the third branch is three times less than the current of the first branch. From this we can conclude that the currents in the branches in a parallel connection are distributed inversely proportional to the resistances of these branches. Thus, a lower current will flow through a branch with high resistance than through a branch with low resistance.
For two parallel branches, you can, of course, also use the formula given above.
However, the total resistance of the conductor in a parallel connection in this case is easier to calculate using the formula:
or finally:
Mixed connection of conductors
A mixed connection of conductors is a connection where there are both series and parallel connections of individual conductors. An example is the connection shown in Figure 6.
Figure 6. Mixed conductor connection diagram
Video 3. Mixed connection of conductors
Example 7. Determine the total resistance of the mixed connection presented in Figure 6 if
r 1 = 2 Ohm, r 2 = 3 Ohm, r 3 = 5 Ohm, r 4 = 4 Ohm, r 5 = 8 ohms and r 6 = 6 ohms.
Find the total resistance of the first branch:
Total resistance of the second branch:
Total circuit resistance:
r = r 1,2 + r 3 + r 4,5,6 = 1.2 + 5 + 1.85 = 8.05 Ohms.
The current in an electrical circuit passes through conductors from the voltage source to the load, that is, to lamps and devices. In most cases, copper wires are used as conductors. The circuit may contain several elements with different resistances. In an instrument circuit, conductors can be connected in parallel or in series, and there can also be mixed types.
An element with resistance is called a resistor; the voltage of this element is the potential difference between the ends of the resistor. Parallel and series electrical connections of conductors are characterized by a single operating principle, according to which the current flows from plus to minus, and the potential decreases accordingly. In electrical circuits, the wiring resistance is taken as 0, since it is negligibly low.
A parallel connection assumes that the elements of the circuit are connected to the source in parallel and are turned on simultaneously. Series connection means that the resistance conductors are connected in strict sequence one after another.
When calculating, the idealization method is used, which greatly simplifies understanding. In fact, in electrical circuits, the potential gradually decreases as it moves through the wiring and elements that are included in a parallel or series connection.
Series connection of conductors
The serial connection scheme means that they are switched on in a certain sequence, one after the other. Moreover, the current strength in all of them is equal. These elements create a total stress in the area. Charges do not accumulate in the nodes of the electrical circuit, since otherwise a change in voltage and current would be observed. With a constant voltage, the current is determined by the value of the circuit resistance, so in a series circuit, the resistance changes if one load changes.
The disadvantage of this scheme is the fact that if one element fails, the others also lose the ability to function, since the circuit is broken. An example would be a garland that does not work if one bulb burns out. This is a key difference from a parallel connection, in which the elements can operate separately.
The sequential circuit assumes that, due to the single-level connection of the conductors, their resistance is equal at any point in the network. The total resistance is equal to the sum of the voltage reduction of individual network elements.
With this type of connection, the beginning of one conductor is connected to the end of another. The key feature of the connection is that all the conductors are on one wire without branches, and one electric current flows through each of them. However, the total voltage is equal to the sum of the voltages on each. You can also look at the connection from another point of view - all conductors are replaced by one equivalent resistor, and the current on it coincides with the total current that passes through all resistors. The equivalent cumulative voltage is the sum of the voltage values across each resistor. This is how the potential difference across the resistor appears.
Usage serial connection It is useful when you need to specifically turn on and off a certain device. For example, an electric bell can ring only when there is a connection to a voltage source and a button. The first rule states that if there is no current on at least one of the elements of the circuit, then there will be no current on the rest. Accordingly, if there is current in one conductor, it is also in the others. Another example would be a battery-powered flashlight, which only lights up if there is a battery, a working light bulb, and a button pressed.
In some cases, a sequential circuit is not practical. In an apartment where the lighting system consists of many lamps, sconces, chandeliers, there is no need to organize a scheme of this type, since there is no need to turn the lighting on and off in all rooms at the same time. For this purpose, it is better to use a parallel connection in order to be able to turn on the light in individual rooms.
Parallel connection of conductors
In a parallel circuit, the conductors are a set, some ends of which are assembled into one node, and the other ends into a second node. It is assumed that the voltage in the parallel type of connection is the same in all sections of the circuit. Parallel sections of the electrical circuit are called branches and pass between two connecting nodes; they have the same voltage. This voltage is equal to the value on each conductor. The sum of the inverse indicators of the resistances of the branches is also the inverse with respect to the resistance of an individual section of the circuit of the parallel circuit.
For parallel and series connections, the system for calculating the resistance of individual conductors is different. In the case of a parallel circuit, the current flows through the branches, which increases the conductivity of the circuit and reduces the total resistance. When several resistors with similar values are connected in parallel, the total resistance of such an electrical circuit will be less than one resistor a number of times, equal to the number resistors in the circuit.
Each branch has one resistor, and the electric current, when it reaches the branching point, is divided and diverges to each resistor, its final value is equal to the sum of the currents at all resistances. All resistors are replaced with one equivalent resistor. Applying Ohm's law, the value of resistance becomes clear - in a parallel circuit, the values inverse to the resistances on the resistors are summed up.
With this circuit, the current value is inversely proportional to the resistance value. The currents in the resistors are not interconnected, so if one of them is turned off, this will in no way affect the others. For this reason, this circuit is used in many devices.
When considering the possibilities of using a parallel circuit in everyday life, it is advisable to note the apartment lighting system. All lamps and chandeliers must be connected in parallel; in this case, turning one of them on and off does not in any way affect the operation of the remaining lamps. Thus, by adding each light bulb to a branch of the circuit, you can turn on and off the corresponding lamp as needed. All other lamps operate independently.
All electrical appliances are connected in parallel into an electrical network with a voltage of 220 V, then they are connected to the distribution panel. That is, all devices are connected regardless of the connection of other devices.
Laws of series and parallel connection of conductors
For a detailed understanding in practice of both types of connections, we present formulas explaining the laws of these types of connections. Power calculations for parallel and series connections are different.
In a series circuit, there is the same current in all conductors:
According to Ohm's law, these types of conductor connections are explained differently in different cases. So, in the case of a series circuit, the voltages are equal to each other:
U1 = IR1, U2 = IR2.
In addition, the total voltage is equal to the sum of the voltages of the individual conductors:
U = U1 + U2 = I(R1 + R2) = IR.
The total resistance of an electrical circuit is calculated as the sum of the active resistances of all conductors, regardless of their number.
In the case of a parallel circuit, the total voltage of the circuit is similar to the voltage of the individual elements:
And the total strength of the electric current is calculated as the sum of the currents that exist in all conductors located in parallel:
To ensure maximum efficiency of electrical networks, it is necessary to understand the essence of both types of connections and apply them expediently, using the laws and calculating the rationality of practical implementation.
Mixed connection of conductors
Series and parallel resistance circuits can be combined in one electrical circuit if necessary. For example, it is possible to connect parallel resistors in a series circuit to another resistor or group of resistors; this type is considered combined or mixed.
In this case, the total resistance is calculated by summing the values for the parallel connection in the system and for the series connection. First, it is necessary to calculate the equivalent resistances of resistors in a series circuit, and then the elements of a parallel circuit. Serial connection is considered a priority, and circuits of this combined type are often used in household appliances and devices.
So, by considering the types of conductor connections in electrical circuits and based on the laws of their functioning, you can fully understand the essence of the organization of circuits of most household electrical appliances. For parallel and series connections, the calculation of resistance and current is different. Knowing the principles of calculation and formulas, you can competently use each type of circuit organization to connect elements in the optimal way and with maximum efficiency.
