Question

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. $R(\sqrt{3} + 1)$

Answer 1

Answer: (B)

$R(\sqrt{3} - 1)$

Answer 2

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 $R_{AB} = \frac{(R_{0} + 2R)R}{R_{0} + 2R + R} = \frac{R_{0}R + 2R^{2}}{R_{0} + 3R} = R_{0}$

$\Rightarrow R_{0}^{2} + 2RR_{0} - 2R^{2} + 0 \Rightarrow R_{0} = R(\sqrt{3} - 1)$