梯形电阻网络的两个通项公式

Deriving of two currenting formulas on ladder-shaped resistance network

通过求解梯形电阻网络中的递推关系,推导出计算梯形电阻网络中等效电阻和节点电压的通项公式;证明了无穷梯形电阻网络等效电阻为常数,且给出其计算公式;提出梯形电阻网络等效电阻按无穷网络简化计算的条件。

By exploring into the recursion relation of ladder resistance network, the formulas of calculating equivalent resistance and node voltage on ladder resistance network have been derived.It is proved that equivalent resistance of infinity ladder resistance network is a constant,whose calculating formula has been derived. Furthermore, the paper gives the condition to simplify the calculation of equivalent resistance on ladder resistance network by treating this network as an infinity ladder resistance one.