question_answer

The equivalent resistance between points P and Q of an infinite network of resistance each of 2\[\Omega \] connected as shown in figure

A)  3.23\[\Omega \]            

B)  4.23\[\Omega \]

C)  6.32\[\Omega \]            

D)  infinite

Correct Answer: A

Solution :

 Suppose the equivalent resistance between points P and Q is R. \[R=\frac{2R}{2+R}+2\] \[{{R}^{2}}-2R-4=0\] \[R=1\pm \sqrt{5}\] Taking +ve sign.                       \[R=\sqrt{5}+1=3.23\,\Omega \]