In calculations of 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 related to electrical engineering must even give definitions for each of the two laws even in the middle of the night without hesitation. Often this is necessary not so much for performing calculations as for understanding the ongoing processes.
Back in 1845, the German physicist Gustav Kirchhoff, based on Maxwell's work (charge conservation and the properties of the electrostatic field) formulated two Rules that allow you to specify the relationship between current and voltage in a closed electric circuit. Thanks to this, it became possible to solve almost any applied tasks related to electricity. Kirchhoff's law, used to calculate a 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.
The wording involves the use of the terms electrical "circuit, node and branch." A branch is any two-sided section of a chain, its arbitrary segment. A contour is a system of looped branches, that is, starting a mental movement from an arbitrary point along any branch, in the end you will still get to the place where the movement began. It is more understandable to call branches “looped”, although this is not entirely correct. A node is a point at which two or more branches meet.
Kirchhoff’s Law 1 is very simple. It is based on the fundamental law of conservation of charge. The first law of Kirchhoff states: the sum of the currents (algebraic) flowing along the branches to a single node is zero. That is, I1 + I2 + I3 = 0. For calculations, it is assumed that the value of the currents flowing into the node has a “+” sign, and the flowing “-”. 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 leakage. This Kirchhoff law is very important for understanding the principles of electrical equipment. For example, he explains why when connecting the windings of an electric motor according to the "star" or "triangle" scheme, an interphase short circuit does not occur .
2 Kirchhoff’s law is usually used to calculate a closed loop with a certain number of branches. It is directly interconnected with the third Maxwell law (unchanged magnetic field). The rule states that the algebraic sum of voltage drops on each branch of the circuit is equal to the sum of the EMF values for all branches of the calculated circuit. Obviously, in the absence of sources of electric energy (EMF) in a closed circuit, the resulting voltage drop will also be zero. In simpler terms, the energy of the source is only converted to consumers, and upon returning, tends to its original value. The use of this law has a number of features, as is the case with the first.
Composing the equation of the circuit, it is generally accepted that the numerical value of the EMF has a positive sign if the initially accepted direction of the circuit bypass (usually clockwise) coincides with its direction, and negative if the directions are opposite. The same applies to resistors: if the direction of current flow is the same as that of the selected bypass, then the “+” sign is attributed to the voltage drop across it. For example, E1 - E2 + E3 = I1R1 - I2R2 + I3R3 + I4R4 ...
As a result of going around all the branches included in the circuit, a system of linear equations is compiled , having decided which, it is possible to find out all the currents of the branches (and nodes). The obtained relations are solved using the method of contour currents.
It is difficult to overestimate the significance of Kirchhoff's laws for electrical engineering. The simplicity of writing formulas and their solution using the methods of classical algebra were the reason for their widespread use.