Question

Twelve equal wires, each of resistance r, are joined to form a skeleton cube. The current enters at one corner and leaves at the diagonally opposite comer. Find the total resistance between these corners.

Answer 1

Applying Kirchhoff’s second rule (ΣE + ΣRI = 0) to the closed mesh XYMLKAX,

we get.

-E + [r × 2I + r × I + r × 2I] = O

or 5rI = ε …….. (i)

where E is the emf of the battery of negligible internal resistance. If r is the resistance of the cube between the diagonally opposite corners A and M, then according to the Ohm’s law, we have

6RI = E ……. (ii)

From eqs. (i) and (ii),

6RI = 5rI

Or

R = 5/6r

Hence, the resistance of the cube between any two diagonally opposite corners is 5/6 of the resistance of each wire.