question_answer

The resistance of haxagon circuit between A and B represented in figure is:

A)  r                  

B)  \[0.5\,r\]

C)  \[2\,r\]                

D)  \[3\,r\]

Correct Answer: B

Solution :

From the analysis of figure (I). It is evident that the potential difference between points a, b and c is zero. The equivalent circuit is as shown in figure (ii). \[\Rightarrow \] \[{{r}_{gF}}={{r}_{de}}=\frac{2r\times 2r}{2r+2r}=r\] \[{{r}_{AB}}=\frac{2r\times 2r}{2r+2r}=\frac{r}{2}=0.5r.\]