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 elemertnry set used is

Options

A. `R`
B. `R (sqrt3 - 1)`
C. `3 R`
D. `R (sqrt3 + 1)`

Answer

B

Explanation

(b) Cut the series form `NY` 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 reduecd to as shown below
The resistance across `EF, = R_(EF) = (R_(0) + 2R)`
Thus `R_(AB) = ((R_(0) + 2R) R)/(R_(0) + 2R + R) = (R_(0) R + 2 R^(2))/(R_(0) + 3R) = R_(0)`
`implies R_(0)^(2) + 2 R R_(0) - 2 R^(2) + 0 implies R_(0) = R (sqrt3 - 1)`