Physics-
General
Easy

Question

A group of N cells whose emf varies directly with the internal resistance as per the equation E subscript N end subscript equals 1.5 r subscript N end subscript are connected as shown in the figure. The current I in the circuit is

  1. 5.1A    
  2. 0.51A    
  3. 1.5A    
  4. 0.15A    

The correct answer is: 1.5A


    Given that
    e m f E subscript N end subscript equals 1.5 r subscript N end subscript
    Where r subscript N end subscript is the internal resistance of nth cell.
    Total emf E equals E subscript 1 end subscript plus E subscript 2 end subscript plus E subscript 3 end subscript plus horizontal ellipsis plus E subscript n end subscript
    equals 1.5 open square brackets r subscript 1 end subscript plus r subscript 2 end subscript plus r subscript 3 end subscript plus horizontal ellipsis plus r subscript n end subscript close square brackets
    Total internal resistance
    r equals r subscript 1 end subscript plus r subscript 2 end subscript plus r subscript 3 end subscript plus horizontal ellipsis plus r subscript n end subscript
    therefore C u r r e n t blank i equals fraction numerator E subscript t o t a l end subscript over denominator r subscript t o t a l end subscript end fraction
    i equals fraction numerator 1.5 open square brackets r subscript 1 end subscript plus r subscript 2 end subscript plus r subscript 3 end subscript plus horizontal ellipsis plus r subscript n end subscript close square brackets over denominator open square brackets r subscript 1 end subscript plus r subscript 2 end subscript plus r subscript 3 end subscript plus horizontal ellipsis plus r subscript n end subscript close square brackets end fraction
    Hence, i equals 1.5 A

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