Kirchhoff's law in electro-technology

In calculating the electric circuits of alternating and direct current, in addition to the famous Ohm formula, the Kirchhoff law is also applied. A person whose work is connected with electrical engineering, even in the middle of the night, without hesitation, to give definitions for each of the two laws. Often this is necessary not so much to perform calculations, but to understand the processes that are taking place.

In the distant 1845, the German physicist Gustav Kirchhoff formulated two Rules on the basis of Maxwell's works (charge conservation and electrostatic field properties ) , allowing to indicate the relationship between the current and voltage in a closed electrical circuit. Thanks to this, it became possible to solve practically any applied tasks connected with electricity. Kirchhoff's law, used to calculate the linear electric circuit, makes it possible to obtain a classical system of linear equations that take into account the voltages and currents that become known after solving the problem posed.

The wording assumes the use of the terms electrical "contour, knot and branch". A branch is any two-sided part of a chain, an arbitrary segment of the chain. The contour is a system of looped branches, that is, by starting a mental movement from an arbitrary point along any branch, you end up in the place where the movement started. More clearly branches call "looped", although this is not entirely correct. A node is a point at which two or more branches meet.

1 Kirchhoff's law is very simple. It is based on the fundamental law of conservation of charge. The first law of Kirchhoff says: the sum of currents (algebraic), flowing along branches to a single node, is zero. That is, I1 + I2 + I3 = 0. For calculations it is considered that the value of the currents flowing into the node has the sign "+", and the resulting "-". Therefore, the extended formula takes the form I1 + I2 - I3 = 0. In other words: the amount of current flowing into the node is equal to the amount of flowing out. This Kirchhoff law is very important for understanding the principles of the operation of electrical equipment. For example, he explains why, when connecting the windings of an electric motor according to the "star" or "triangle" scheme, there is no interfacial short circuit.

2 Kirchhoff's law is usually used to calculate a closed loop with a certain number of branches. It is directly related to the third Maxwell's law (an unchanging magnetic field). The rule states that the algebraic sum of the stress drops on each of the branches of the contour equals the sum of the values of the emf for all branches of the calculated contour. It is obvious that in the absence of electric energy (EMF) sources in the closed circuit, the total voltage drop will also be zero. In a more simple language, the energy of the source is only converted to consumers, and when returning it tends to its original value. The use of this law has a number of features, as in the case of the former.

Constructing the equation of the circuit, it is considered that the numerical value of the EMF has a positive sign if the initially accepted direction of circumvention (usually clockwise) coincides with its direction, and negative if the directions are opposite. The same applies to resistors: if the current direction is the same as for the selected bypass, then the "+" sign is assigned to the voltage drop on it. For example, E1 - E2 + E3 = I1R1 - I2R2 + I3R3 + I4R4 ...

As a result of traversing all branches entering the contour, a system of linear equations is compiled , deciding which, it is possible to find out all the currents of the branches (and nodes). The resulting relationships are solved using the contour current method.

It is difficult to overestimate the importance of Kirchhoff's laws for electrical engineering. The simplicity of writing formulas and their solution with the help of methods of classical algebra were the reason for their wide use.