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 \[{{R}_{AB}}=\frac{({{R}_{0}}+2R)R}{{{R}_{0}}+2R+R}=\frac{{{R}_{0}}R+2{{R}^{2}}}{{{R}_{0}}+3R}={{R}_{0}}\] \[\Rightarrow R_{0}^{2}+2R{{R}_{0}}-2{{R}^{2}}+0\Rightarrow {{R}_{0}}=R(\sqrt{3}-1)\]You need to login to perform this action.
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