question_answer

Consider the infinite resistance connection shown below each of resistor having resistance \[r\] If R be the equivalent resistance, then it can expressed in terms of r as.

A)  \[\frac{(1+\sqrt{5})}{2}r\]                          

B)  \[\frac{(1-\sqrt{5})}{2}r\]

C)  \[\frac{(\sqrt{3}+1)}{2\sqrt{3}}r\]                           

D)  \[\frac{(\sqrt{7}+1)}{\sqrt{3}}r\]

Correct Answer: A

Solution :

                Redrawing the resistance connection The equivalent resistance \[R=r+\frac{rR}{r+R}\Rightarrow {{R}^{2}}-rR-{{r}^{2}}=0\] \[\Rightarrow \]               \[R=\frac{r+\sqrt{{{r}^{2}}+4{{r}^{2}}}}{2}=\frac{(1+\sqrt{5})}{2}r\]