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Question 31588
JEE Physics · Hard

Capacitance: Infinite Ladder Network MCQ

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Infinite Ladder NetworkHardQuestion 31588

Question

An infinite ladder network of capacitors (C horizontally, C vertically repeated) has equivalent capacitance from one end:
  1. A
    C/2
  2. B
    C(√5−1)/2
    Correct
  3. C
    C(√3−1)
  4. D
    2C

Correct answer

C(√5−1)/2

Explanation

Let X be the equivalent capacitance. The network satisfies X = C + CX/(C+X) (series-parallel self-similarity). Solving: X²+CX−C² = 0 gives X = C(√5−1)/2.

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