Physics-
General
Easy

Question

Six equal resistances are connected between points P, Q and R as shown in the figure. Then the net resistance will be maximum between

  1. P and Q    
  2. Q and R    
  3. P and R    
  4. Any two points    

The correct answer is: P and Q


    Resistance between P and Q
    R subscript P Q end subscript equals R vertical line vertical line open parentheses fraction numerator R over denominator 3 end fraction plus fraction numerator R over denominator 2 end fraction close parentheses equals fraction numerator R cross times fraction numerator 5 over denominator 6 end fraction R over denominator R plus fraction numerator 5 over denominator 6 end fraction R end fraction equals fraction numerator 5 over denominator 11 end fraction R
    Resistance between Q and R
    R subscript Q R end subscript equals fraction numerator R over denominator 2 end fraction vertical line vertical line open parentheses R plus fraction numerator R over denominator 3 end fraction close parentheses equals fraction numerator fraction numerator R over denominator 2 end fraction cross times fraction numerator 4 R over denominator 3 end fraction over denominator fraction numerator R over denominator 2 end fraction plus fraction numerator 4 R over denominator 3 end fraction end fraction equals fraction numerator 4 over denominator 11 end fraction R
    Resistance between P and R
    R subscript P R end subscript equals fraction numerator R over denominator 3 end fraction vertical line vertical line open parentheses fraction numerator R over denominator 2 end fraction plus R close parentheses equals fraction numerator fraction numerator R over denominator 3 end fraction cross times fraction numerator 3 R over denominator 2 end fraction over denominator fraction numerator R over denominator 3 end fraction plus fraction numerator 3 R over denominator 2 end fraction end fraction equals fraction numerator 3 over denominator 11 end fraction R
    Hence it is clear that P subscript P Q end subscript is maximum.

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