Physics-
General
Easy

Question

The equivalent resistance between the points A and B will be (each resistance is
15 capital omega)

  1. 30blank capital omega    
  2. 8blank capital omega    
  3. 10blank capital omega    
  4. 40blank capital omega    

The correct answer is: 8blank capital omega


    The circuit can be shown as given below

    The equivalent resistance between D and C.
    R subscript D C end subscript equals fraction numerator 15 cross times open parentheses 15 plus 15 close parentheses over denominator 15 plus open parentheses 15 plus 15 close parentheses end fraction
    equals fraction numerator 15 cross times 30 over denominator 15 plus 30 end fraction
    equals fraction numerator 15 cross times 30 over denominator 45 end fraction equals 10 capital omega
    Now, between A and B, the resistance of upper part ADCB,
    R subscript 1 end subscript equals 15 plus 10 plus 15 equals 40 capital omega
    Between A and B, the resistance of middle part AOB
    R subscript 2 end subscript equals 15 plus 15 equals 30 capital omega
    Therefore, equivalent resistance between A and B
    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R subscript 1 end subscript end fraction plus fraction numerator 1 over denominator R subscript 2 end subscript end fraction plus fraction numerator 1 over denominator R subscript 3 end subscript end fraction
    equals fraction numerator 1 over denominator 40 end fraction plus fraction numerator 1 over denominator 30 end fraction plus fraction numerator 1 over denominator 15 end fraction
    equals fraction numerator 3 plus 4 plus 8 over denominator 120 end fraction
    equals fraction numerator 15 over denominator 120 end fraction
    ⟹ R to the power of ´ end exponent equals fraction numerator 120 over denominator 15 end fraction equals 8 capital omega

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