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Four infinite ladder network containing identical resistances of R ohm each, are combined as shown in figure. The equivalent resistance between A and B is R_AB and between A and C is R_AC. Then the value of $\frac{R_{AB}}{R_{AC}}$ is

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$\frac{3}{4}$

$\frac{4}{3}$

$\frac{1}{2}$

answer is A.

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Detailed Solution

Let the equivalent resistance of one infinite ladder be x. Then the complete network reduces to

$\begin{array}{l} ∴ R_{AB} = \frac{x \times 3 x}{x + 3 x} = \frac{3}{4} x {andR}_{AC} = \frac{2 x \times 2 x}{2 x + 2 x} = x \\ Hence \frac{R_{AB}}{R_{AC}} = \frac{3}{4} \end{array}$

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