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## Q. 2.18

Consider the following circuit involving a one-dimensional infinite array of 1 Ω resistors connected to a 2V voltage source.Find $i_{x}$.

## Verified Solution

First we assume that the equivalent resistance of the array is $R_{eq}$.Then, considering just the first loop, we have

(1 ∥ $R_{eq}$) + 2 = $R_{eq}$,

which can be solved to obtain $R_{eq}=(1+\sqrt{3} )\Omega$ Therefore

$i_{x}=\frac{2}{1+\sqrt{3} }=(\sqrt{3}-1 ) A$