Question

Four infinite ladder network containing identical resistances of $R\Omega$ each, are combined as shown in figure. The equivalent resistance between $A$ and $B$ is $R_{AB}$ and between $A$ and $C$ is $R_{AC}$. If the value of $\frac{R_{AB}}{R_{AC}}$ is $\frac{x}{4}$, then the value of $8x$ is

Answer 1

Each arm is an infinite ladder. Let $R_{AB}=R_{BC}=R_{CD}=R_{DA}=y$

$3y,y$ are parallel across $AB$, so
$R_{AB}=\frac{3y\times y}{3y+y}=\frac{3y}{4}$

$2y,2y$ are parallel across $AC$, so
$R_{AC}=\frac{2y\times 2y}{4y}=y$

$\frac{R_{AB}}{R_{AC}}=\frac{\frac{3y}{4}}{y}=\frac{3}{4}$

$\Rightarrow x=3$
$\Rightarrow 8x=24$