Question

An infinite ladder network of resistances is constructed with $1\,\Omega$ and $2\,\Omega$ resistance as shown in figure.

The $6 \,V$ battery between $A$ and $B$ has negligible internal resistance. The equivalent resistance between $A$ and $B$ is

• A. $1\,\Omega$
• B. $2\,\Omega$
• C. $3\,\Omega$
• D. $4\,\Omega$

Answer 1

Answer: (B)

The equivalent circuit is

$R_{eq}=1+\frac{2\times R_{eq}}{\left(2+R_{eq}\right)}=\frac{2+3R_{eq}}{2+R_{eq}}$
i.e., $R^{2}_{eq}-R_{eq}-2=0$
$\Rightarrow R_{eq}=\frac{1}{2}\left[1 \pm\sqrt{1+8}\right]=2\,\Omega$