Infinite ladder GATE Notes | EduRev

GATE : Infinite ladder GATE Notes | EduRev

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Req =  ?
  • a)
    11.86 Ω 
  • b)
    10 Ω
  • c)
    25 Ω 
  • d)
    11.18 Ω
Correct answer is option 'D'. Can you explain this answer?

Ref: https://edurev.in/question/485654/Req-a-11-86-Omegab-10Omegac-25-Omegad-11-18OmegaCo

*As ladder is infinitely long. so choose repeating element and mark it as Req /Rnet.* 
 here choose 10 ohm- 10 ohm as repeating.
then connect that resistance in series with the element which chosen as Repeating ie across CD. Now solve first series combination 
R1=(10 Req)
then connect that solved resistance in parallel across AB solve parallel combination 
R2=(100 10Req)/(20 Req)
and equate with Req as (Resistance across AB=Resistance across CD). 
Req=(100 10Req)/(20 Req)
solve this for Req you get quadratic equation 
By solving we get Req=6.18ohm
Now solve the series combination to get final euivalant Resistance 
final Req = 5 6.18=11.18 ohmsImage
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