Twelve wires, each with an equal resistance r , are connected to form a cube as shown in the figure. Calculate the equivalent resistance between the diagonally opposite points a and f .

Step-by-step solution

Let the total current entering at junction a be I and leaving at junction f be I . Due to the symmetry of the cube, the current divides equally into three identical paths at junction a . Current in branches ab , ad , and ah is I 3 . At junction b , the current I 3 further divides equally into branches bc and be because the paths to f are symmetric. Current in branches bc and be is I 6 . Similarly, the current in branches dc , dg , he , and hg is I 6 . At junction c , currents from bc and dc combine. So, the current