Question:

Each resistance in the given cubical network has resistance of 1 Ω and equivalent resistance between A and B is
cubical network has resistance of 1 Ω

Updated On: Apr 8, 2025
  • \(\frac{5}{6} \Omega\)
  • \(\frac{6}{5} \Omega\)
  • \(\frac{5}{12} \Omega\)
  • \(\frac{12}{5} \Omega\)
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is A

Approach Solution - 1

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): \(\frac{5}{6} \Omega\)

Was this answer helpful?
2
3
Hide Solution
collegedunia
Verified By Collegedunia

Approach Solution -2

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 \({\frac{5}{6}} \, \Omega \).
 

Was this answer helpful?
0
0