Twelve identical wires each of resistance 12 ohms are arranged to form the edges of a cube.calculate p.d developed between these corners and the equivalent resistance.
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Twelve wires, each having resistence r are joined to form a cube. What is the equivalent resistance between diagonal ends of a face?
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Sushil Paul, Founder and Techie at Shrimp Hoard Technologies
Answered May 19, 2016
Equivalent resistance between two vertices on the face diagonal
The picture below shows resistor cube whose vertices on one of its face diagonals are connected to a voltage source. These two vertices are labelled by A, and B.
In front of electric current I, entering A, edges labelled by AC are symmetric paths , with equal electric currents represented by i1 ; but the edge labelled by AE differs from AC edges and electric current flowing on it, is: i2=I - 2i1 . So electric potential on vertices labelled by C, are the same, and these vertices can be shorted. This kind of argument is applicable to the vertices labelled by D, and they can be shorted.
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3 ANSWERS

Sushil Paul, Founder and Techie at Shrimp Hoard Technologies
Answered May 19, 2016
Equivalent resistance between two vertices on the face diagonal
The picture below shows resistor cube whose vertices on one of its face diagonals are connected to a voltage source. These two vertices are labelled by A, and B.
In front of electric current I, entering A, edges labelled by AC are symmetric paths , with equal electric currents represented by i1 ; but the edge labelled by AE differs from AC edges and electric current flowing on it, is: i2=I - 2i1 . So electric potential on vertices labelled by C, are the same, and these vertices can be shorted. This kind of argument is applicable to the vertices labelled by D, and they can be shorted.
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