Kirchhoff’s Laws

Career Gustav Kirchhoff in many respects typical for the German physicist of the XIX century. Germany later approached its western neighbors in the industrial revolution and therefore needed more advanced technologies that would facilitate the accelerated development of the industry. As a result, scientists, especially natural scientists, were highly valued in Germany. In the year of graduation, Kirchhoff married the professor’s daughter, “observing, therefore, as one of his biographers writes,” two compulsory conditions for a successful academic career. ” But before that, at the age of twenty-one, he formulated the basic laws for calculating currents and voltages in electric circuits, which now bear his name.

The middle of the XIX century was just the time of active research of electrical circuit properties, and the results of these studies quickly found practical applications. The basic rules for calculating simple chains, such as Ohm’s law, have already been well worked out. The problem was that from wires and various elements of electrical circuits it was technically possible to manufacture very complex and branched networks – but nobody knew how to model them mathematically to calculate their properties. Kirchhoff succeeded in formulating rules that make it easy to analyze the most complex chains, and Kirchhoff’s laws are still an important working tool for specialists in the field of electronic engineering and electrical engineering.

Both Kirchhoff’s laws are formulated quite simply and have an understandable physical interpretation. The first law says that if we consider any node in a chain (that is, a branch point where three or more wires meet), then the sum of the electric currents entering the circuit will be equal to the sum of the outgoing ones, which, generally speaking, is a consequence of the law of conservation of electric charge. For example, if you have a T-junction of an electrical circuit and two currents to it, the current flows through the third wire in the direction from this node, and it will be equal to the sum of the two incoming currents. The physical meaning of this law is simple: if it had not been fulfilled, an electrical charge would continuously accumulate in the node, and this never happens.

The second law is no less simple. If we have a complex, branched chain, it can be mentally divided into a series of simply closed circuits. The current in the circuit can be distributed in different ways along these contours, and it is most difficult to determine which route the currents will flow in a complex circuit. In each of the circuits, electrons can either acquire additional energy (for example, from a battery) or lose it (for example, on a resistance or other element). Kirchhoff’s second law states that the net increment of the electron energy in any closed circuit of the circuit is zero. This law also has a simple physical interpretation. If this were not so, each time, passing through a closed circuit, the electrons would acquire or lose energy, and the current would continuously increase or decrease. In the first case, it would be possible to get a perpetual motion machine, and this is forbidden by the first law of thermodynamics; in the second, any currents in electrical circuits would inevitably decay, but we do not observe this.

The most common application of Kirchhoff’s laws is observed in so-called sequential and parallel chains. In a sequential chain (a bright example of such a chain is a Christmas tree garland consisting of successively connected lamps), the electrons from the power source through the series of wires pass through all the lamps successively, and on the resistance of each of them, the voltage falls according to Ohm’s law.

In a parallel circuit, the wires are, on the contrary, connected in such a way that an equal voltage is supplied to each element of the circuit from the power supply, which means that the current in each element of the circuit is different, depending on its resistance. An example of a parallel circuit is the “ladder” lamp: the voltage is applied to the tires, and the lamps are mounted on the cross bars. The currents passing through each node of such a chain are determined by Kirchhoff’s second law

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