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KVPY2010PhysicsAlternating Current

Consider the infinite ladder circuit shown below. For which angular frequency will the circuit behave like a pure inductance?

Options

  1. ALC 2
  2. B1 LC
  3. C2 L C
  4. D2 ~L C

Correct answer

C. 2 L C

Step-by-step solution

Let the equivalent impedance of the circuit be Z So Z= L+Z^ now Z^ = Z X_ C Z+X_ C Z= L+ ( Z 1 C Z+ 1 C ) on ving we get Z= L C ( L C)²-4 L C 2 C for Z to be purely inductive ² L² C²-4 L C=0 or = 2 L C

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