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, \[{{R}_{2}}=\frac{r}{4}\] \[{{R}_{PQ}}={{R}_{1}}+{{R}_{2}}=\frac{r}{2}\]