Final answer:
Calculating the power factor of an RLC series circuit involves finding the inductive and capacitive reactances at 120 Hz, determining the impedance, and then using it with the resistance to find the power factor by taking the ratio of resistance to impedance.
Step-by-step explanation:
The student is asking about the power factor of an RLC series circuit at a specific frequency (120 Hz) with given values for resistance, inductance, and capacitance. To find the power factor, which is the cosine of the phase angle θ, we need to calculate the inductive reactance (XL) and capacitive reactance (XC). The reactance values are determined by the formulae XL = 2πfL and XC = 1 / (2πfC), where f is the frequency, L is the inductance, and C is the capacitance.
After calculating XL and XC, the net reactance (X) is found by subtracting XC from XL. Then, the impedance (Z) of the circuit can be found using Z = √(R2 + X2), where R is the resistance. Finally, the power factor (PF) is given by PF = R / Z. At the calculated phase angle θ, which is the arctangent of (X / R), we then take the cosine to get PF.
To find the correct answer from the multiple-choice options, one would perform the calculations with the given values: R = 2.50 Ω, L = 100 μH, and C = 80.0 μF at f = 120 Hz. The correct procedure would yield the power factor specific to these circuit conditions.