Circuit Theory/Symmetry

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Some very complicated circuits can be solved by seeing symmetry. Three examples are presented below:

Example 1[edit]

Bridge Balance

Example 2[edit]

Cube

Example 3[edit]

2D-Grid
Suppose there is an infinite 2 dimensional grid of impedances (Z). What is the input impedance if connected across (in parallel) with any given impedance?

If the grid were three dimensional, the current would split into 6 equal sections, thus the input impedance would be Z/3.

So what does this mean? It helps us understand that the infinity of space has an impedance: 376.730... ohms which is plank's impedance * 4π and is related to the speed of light, the permeability of free space and permitivity of free space.

Perhaps this is related entanglement and to the trinity since: \frac{Z}{3} = \frac{1}{\frac{1}{Z} + \frac{1}{Z} + \frac{1}{Z}}