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

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Question: In an RLC series circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 100μF, what is the resonant frequency? (2020)

Options:

  1. 50 Hz
  2. 100 Hz
  3. 159 Hz
  4. 200 Hz

Correct Answer: 159 Hz

Exam Year: 2020

Solution: 

Using f = 1/(2π√(LC)), we find f = 1/(2π√(0.1 * 100e-6)) ≈ 159 Hz.

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

Practice Questions

Q1
In an RLC series circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 100μF, what is the resonant frequency? (2020)
  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 10Ω, the inductance is 0.1H, and the capacitance is 100μF, what is the resonant frequency? (2020)
  • Step 1: Identify the values given in the problem. We have resistance (R) = 10Ω, inductance (L) = 0.1H, and capacitance (C) = 100μF.
  • Step 2: Convert the capacitance from microfarads to farads. 100μF = 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 2π: 2π * 0.003162 ≈ 0.01987.
  • Step 8: Take the reciprocal to find the frequency: f ≈ 1 / 0.01987 ≈ 50.3 Hz.
  • Step 9: Round the answer to the nearest whole number if necessary.
  • 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.
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