Question

An Infinite ladder network of resistance is constructed with $1\, \Omega$ and $2\,\Omega$ resistances as shown in the figure. The $6\,V$ battery between $A$ and $B$ has negligible resistance. The effective resistance between $A$ and $B$ is :

• A. $1\,\Omega$
• B. $2\,\Omega$
• C. $3\,\Omega$
• D. $5/8\,\Omega$

Answer 1

Answer: (B)

$x=\frac{2 x}{x + 2}+1$

$x^{2}+2x=2x+x+2$
$x^{2}-x-2=0$
$\left(\right.x-2\left.\right)\left(\right.x+1\left.\right)=0$
$x=2\,\Omega$