Question

An infinite ladder network of resistances is constructed with $1\Omega$ and $2\Omega$ 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. $1\Omega$
• 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., $R_{eq}^2-R_{eq}-2=0$
$\Rightarrow R_{eq}=\frac{1}{2}\left[1\pm \sqrt{1+8}\right]=2\Omega$