Physics-
General
Easy

Question

In the following figure, 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 sets used is

  1. R    
  2. R open parentheses square root of 3 minus 1 close parentheses    
  3. 3R    
  4. R open parentheses square root of 3 plus 1 close parentheses    

The correct answer is: R open parentheses square root of 3 minus 1 close parentheses


    Let the resistance connected between C and D be R to the power of ´ end exponent; then
    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R end fraction plus fraction numerator 1 over denominator R to the power of ´ end exponent plus 2 R end fraction
    and the resistance of entire circuit between A and B does not change with the number of elementary sets used.
    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R end fraction plus fraction numerator 1 over denominator R to the power of ´ end exponent plus 2 R end fraction or R to the power of ´ 2 end exponent plus 2 R to the power of ´ end exponent R minus 2 R to the power of 2 end exponent equals 0
    \ R to the power of ´ end exponent equals negative R plus-or-minus R square root of 3 or R to the power of ´ end exponent equals R left parenthesis square root of 3 minus 1 right parenthesis

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