Question

Consider an infinite ladder of network shown in figure. $A$ voltage is applied between points $A$ and $B$. If the voltage is halved after each section, the ratio of $\frac{R_{2}}{R_{1}}$ is____.

Answer 1

Voltage across $A B=V$, Voltage across $A' B'=\frac{V}{2}$ i.e., Voltage across $R_{2}=\frac{V}{2}$
Now from Kirchhoff's law it is obvious that voltage across
$R_{1}=V-\frac{V}{2}=\frac{V}{2}$

When the voltage is halved, current is also halved, i.e., current in $R_{2}$ is half of that in $R_{1}$.
So $R_{1} i=R_{2} \frac{i}{2}$
$\Rightarrow \frac{R_{2}}{R_{1}}=2$