Physics-
General
Easy

Question

Six resistors, each of value 3blank capital omega are connected as shown in the figure. A cell of emf 3V is connected across A B.The effective resistance across A B and the current through the arm A B will be

  1. 0.6blank capital omega, 1 A    
  2. 1.5 blank capital omega , 2 A    
  3. 0.6 capital omega,2 A    
  4. 1.5 capital omega, 1 A    

The correct answer is: 1.5 capital omega, 1 A


    The equivalent circuit is shown as

    We can emit the resistance in the arm DF as balance condition is satisfied.
    Therefore, the 3capital omega resistances in arm CD and DE are in series.
    therefore R to the power of ´ end exponent equals 3 plus 3 equals 6 capital omega
    Similarly, for arms CF and FE, R’’=6capital omega
    R to the power of ´ blank end exponent a n d R ´ ´ are in parallel
    therefore blank fraction numerator 1 over denominator R to the power of ´ ´ ´ end exponent end fraction equals fraction numerator 1 over denominator 6 end fraction plus fraction numerator 1 over denominator 6 end fraction equals fraction numerator 2 over denominator 6 end fraction equals fraction numerator 1 over denominator 3 end fraction
    R’’’=3capital omega
    Now, R’’’ and 3capital omega resistances are in parallel
    therefore blank fraction numerator 1 over denominator R end fraction equals fraction numerator 1 over denominator 3 end fraction plus fraction numerator 1 over denominator 3 end fraction
    ⟹ R equals 1.5 capital omega
    Moreover, V across AB=3V and resistance in the arm=3capital omega
    ∴ Current through the arm will be
    equals fraction numerator 3 V over denominator 3 capital omega end fraction equals 1 A.

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