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The equivalent resistance of the following infinite network of resistances is :

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less than $4 Ω$

$4 Ω$

more than $4 Ω$ but less than $12 Ω$

$12 Ω$

answer is C.

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Detailed Solution

$4 + \frac{2 x}{2 + x} = x$

$8 + 6 x = 2 x + x^{2} \Rightarrow x^{2} - 4 x - 8 = 0$

$x = \frac{4 \pm \sqrt{16 + 32}}{2} = \frac{4 \pm 4 \sqrt{3}}{2}$

$so, finally x = 2 + 2 \sqrt{3} = 5.4 Ω$

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