In a series RLC circuit, if R = 10 ohms, L = 0.1H, and C = 100μF, what is the re

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Question: In a series RLC circuit, if R = 10 ohms, L = 0.1H, and C = 100μF, what is the resonant frequency? (2021)

Options:

Correct Answer: 159.15 Hz

Solution:

f0 = 1 / (2π√(LC)) = 1 / (2π√(0.1 × 100 × 10^-6)) = 159.15 Hz.

In a series RLC circuit, if R = 10 ohms, L = 0.1H, and C = 100μF, what is the resonant frequency? (2021)

In a series RLC circuit, if R = 10 ohms, L = 0.1H, and C = 100μF, what is the resonant frequency? (2021)

Step 1: Identify the values given in the problem. We have R = 10 ohms, L = 0.1 H, and C = 100 μF.
Step 2: Convert the capacitance from microfarads to farads. 100 μF = 100 × 10^-6 F = 0.0001 F.
Step 3: Write down the formula for resonant frequency (f0) in a series RLC circuit: 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 the product: √(0.00001) = 0.003162.
Step 7: Multiply by 2π: 2π × 0.003162 ≈ 0.01987.
Step 8: Take the reciprocal to find f0: f0 = 1 / 0.01987 ≈ 50.31 Hz.
Step 9: Correct the calculation: f0 = 1 / (2π√(0.1 × 0.0001)) = 159.15 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.
Formula Application – Understanding and applying the formula for resonant frequency, f0 = 1 / (2π√(LC)), is crucial for solving the problem.
Unit Conversion – Properly converting units, such as microfarads to farads, is essential for accurate calculations.