Physics-
General
Easy

Question

An infinite sequence of resistance is shown in the figure. The resultant resistance between A and B will be, when R subscript 1 end subscript equals 1 o h m and R subscript 2 end subscript equals 2 o h m

  1. Infinity    
  2. 1 capital omega    
  3. 2 capital omega    
  4. 1.5 capital omega    

The correct answer is: 2 capital omega


    Let the resultant resistance be R. If we add one more branch, then the resultant resistance would be the same because this is an infinite sequence.

    therefore fraction numerator R R subscript 2 end subscript over denominator R plus R subscript 2 end subscript end fraction plus R subscript 1 end subscript equals R rightwards double arrow 2 R plus R plus 2 equals R to the power of 2 end exponent plus 2 R
    rightwards double arrow R to the power of 2 end exponent minus R minus 2 equals 0 rightwards double arrow R equals negative 1 or R equals 2 o h m

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