Study on the electrical properties of a 2×6×n cascaded cobweb resistor network

Due to their excellent topological properties, cobweb models are widely used in fields such as material design and simulation calculations. This study focuses on the electrical characteristics of a 2×6×n cascaded cobweb resistor network constructed with cobweb models as basic units. The complex structure of such networks makes it difficult to solve using traditional methods. To address this issue, an optimized recurrence-transformation method is proposed in this paper. First, the cascaded network is equivalently transformed into a single-stage network. Second, a nonlinear recurrence equation for the single-stage network is established. Third, the nonlinear recurrence equation is converted into a linear recurrence equation. Finally, the equivalent resistance of the target resistor network is solved with the help of the linear recurrence equation. This method avoids complex matrix operations involved in traditional methods and features simplicity and convenience. Additionally, it can be extended to other two-terminal cascaded networks.