question_answer

The effective resistance across the points\[P\] and \[Q\] is

A) \[\frac{r}{4}\]                                   

B) \[\frac{r}{2}\]

C) \[\frac{r}{8}\]                                   

D)  \[\frac{r}{16}\]

Correct Answer: B

Solution :

Since, the potential at \[{{A}_{1}}F\] is same. The potential at \[A,\,\,O\] and \[E\] is same. The potential at \[C\] and \[D\] is same. \[\therefore \]The circuit can be reduced to  The equivalent resistance of part (i) is                                 \[\frac{1}{{{R}_{1}}}=\frac{1}{r}+\frac{1}{r}+\frac{1}{r}+\frac{1}{r}\] or                            \[{{R}_{1}}=\frac{r}{4}\] Similarly,              \[{{R}_{2}}=\frac{r}{4}\]                                 \[{{R}_{PQ}}={{R}_{1}}+{{R}_{2}}=\frac{r}{2}\]