# 12 WIRES , EACH OF RESISTANCE r ARE JOINED TOGETHER TO FORM A CUBE. FIND THE EQUIVALENT RESISTANCE IN THE EDGE OF CUBE.

Aman Bansal
592 Points
12 years ago

Dear Kareena,

This is the cube structure consisting of 12 resistors electrically connected between the 8 vertices. Each resistor is 1 Ω, but any value can be used so long as they are all the same.

Here is where the intuition comes into play. Color coding is used to help keep track of the resistors and associated nodes (below). Due to symmetry, the potential (voltage) at the three nodes labeled "α" are equal. Since no current flows between nodes with a potential difference of 0 V, they can be shorted together without affecting the circuits integrity. The same can be done for the nodes labeled "β."

Once you short those nodes, you obtain the equivalent circuit shown below. As you can see, there are two sets of three resistors in parallel, in series with one set of six resistors in parallel. So, you have 1/3 Ω in series with 1/6 Ω in series with 1/3 Ω, which equals 5/6 Ω.

Best Of luck

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Thanks

Aman Bansal