question_answer

In the arrangement shown, the magnitude of each resistance is\[2\Omega \]. The equivalent resistance between O and A is given by

A) \[\frac{14}{15}\Omega \]      

B) \[\frac{7}{15}\Omega \]

C) \[\frac{4}{3}\Omega \]                      

D) \[\frac{5}{6}\Omega \]

Correct Answer: A

Solution :

[a] B and D are symmetrical w.r.t O and A \[\Rightarrow \]   equipotential \[\therefore \]   Circuit becomes                         \[\therefore \,\,\,{{R}_{OA}}=\frac{(R)\,(7R/8)}{R+\frac{7R}{8}}=\frac{7R}{15}=\frac{14}{15}\,\,\Omega \]