Equivalent Resistance Calculation in Tetrahedron Wire
In order to determine the equivalent resistance between corners 1-2 and 1-3 in a tetrahedron wire with resistance r in each edge, we need to analyze the circuit and apply the principles of electrical circuits.

Resistance between Corners 1-2
- To calculate the resistance between corners 1-2, we need to consider the paths available for current flow.
- In a tetrahedron wire, there are multiple paths that current can take from corner 1 to corner 2.
- One way to approach this problem is by breaking down the tetrahedron into simpler series and parallel combinations of resistors.
- By analyzing the different paths and combinations, we can then calculate the equivalent resistance between corners 1-2.

Resistance between Corners 1-3
- Similarly, to find the resistance between corners 1-3, we need to analyze the circuit and identify the paths for current flow.
- By breaking down the tetrahedron wire into simpler configurations, we can determine the equivalent resistance between corners 1-3.
- This process involves understanding the connections between the edges and applying the relevant circuit analysis techniques.
In conclusion, by carefully analyzing the tetrahedron wire and applying circuit analysis principles, we can calculate the equivalent resistance between corners 1-2 and 1-3. This exercise helps in understanding the behavior of complex circuits and strengthens our problem-solving skills in electronics and communication engineering.