Question

Shown in the figure is an infinite network of resistors each of resistance $1\Omega$ . The effective resistance in between $A$ and $B$ is

• A. Less than $1\Omega$
• B. $1\Omega$
• C. More than $1\Omega$ but less than $3\Omega$
• D. $3\Omega$

Answer 1

Answer: (C)

The effective resistance of the infinite ladder between $A$ and $P$ will be less than one.
$R_{AP}<1\Omega$
Similarly, the effective resistance of the infinite ladder between $B$ and $Q$ will also be less than one.
$R_{BQ}<1\Omega$
Therefore resistance between $A$ and $B$ is
$R_{AB}=R_{AP}+R_{PQ}+R_{QB}$
As $R_{PQ}=1\Omega$
Therefore $1\Omega <R_{AB}<3\Omega$