Resistor networks are practical electric circuits and provide meaningful models to represent natural or artificial conductive structures. They can also be used to demonstrate how, in physics, general properties can be derived elegantly by combining general principles with symmetry properties. Here, this typical approach of physics is illustrated in the case of two-point resistances in the 2 n globe network. It is a particular case of resistor networks on a sphere, where the n nodes of an equatorial frame of n identical resistors are connected by equal resistors to two axial poles. Recurrence relations are obtained using only Kirchhoff’s laws and Kennelly’s theorem. When complementing with relations derived using van Steenwijk’s method, explicit relations are obtained for all two-point resistances to any order n. Such analytical exact results are useful to test the results of numerical or integral methods. This complete treatment of the 2 n globe network can be used to illustrate for students the efficient ways of physics to derive analytical results and understand their origin.

电阻网络是实用的电路，并提供有意义的模型来表示自然或人工导电结构。它们还可用于演示如何在物理学中通过将通用原理与对称特性相结合来优雅地推导出通用特性。在这里，以 2 n地球网络中的两点电阻为例说明了这种典型的物理学方法。这是球体上电阻网络的一个特例，其中n的赤道坐标系的n个节点相同的电阻器通过相同的电阻器连接到两个轴向极。递归关系仅使用基尔霍夫定律和肯内利定理获得。当与使用 van Steenwijk 方法导出的关系进行补充时，对于任何阶数n 的所有两点电阻都可以获得显式关系。这种解析精确结果可用于检验数值或积分方法的结果。这种对 2 n地球网络的完整处理可用于向学生说明物理学推导分析结果和理解其起源的有效方法。