Abstract
The properties of the regime parameters of the electric circuit are investigated in the paper by analyzing the dependence of the complex current on the complex resistance in linear electric circuits. The electrical circuit is considered as an active four-terminal network. The dependence is a fractional-linear function of the complex variable. The article uses a circle property, a property of preserving angles, and the maximum principle of the module of a fractional linear function of a complex variable. The image of the mapping of the domain is a circle, the coordinates of the center and the radius of which are determined in this paper. The inverse mapping is analyzed with the help of which the sets of values of resistances are determined for which the current of the branch of interest does not vary in module or in phase. Via mappings on the complex plane, the values of the resistances at which the module (phase) of the current of the electrical circuit branch of interest takes the maximum or minimum value are also determined.
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