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

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

Options:

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

Correct Answer: 159.15Hz

Solution: 

The resonant frequency (f0) is given by f0 = 1 / (2π√(LC)). Here, L = 0.1H and C = 100μF, so f0 = 1 / (2π√(0.1 * 0.0001)) = 159.15Hz.

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

Practice Questions

Q1
In a series RLC circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 100μF, what is the resonant frequency?
  1. 159.15Hz
  2. 100Hz
  3. 50Hz
  4. 200Hz

Questions & Step-by-Step Solutions

In a series RLC circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 100μF, what is the resonant frequency?
Correct Answer: 159.15Hz
  • 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: Write down the formula for resonant frequency (f0). The formula is f0 = 1 / (2π√(LC)).
  • Step 4: Substitute the values of L and C into the formula. We have L = 0.1H and C = 0.0001F.
  • Step 5: Calculate the product of L and C. This gives us LC = 0.1 * 0.0001 = 0.00001.
  • Step 6: Take the square root of the product LC. √(0.00001) = 0.003162.
  • Step 7: Multiply the square root by 2π. 2π * 0.003162 ≈ 0.01987.
  • Step 8: Finally, take the reciprocal of the result from Step 7 to find f0. f0 = 1 / 0.01987 ≈ 50.31Hz.
  • Resonant Frequency – The frequency at which a series RLC circuit oscillates with maximum amplitude, determined by the inductance (L) and capacitance (C) values.
  • RLC Circuit Components – Understanding the roles of resistance (R), inductance (L), and capacitance (C) in determining circuit behavior.
  • Formula Application – Applying the formula for resonant frequency correctly, including unit conversions for capacitance.
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