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Given R 1 = 1 Ω , R 2 = 2 Ω , C 1 = 2 μ F , C 2 = 4 μ F . The time constants (in μs ) for the circuits I , I I , I I I are respectively:

Options

  1. A18 , 8 9 , 4
  2. B18,4 , 8 9
  3. C4 , 8 9 , 18
  4. D8 9 , 18 , 4

Correct answer

D. 8 9 , 18 , 4

Step-by-step solution

In figure I Effective resistance ( parallel combination) R 1 = 1 × 2 1 + 2 = 2 3   Ω and effective capacitance (series combination) C 1 = 2 × 4 2 + 4 = 4 3   μ F Time constant τ 1 = R 1 C 1 = 8 9   μs In figure II R 2 = 1 + 2 = 3   Ω C 2 = 2 + 4 = 6   μ F τ 2 = 18   μs In figure III, R 3 = 1 × 2 1 + 2 = 2 3   Ω C 3 = 2 + 4 = 6   μ F ;   τ 3 = 4   μs

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