Solving tasks of the increased level of complexity for calculating parameters of branched electrical circuits

Abstract. This article discusses the examples of solving and correctly designing tasks of the increased level of complexity and Olympiad ones in Physics on the theme “Current branching. Kirchhoff’s Laws”. The reader is reminded of Kirchhoff’s laws and introduced to the procedure used in solving tasks by means of these laws. Using the example of four tasks, the detailed element-by-element analysis of the way of the solution is carried out with the analysis and justification of all stages of the solution. The necessity of studying the first and second Kirchhoff’s laws in physical and engineering classes is substantiated. General approaches are noted in the calculation of resistances and currents of branched electrical circuits, the necessity of building an equivalent circuit and a critical assessment of the obtained numerical result are indicated, as well as the importance of solving it firstly in a general (parametric) form. The authors consider tasks with the possibility of both the complete analytical solution and the numerical one of a system of linear equations where the parametric solution is unreasonably cumbersome and could lead to mathematical errors. In the considered examples the algorithm for compiling and solving a system of equations is explained in detail, the application of which is optimal in the conditions of each specific task.

Keywords: Kirchhoff’s laws, mixed connection, measuring bridge, bypass direction.