Physics-
General
Easy

Question

Thirteen resistances each of resistance Rcapital omega are connected in the circuit as shown in the figure. The effective resistance between points A and B is

  1. fraction numerator 4 R over denominator 3 end fraction capital omega    
  2. 2Rcapital omega    
  3. Rcapital omega    
  4. fraction numerator 2 over denominator 3 end fraction R capital omega    

The correct answer is: fraction numerator 2 over denominator 3 end fraction R capital omega


    Resistance R bisecting the circuit can be neglected due to the symmetry of the circuit.
    Now, there are four triangles
    Effective resistance of each triangle
    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 2 R end fraction
    equals fraction numerator 2 plus 1 over denominator 2 R end fraction equals fraction numerator 3 over denominator 2 R end fraction
    therefore R to the power of ´ end exponent equals fraction numerator 2 over denominator 3 end fraction R
    Now the given circuit reduced to

    Therefore, effective resistance between A and B,
    fraction numerator 1 over denominator R subscript A B end subscript end fraction equals fraction numerator 1 over denominator 2 R to the power of ´ end exponent end fraction plus fraction numerator 1 over denominator 2 R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R to the power of ´ end exponent end fraction
    ⟹ R subscript A B end subscript equals R to the power of ´ end exponent equals fraction numerator 2 R over denominator 3 end fraction capital omega

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