question_answer

In the figure, the value of resistors to be connected between C and D so that the resistance of the entire circuit between A and B does not change with the number of elementary sets used is

A)                    R

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

C)                    3 R                                    

D)            \[R(\sqrt{3}+1)\]

Correct Answer: B

Solution :

             Cut the series from XY and let the resistance towards right of XY be \[{{R}_{0}}\]whose value should be such that when connected across AB does not change the entire resistance. The combination is reduced to as shown below.                    The resistance across \[EF,={{R}_{EF}}=({{R}_{0}}+2R)\]                    Thus \[{{R}_{AB}}=\frac{({{R}_{0}}+2R)R}{{{R}_{0}}+2R+R}=\frac{{{R}_{0}}R+2{{R}^{2}}}{{{R}_{0}}+3R}={{R}_{0}}\]                    \[\Rightarrow R_{0}^{2}+2R{{R}_{0}}-2{{R}^{2}}+0\Rightarrow {{R}_{0}}=R(\sqrt{3}-1)\]