Question

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 $

Answer 1

Answer: (A)

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 $