question_answer

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

A)  Infinity                

B)  \[1\Omega \]

C)  \[2\Omega \]                   

D)  \[1.5\Omega \]

Correct Answer: C

Solution :

Let net resistance is R then \[\frac{R.2}{2+R}+1=R\] \[{{R}^{2}}-R-2=0\]\[R=\frac{1\pm \sqrt{{{1}^{2}}-4(1)\,(-2)}}{2}\] \[R=2\Omega \]