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

In an RLC series circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 100μF, what is the resonant frequency? (2020)

In an RLC series circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 100μF, what is the resonant frequency? (2020)

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: 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 frequency: f ≈ 1 / 0.01987 ≈ 50.3 Hz.
Step 9: Round the answer to the nearest whole number if necessary.

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