In a series RLC circuit, if the resistance is 5Ω, inductance is 0.1H, and capacitance is 100μF, what is the resonant frequency? (2022)

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Q: In a series RLC circuit, if the resistance is 5Ω, inductance is 0.1H, and capacitance is 100μF, what is the resonant frequency? (2022)

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

Steps: 9

Step 1: Identify the values given in the problem. We have resistance (R) = 5Ω, 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 resonant frequency: f ≈ 1 / 0.01987 ≈ 50.3 Hz.
Step 9: Round the answer to the nearest whole number if necessary.