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