Question

An infinite ladder network of resistances is constructed with $1\Omega$ and $2\Omega$ resistances. The $6V$ battery has negligible internal resistance. The current that passes through the $2\Omega$ resistance nearest to the battery is

• A. $1A$
• B. $1.5A$
• C. $2A$
• D. $2.5A$

Answer 1

Answer: (B)

Let $x$ be the equivalent resistance of the infinite ladder then,
the equivalent circuit is

also, the equivalent resistance is
$x=1+\frac{2x}{2+x}$
$x^2-x-2=0$
$x=\frac{1+\sqrt{1+8}}{2}=2\Omega$
current through the battery is $3A$ .

Current through $2\Omega$ resistor is
$i=3\left(\frac{x}{2+x}\right)=3\left(\frac{2}{2+2}\right)=1.5A$