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For the given circuit, determine the correct descending order of time constants...

 

Question

For the given circuit, determine the correct descending order of time constants.










Given:

  • (a) Vsupply = 250 V, C = 3 μF
  • (b) Vsupply = 150 V, C = 1 μF
  • (c) Vsupply = 100 V, C = 2 μF
  • (d) Vsupply = 250 V, C = 6 μF
  • (e) Vsupply = 80 V, C = 0.5 μF

Options:

  • A. (a), (c), (b), (e), (d)
  • B. (c), (e), (a), (b), (d)
  • C. (b), (d), (a), (c), (e)
  • D. (d), (a), (c), (b), (e)

Solution

Step 1: Formula

Time constant is given by:

Ï„ = Rth × C

Step 2: Find Thevenin Resistance

Deactivate the voltage source (replace with short circuit).

Compute equivalent resistance:

  • 30kΩ || 70kΩ = (30 × 70) / (30 + 70) = 21kΩ
  • 9kΩ + 21kΩ = 30kΩ
  • 20kΩ || 30kΩ = (20 × 30) / (20 + 30) = 12kΩ
  • Total: Rth = 8kΩ + 12kΩ = 20kΩ

Step 3: Compare Time Constants

Since Rth is same for all cases, Ï„ ∝ C

Case Capacitance (μF) Time Constant Order
(d)6Largest
(a)3
(c)2
(b)1
(e)0.5Smallest

Final Answer

(d), (a), (c), (b), (e)

Option D

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