question_answer

An infinite sequence of resistance is shown in the figure. The resultant resistance between A and B will be, when \[{{R}_{1}}=1\,ohm\] and \[{{R}_{2}}=2\,ohm\]                                 [MP PET 1993]

A)            Infinity                                    

B)            \[1\,\Omega \]

C)                    \[2\,\Omega \]            

D)            \[1.5\,\Omega \]

Correct Answer: C

Solution :

             Let the resultant resistance be R. If we add one more branch, then the resultant resistance would be the same because this is an infinite sequence.                    \[\therefore \frac{R{{R}_{2}}}{R+{{R}_{2}}}+{{R}_{1}}=R\Rightarrow 2R+R+2={{R}^{2}}+2R\]            \[\Rightarrow {{R}^{2}}-R-2=0\Rightarrow R=-1\] or \[R=2\,ohm\]