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Physics-

General

Easy

Question

The circuit diagram shown consists of a large number of element (each element has two resistors R₁ and R₂). The resistance of the resistors in each subsequent element differs by a factor of K = 1/2 from the resistance of the resistors in the previous elements. The equivalent reistance between A and B shown in figure is :

$\frac{R_{1} - R_{2}}{2}$
$\frac{(R_{1} - R_{2}) + \sqrt{6 R_{1} R_{2}}}{2}$
$\frac{(R_{1} - R_{2}) + \sqrt{R_{1}^{2} + R_{2}^{2} + 6 R_{1} R_{2}}}{2}$
None of these

The correct answer is: $fraction numerator open parentheses R subscript 1 end subscript minus R subscript 2 end subscript close parentheses plus square root of R subscript 1 end subscript superscript 2 end superscript plus R subscript 2 end subscript superscript 2 end superscript plus 6 R subscript 1 end subscript R subscript 2 end subscript end root over denominator 2 end fraction$

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