Parallel and serial connection of conductors - ways of switching an electrical circuit. Electrical circuits of any complexity can be represented by the indicated 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 — the connection is called serial. A chain is formed. To turn on the next link, you need to break the electrical circuit by inserting a new conductor there.
- The beginnings of conductors are connected by one point, the ends by another, the connection is called parallel. Bundle is called branching. Each individual conductor forms a branch. Common points are referred to as nodes of the electrical network.

In practice, the mixed inclusion of conductors is more common, some are connected in series, some - in parallel. It is necessary to break the chain with simple segments, solve the problem for each separately. An arbitrarily complex electrical circuit can be described by parallel, serial connection of conductors. This is done in practice.

## Using Parallel and Serial Connections of

### Conductors Terms Applied to Electrical Circuits

Theory is the basis for building strong knowledge, few know how voltage( potential difference) differs from voltage drop. In terms of physics, the internal circuit is called the current source, located outside - is called external. The delimitation helps to describe the field distribution correctly. The current does the work. In the simplest case, the generation of heat according to the Joule-Lenz law. The charged particles, moving in the direction of a lower potential, collide with the crystal lattice, give off energy. There is a heating resistance.

To ensure movement, it is necessary to maintain a potential difference at the ends of the conductor. This is called the voltage section of the circuit. If you just put the conductor in the field along the lines of force, the current will flow, it will be very short. The process will end with the onset of equilibrium. The external field will be balanced by its own field of charges, the opposite direction. The current will stop. For the process to become continuous, external force is needed.

The current source is such a drive for the movement of an electrical circuit. To maintain potential, work is done inside. Chemical reaction, as in a galvanic cell, mechanical forces - hydroelectric generator. The charges inside the source move in the opposite field. This is accomplished by the work of outside forces. You can paraphrase the above wording, say:

- The outer part of the circuit, where the charges move, carried away by the field.
- The interior of the circuit where the charges move against the intensity.

The generator( current source) is equipped with two poles. Possessing less potential is called negative, the other is positive. In the case of alternating current, the poles are constantly changing places. The direction of movement of the charges varies. The current flows from the positive pole to the negative. The movement of positive charges goes in the direction of decreasing potential. According to this fact, the concept of a potential drop is introduced:

The potential drop of a chain section is called the loss of potential within a segment. Formally, this tension. For the branches of the parallel circuit is the same.

Voltage drop means something else. The value characterizing the heat loss is numerically equal to the product of the current and the active resistance of the area. The laws of Ohm and Kirchhoff, discussed below, are formulated for this case. In electric motors, transformers, the potential difference may differ significantly from the voltage drop. The latter characterizes the losses in active resistance, while the former takes into account the complete operation of the current source.

Here we explain: some of the energy is converted into magnetic flux or chemical interaction, the circuit in the area cannot be considered consistent. There is a branching, due to the presence of the reactive component of the impedance, or other forces. The motor winding is endowed with a pronounced inductive resistance, by means of which the magnetic field is transmitted to perform work. Power is shifted in phase, part of it goes to heat. In practice, it is considered a parasitic phenomenon. The laws of sequential and external connection of conductors in physics are formulated for the simplest cases. Constant is the current of one direction, constant amplitude, engineers understand by this the rectified voltage.

When solving physical problems, for simplicity, the engine may include an emf in its composition, 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 course differs isolation from reality. That is why students, having opened a mouth, listen to the phenomena which are taking place in electrical engineering. In the period preceding the era of the industrial revolution, the main laws were discovered, the scientist should unite the role of theorist and talented experimenter. Prefaces to the works of Kirchhoff openly speak about this( the works of George Ohm have not been translated into Russian).The teachers literally lured people with additional lectures, flavored with visual, amazing experiments.

### The laws of Ohm and Kirchhoff as applied to the series and parallel connection of conductors

To solve real problems, the laws of Ohm and Kirchhoff are used. The first one derived equality in a purely empirical way - experimentally - the second one began by mathematical analysis of the problem, then he checked the guesses with practice. Let us give some information that helps to solve the problem:

- In the treatise on the mathematical study of electroplating circuits, Georg Ohm: the current when the conductors are connected in series is the same. The magnetic needle in each section of the chain was deflected in experiments by a fixed angle. The discovery of Ohm's law was preceded by the report of Oersted on the action of a conductor with a current on a sea compass. The strength of the current was usually characterized by the deviation of the magnetic needle from the initial position. For greater loyalty, Om possessed experience in the direction of the Earth meridian.
- In a node of a parallel electrical circuit, the current forks. Kirchhoff received the rule, investigating the passage of electricity through a metal round plate, seeking to obtain a generalized formula for all cases. The conceived was succeeded, two Kirchhoff laws became a by-product, one says: the sum of the currents of the chain node is zero. Inbox is taken with one sign, outgoing - with another.
- Kirchhoff's Second Law will help analyze a sequential circuit. It states: in a closed( read - sequential) circuit, the sum of the voltage drops is equal to the sum of the EMF.Remember, the current at each point is constant( see above).EMF - current sources, the field is directed opposite to the other part of the circuit, which is usually called external. The law is based on the fact that the use of a consistent inclusion of batteries with the summation of the effect of voltage. Two tablets of 1.5 V, being included, give 3 volts. In a series circuit, the voltage is added.
- The last rule hardly needs proof. Claims: the voltage on the branches of the chain with both common nodes is the same. The fact is easy to understand by the example of a carrying extension. No matter how many devices are turned on, the mains voltage will remain the same. Therefore, we do not find it necessary to give the axiom of evidence. Advanced users will notice: the real source voltage drops when overloaded, let's say: the permissible norms are monitored by the plugs of the distribution board.

## Calculate the resistances of elements in series and parallel connection

The algorithm for calculating real circuits is simple. Here are some theses regarding the subject under consideration:

- When connected in series, the resistors are summed, and in parallel - the conductivity:
- For resistors, the law is written in unchanged form. With parallel connection, the final resistance is equal to the product of the original divided by the total amount. When consistent - nominal values are added together.
- Inductance acts as a reactance( j * ω * L), behaves like a normal resistor. In terms of writing a formula is no different. Nuance, for any purely imaginary impedance that you need to multiply the result by the operator j, the circular frequency ω( 2 * Pi * f).When the inductance coils are connected in series, the ratings are summed, and in parallel - the inverse values are added.
- The imaginary resistance of the capacitance is written as: -j / ω * C.It is easy to notice: adding the values of the series connection, we get the formula, just as for resistors and inductances was at parallel. For capacitors, the opposite is true. When connected in parallel, the nominal values are added, with a sequential - the inverse values are summed.

Abstracts easily extend 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, characteristics. Power sources are treated in the same way: when connected in series, the ratings are added. Parallel is often found at substations, where transformers are placed side by side. The voltage will be one( controlled by the equipment), divided between the branches. The transformation ratio is strictly equal, blocking the occurrence of negative effects.

Some people have a problem: two batteries of different denominations are connected in parallel. The case is described by the second Kirchhoff law; it cannot present any difficulty to physics. With the inequality of the values of the two sources, the arithmetic average is taken, if we ignore the internal resistance of both. Otherwise, Kirchhoff equations are solved for all contours. The currents will be unknown( only three), the total number of which is equal to the number of equations. For a full understanding of the led figure.

Let's look at the image: according to the problem statement, the source of E1 is stronger than E2.We take the direction of the currents in the circuit for sound reasons. But if they had been inserted incorrectly, after solving the problem, one would have turned out with a negative sign. Should then change direction. Obviously, the current flows in the external circuit as shown in the figure. We compile the Kirchhoff equations for the three circuits, this is what follows:

- The work of the first( strong) source is spent on creating current in the external circuit, overcoming the weakness of the neighbor( current I2).
- The second source does not perform useful work in the load, struggling with the first. Otherwise you will not tell.

Switching batteries of different ratings in parallel in parallel is certainly harmful. What is observed at the substation when using transformers with different transmission coefficient. Equalization currents do not perform any useful work. Different batteries connected in parallel will begin to function effectively when the strong one progresses to the level of the weak one.