Question

An infinite ladder network of resistance is constructed with a $1\Omega$ and $2\Omega$ resistance as shown in figure. What is the value of effective resistance between $\text{A}$ & $\text{B}$? (Give integer value)

• A. 2.00
• B. 2
• C. 2.0

Answer 1

Answer: (A), (B), (C)

Let the effective resistance between points between $\text{C}$ & $\text{D}$ be $R$, then the circuit can be redrawn as shown below.


The effective resistance between $\text{A}$ & $\text{B}$ is

$R_{eq}=1+\frac{2\times R}{R+2}$

This resistance $R_{eq}$ can be taken as $R$ because if we add one identical item in infinite item, then the result will be same. Therefore,

$\therefore R=1+\frac{2\times R}{R+2}$

$\Rightarrow R^2+2R=3R+2$

$\Rightarrow R^2-R-2=0$

$\Rightarrow (R+1)(R-2)=0$

Taking positive value, because resistance can't be negative

$\therefore R=2\Omega$

Accepted answer : $2$