question_answer

The resistance between the terminal points A and B of the given infinitely long circuit will be                      [MP PMT/PET 1998]

A)                    \[(\sqrt{3}-1)\]

B)                                      \[(1-\sqrt{3})\]

C)                    \[(1+\sqrt{3})\]

D)            \[(2+\sqrt{3})\]

Correct Answer: C

Solution :

                     Let equivalent resistance between A and B be R, then equivalent resistance between C and D will also be R.                    \[{R}'=\frac{R}{R+1}+2=R\] or \[{{R}^{2}}-2R-2=0\]            \ \[R=\frac{2\pm \sqrt{4+8}}{2}=\sqrt{3}+1\]