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99 Percentile Qs Bank for JEE MainPhysicsCurrent Electricity

A resistance network is connected to a battery as shown in the figure below. If the internal resistance of the battery is 5 , then the value of R (in ) for maximum power delivered to the network is

Options

  1. A2
  2. B4
  3. C5
  4. D6

Correct answer

A. 2

Step-by-step solution

Given is an unbalanced Wheatstones' bridge, in which current distribution will be as shown Now in loop A B C A , using KVL we have, aligned & -3 R i₁-4 R (i₁-i₂ )+2 R i₂=0 & -3 R i₁-4 R i₁+4 R i₂+2 R i₂=0 & 7 i₁=6 i₂ & & i₁= 6 7 i₂ & aligned Also, i₁+i₂=i Hence, ( 6 7 +1 ) i₂=i or i₂= 7 13 i i₁= 6 7 i₂= 6 7 7 13 i i₁= 6 13 i Now from loop A B D A (which includes cell), we have, 3 R i₁+2 R i₂ V (nearly because internal resistance in not taken in account) 3 R 6 13 i+2 R 7 13 i i R_ eq R_ eq =R ( 18+14 13 )= 32 13 R F

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