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In a series RLC circuit, if the resistance is 5Ω, the inductance is 0.2H, and th

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Question: In a series RLC circuit, if the resistance is 5Ω, the inductance is 0.2H, and the capacitance is 10μF, what is the resonant frequency? (2023)

Options:

  1. 50Hz
  2. 100Hz
  3. 159.15Hz
  4. 200Hz

Correct Answer: 159.15Hz

Exam Year: 2023

Solution: 

Resonant frequency f0 = 1/(2π√(LC)) = 1/(2π√(0.2 * 10e-6)) = 159.15Hz.

In a series RLC circuit, if the resistance is 5Ω, the inductance is 0.2H, and th

Practice Questions

Q1
In a series RLC circuit, if the resistance is 5Ω, the inductance is 0.2H, and the capacitance is 10μF, what is the resonant frequency? (2023)
  1. 50Hz
  2. 100Hz
  3. 159.15Hz
  4. 200Hz

Questions & Step-by-Step Solutions

In a series RLC circuit, if the resistance is 5Ω, the inductance is 0.2H, and the capacitance is 10μF, what is the resonant frequency? (2023)
  • Step 1: Identify the values given in the problem. We have resistance (R) = 5Ω, inductance (L) = 0.2H, and capacitance (C) = 10μF.
  • Step 2: Convert the capacitance from microfarads to farads. 10μF = 10 * 10^-6 F = 10e-6 F.
  • Step 3: Use the formula for resonant frequency: f0 = 1 / (2π√(LC)).
  • Step 4: Substitute the values of L and C into the formula: f0 = 1 / (2π√(0.2 * 10e-6)).
  • Step 5: Calculate the product of L and C: 0.2 * 10e-6 = 2e-7.
  • Step 6: Find the square root of the product: √(2e-7).
  • Step 7: Calculate 2π times the square root value from Step 6.
  • Step 8: Finally, take the reciprocal of the result from Step 7 to find f0.
  • Resonant Frequency in RLC Circuits – The resonant frequency is the frequency at which the inductive and capacitive reactances are equal, resulting in maximum current flow in the circuit.
  • Formula Application – Understanding and applying the formula for resonant frequency, f0 = 1/(2π√(LC)), where L is inductance and C is capacitance.
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