The given network forms a cube with resistors of 1 \(\Omega\) each along the edges. The equivalent resistance between two opposite corners (A and B) of a cube with resistors along the edges can be calculated by symmetry and applying the rules of series and parallel resistances. After applying Kirchhoff’s rules and simplifying, the equivalent resistance between A and B is: \[ R_{\text{eq}} = \frac{5}{6} \, \Omega \]
So, the correct answer is (A): \(\frac{5}{6} \Omega\)
This is a cube-shaped resistor network, with each edge having a resistance of 1 \( \Omega \). To find the equivalent resistance between points A and B, we can use symmetry and reduce the network step by step.
1. Use of Symmetry:
The cube has 12 edges, each with resistance 1 \( \Omega \). Due to the symmetry of the cube, we can analyze the equivalent resistance by grouping the resistances in parallel and series combinations.
2. Simplification by Symmetry:
- From A, there are three paths that go to neighboring points, each with a resistance of 1 \( \Omega \).
- The three paths are in parallel.
- After simplifying the three resistances, the equivalent resistance between A and B is reduced to \( \frac{1}{3} \, \Omega \).
3. Combining Further:
- After reducing these resistances step-by-step through the network (which involves considering additional paths between points), the final equivalent resistance between A and B becomes \( \frac{5}{6} \, \Omega \).
Thus, the equivalent resistance between A and B is \({\frac{5}{6}} \, \Omega \).