question_answer

A cube is constructed from 12 identical wires. Current enters one comer of the cube and it leaves the opposite comer. If the resistance of each wire is r, then equivalent resistance will be

A)  \[\frac{6\,r}{5}\]

B)  \[\frac{5\,r}{6}\]

C)  \[\frac{5\,r}{12}\]

D)  \[\frac{12\,r}{5}\]

Correct Answer: B

Solution :

Let a current \[(6I)\] enter at A and leave at M. The current distribution is as shown. Let equivalent resistance be R. Each of the 12 wires have resistance r. \[\therefore \] \[E=2Ir+Ir+2Ir\] From Ohm?s law, \[E=IR\] \[(6I)R=5Ir\] \[\Rightarrow \] \[R=\frac{5}{6}r\]