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Physics-

General

Easy

Question

The equivalent resistance between points A and B of an infinite network of resistances each of $1 capital omega$ connected as shown,

Infinite
$2 Ω$
$\frac{1 + \sqrt{5}}{2} Ω$
Zero

The correct answer is: $fraction numerator 1 plus square root of 5 over denominator 2 end fraction capital omega$

Similar to Q. No. 30. By formula $R equals R subscript 1 end subscript plus fraction numerator R subscript 2 end subscript cross times R over denominator R subscript 2 end subscript plus R end fraction$
\ $R equals 1 plus fraction numerator 1 cross times R over denominator 1 plus R end fraction$ Þ $R to the power of 2 end exponent plus R equals 1 plus R plus R$
Þ $R to the power of 2 end exponent minus R minus 1 equals 0$ or $R equals fraction numerator 1 plus-or-minus square root of 1 plus 4 end root over denominator 2 end fraction$ $equals fraction numerator 1 plus-or-minus square root of 5 over denominator 2 end fraction$
Since R cannot be negative, hence $R equals fraction numerator 1 plus square root of 5 over denominator 2 end fraction capital omega$

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