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In a series RLC circuit, if the resistance is 10 ohms, inductance is 0.1 H, and

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Question: In a series RLC circuit, if the resistance is 10 ohms, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2021)

Options:

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

Correct Answer: 159 Hz

Exam Year: 2021

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 10 ohms, inductance is 0.1 H, and

Practice Questions

Q1
In a series RLC circuit, if the resistance is 10 ohms, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2021)
  1. 50 Hz
  2. 100 Hz
  3. 159 Hz
  4. 200 Hz

Questions & Step-by-Step Solutions

In a series RLC circuit, if the resistance is 10 ohms, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2021)
  • Step 1: Identify the values given in the problem. We have resistance (R) = 10 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 2π: 2π * 0.003162 ≈ 0.01987.
  • Step 8: Finally, calculate 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, resulting in maximum current flow in the circuit.
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