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

Answer: 2

Voltage across $AB=V$, Voltage across $A^{\prime }{B}^{\prime }=\frac{V}{2}$ 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 $R_{1}i=R_2\frac{i}{2}$
$\Rightarrow \frac{R_2}{R_1}=2$