A STUDY ON THE EQUIVALENT RESISTANCE OF A CLASS OF 2×N ORDER K-SHAPED RESISTOR NETWORKS

Circuit structures are usually complex and diverse, and many circuit network problems are full of challenges. This paper analyzes and explores a class of multi-parameter 2×n order K-shaped resistor network models. By using creative thinking and rigorous calculations, an analytical expression for the equivalent resistance is derived. The research methods employed in this paper include three aspects: first, establishing three equivalent models for the circuit network; second, setting up a recursive difference equation; and third, using variable substitution techniques to solve the difference equation. The paper discusses some special cases of the equivalent resistance and compares and verifies the conclusions of these special cases with other related results. The research work in this paper has positive significance in promoting the coordinated development of teaching and scientific research, and it provides good guidance for cultivating college students' scientific inquiry and creative thinking abilities.