Question

An infinite ladder network is constructed with $1\Omega$ and $2\Omega$ resistors as shown. The effective resistance between $A$ and $B$ is

• A. $1\Omega$
• B. $2\Omega$
• C. $3\Omega$
• D. $4\Omega$

Answer 1

The correct option is B $2\Omega$

Let the equivalent resistance between $A$ and $B$ be $X$. If we retain the basic repetitive unit then the remiaing circuit is identical to the total circuit and hence will also posses a resistance $X$.

$R_{AB}=X=\frac{2X}{2+X}+1$

$\Rightarrow 2X=(2+X)(X-1)$

$\Rightarrow 2X=2X+X^2-X-2$

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

$\Rightarrow X^2-2X+X-2=0$

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

$\therefore X=2\Omega$

Hence, the correct answer is (B).