An infinite ladder network is constructed with `1Omega `and `2Omega` resistors as shown. Find the equivalent resistance points `A` and `B`.
Text Solution
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Let the equivalent resistance between `A` and `B` is `x`. We may consider the given circuit as shown in figure. in this diagram `R_(AB)=(2x)/(2+x)+1` or `x+(2x)/(2+x)+1` (as `R_(AB)=x)` or `x(2+x)=2x+2+x` or `x^2-x-x-2=0` `x=(1+-sqrt(1+8))/2=-1Omega` and `2Omega` Ignoring the negative value, we have `R_(AB)=x=2Omega`
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