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In an RLC series circuit, if the resistance is 10 Ω, inductance is 0.1 H, and ca

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Question: In an RLC series circuit, if the resistance is 10 Ω, 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 Hz
  4. 200 Hz

Correct Answer: 159 Hz

Exam Year: 2023

Solution: 

The resonant frequency f0 = 1/(2π√(LC)) = 1/(2π√(0.1 * 100e-6)) = 159 Hz.

In an RLC series circuit, if the resistance is 10 Ω, inductance is 0.1 H, and ca

Practice Questions

Q1
In an RLC series circuit, if the resistance is 10 Ω, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2023)
  1. 50 Hz
  2. 100 Hz
  3. 159 Hz
  4. 200 Hz

Questions & Step-by-Step Solutions

In an RLC series circuit, if the resistance is 10 Ω, 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) = 10 Ω, 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: f0 = 1 / (2π√(LC)).
  • Step 4: Substitute the values of L and C into the formula: f0 = 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 2π: 2π * 0.003162 ≈ 0.01987.
  • Step 8: Finally, calculate the resonant frequency: f0 = 1 / 0.01987 ≈ 50.3 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, f0 = 1/(2π√(LC)), is crucial for solving the problem.
  • Unit Conversion – Properly converting capacitance from microfarads to farads is essential for accurate calculations.
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