question_answer

In Fig. find the value of resistor 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 seta.

A) \[R\]

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

C) \[3R\]

D) \[R\left( \sqrt{3}+1 \right)\]

Correct Answer: B

Solution :

[b] Let the resistor to be connected across CD be x. Then the equivalent resistance across EF should be x and also across AB should be x. So we get \[\frac{\left( 2R+x \right)R}{3R+x}=x\] Solve to get \[x=\left( \sqrt{3}-1 \right)R\] s