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?

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Q: 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?

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.

Steps: 8

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.