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

In an RLC series circuit, if the resistance is 10 Ω, the inductance is 0.1 H, and the capacitance is 100 μF, what is the resonant frequency? (2023)

In an RLC series circuit, if the resistance is 10 Ω, the inductance is 0.1 H, and the capacitance is 100 μF, what is the resonant frequency? (2023)

Step 1: Identify the values given in the problem. We have resistance (R) = 10 Ω, 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: 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 0.00001: √(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 ≈ 50.3 Hz.
Step 9: Correct the calculation: f0 = 1 / (2π√(0.1 * 0.0001)) = 159 Hz.

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