An infinite ladder network of resistances is constructed with $1 Ω$ and $2 Ω$ resistances as shown

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Effective resistance between A and B is $1 Ω$

Effective resistance between A and B is $2 Ω$

Current through $2 Ω$ resistor nearest to battery is 6A

Current through $2 Ω$ resistor nearest to battery is 3A

answer is B, D.

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Detailed Solution

$x = \frac{(x + 1) 2}{2 + x + 1} \Rightarrow x^{2} + 3 x - 2 x - 2 = 0 \Rightarrow x^{2} + x - 2 = 0$

$x = 1 Ω; i = \frac{V}{R} = \frac{6}{1} = 6 A$

Option (b) is correct. Option (a) is wrong.
$6 A$ current flows through battery. Because $x = 1 Ω$ , the current divides equally at the first junction of the upper branch. Current through $2 Ω$ resistor nearest to battery is 3A. Option (d) is correct, option (c) is wrong.

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