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The equivalent resistance between points A and B of an infinite network of resistance each of 1 $Ω$ connected as shown is

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infinite

2 $Ω$

zero

$(\frac{1 + \sqrt{5}}{2})$

answer is D.

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Detailed Solution

$\begin{array}{l} x = 1 + \frac{x}{1 + x} \Rightarrow x + x^{2} = 1 + 2 x \\ x^{2} - x - 1 = 0 \\ x = \frac{1 \pm \sqrt{1 + 4}}{2} = \frac{1 \pm \sqrt{5}}{2} \\ R_{eff} = \frac{1 + \sqrt{5}}{2} \end{array}$

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