question_answer

In the figure, each segment (side of small triangle) has resistance R and the wire used in circumference of the circle has   negligible resistance. Find the equivalent resistance between point O and A.                                              

A) \[\frac{R}{4}\]              

B) \[\frac{R}{3}\]

C) \[\frac{R}{8}\]              

D) \[\frac{R}{5}\]

Correct Answer: A

Solution :

[a] Points A, B, C, D, E and F are equipotentials. From symmetry, points P, Q, R, S, T and U are equipotential and 1, 2, 3, 4, 5 and 6 are also equipotential. The circuit can be redrawn as \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,{{R}_{eq}}=\frac{R}{4}\]