question_answer

An infinite ladder network of resistances is constructed with 1 Q and 2 Q. resistances as shown in fig. The effective resistance between A and B is

A) \[2\Omega \]                 

B) \[3\,\Omega \]

C) \[4\,\Omega \]                           

D) \[5\,\Omega \]

Correct Answer: A

Solution :

[a] We have, \[r=\frac{2r}{r+2}+1,\] which gives , \[{{r}^{2}}-r-2=0\] or \[\left( r-2 \right)\left( r+\text{ }1 \right)=0\] \[\therefore \,\,r=2\,\Omega \] Here the rest of the infinite ladder has been replaced by r.