question_answer

The resistance between the terminal point P and Q of the given infinitely long circuit will be (in\[\Omega \]) while each resistance 'R' is one ohm:            

A)      \[1+\sqrt{3}\]             

B) \[4-\sqrt{3}\]

C) \[2\sqrt{2}\]                            

D) \[4-\sqrt{2}\]

Correct Answer: A

Solution :

Let \[{{R}_{PQ}}={{R}_{eq}}\] Then \[{{R}_{RS}}={{R}_{eq}}\] The circuit can be redrawn as shown in below figure \[\Rightarrow {{R}_{eq}}=1+\frac{1\times {{R}_{eq}}}{1+{{R}_{eq}}}+1\] \[\Rightarrow R_{eq}^{2}=2{{R}_{eq}}-1=0\] \[\therefore {{R}_{eq}}=\frac{2+\sqrt{4+4}}{2}=(1+\sqrt{3})\,Q\]