question_answer

Twelve wires each of resistance \[6\,\Omega \] are connected to form a cube as shown in the adjoining figure. The current enters at a corner A and leaves at the diagonally opposite comer G. The equivalent resistance across the comers A and G is-

A) \[12\,\Omega \]              

B) \[6\,\Omega \]

C) \[3\,\Omega \]               

D) \[5\,\Omega \]              

Correct Answer: D

Solution :

\[{{R}_{AG}}\,\,=\,\,\frac{R}{3}+\frac{R}{6}+\frac{R}{3}=\frac{5R}{6}\] \[=\,\,\,\frac{5}{6}\times 6\,\Omega \,\,=\,\,5\,\Omega \]