Question

An infinite ladder network of resistance is constructed with 1$81.15\Omega$ and 2$51.18\Omega$ resistance as shown in figure. The 6V battery between A and B has negligible internal resistance. The equivalent resistance between A and B is

• A. 1$18.15\Omega$
• B. 2$r_{1}$
• C. 3$r_{1}$
• D. 4$r_{2}$

Answer 1

Answer: (B)

2$r_{1}$

Answer 2

: The equivalent circuit is,

$R_{eq} = 1 + \frac{2 \times R_{eq}}{(2 + R_{eq})} = \frac{2 + 3R_{eq}}{2 + R_{eq}}$ i.e. $R_{eq}^{2} - R_{eq} - 2 = 0$

$\Rightarrow R_{eq} = \frac{1}{2}\left\lbrack 1 \pm \sqrt{1 + 8} \right\rbrack = 2\Omega.$