# Circuit Theory/Symmetry

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

Bridge Balance

Cube

## Example 3

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: ${\displaystyle {\frac {Z}{3}}={\frac {1}{{\frac {1}{Z}}+{\frac {1}{Z}}+{\frac {1}{Z}}}}}$