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In a series RLC circuit, if the resistance is 4 ohms, inductance is 0.1 H, and c

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Question: In a series RLC circuit, if the resistance is 4 ohms, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2023)

Options:

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

Correct Answer: 159.15 Hz

Exam Year: 2023

Solution: 

Resonant frequency f = 1/(2π√(LC)) = 1/(2π√(0.1 * 100e-6)) = 159.15 Hz.

In a series RLC circuit, if the resistance is 4 ohms, inductance is 0.1 H, and c

Practice Questions

Q1
In a series RLC circuit, if the resistance is 4 ohms, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2023)
  1. 50 Hz
  2. 100 Hz
  3. 159.15 Hz
  4. 200 Hz

Questions & Step-by-Step Solutions

In a series RLC circuit, if the resistance is 4 ohms, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2023)
  • Step 1: Identify the values given in the problem. We have resistance (R) = 4 ohms, inductance (L) = 0.1 H, and capacitance (C) = 100 μF.
  • Step 2: Convert the capacitance from microfarads to farads. 100 μF = 100 * 10^-6 F = 0.0001 F.
  • Step 3: Use the formula for resonant frequency: f = 1 / (2π√(LC)).
  • Step 4: Substitute the values of L and C into the formula: f = 1 / (2π√(0.1 * 0.0001)).
  • Step 5: Calculate the product of L and C: 0.1 * 0.0001 = 0.00001.
  • Step 6: Find the square root of 0.00001: √(0.00001) = 0.003162.
  • Step 7: Multiply by 2Ï€: 2Ï€ * 0.003162 ≈ 0.01987.
  • Step 8: Finally, take the reciprocal to find the resonant frequency: f ≈ 1 / 0.01987 ≈ 50.31 Hz.
  • Resonant Frequency in RLC Circuits – The resonant frequency is the frequency at which the inductive and capacitive reactances are equal in magnitude, resulting in maximum current flow in the circuit.
  • Formula Application – Understanding and correctly applying the formula for resonant frequency, f = 1/(2π√(LC)), is crucial for solving the problem.
  • Unit Conversion – Properly converting units, such as microfarads to farads, is essential to avoid calculation errors.
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