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Chapter 2

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}.

Step-by-Step

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