Final answer:
The power factor of the RLC series circuit can be calculated by finding the impedance and resistance, and then dividing them. At a frequency of 7.50 Hz, the power factor is 0.71.
Therefore, the correct answer is option (c) 0.71.
Step-by-step explanation:
The power factor of an RLC series circuit can be calculated using the equation:
Power Factor (PF) = cos(φ)
where φ is the phase angle difference between the current and voltage waveforms. In this case, the circuit has an inductor and a capacitor, which means it is inductive at low frequencies and capacitive at high frequencies. At the given frequency of 7.50 Hz, the circuit is inductive. The power factor can be calculated as:
PF = cos(φ) = R / Z
where R is the resistance, and Z is the impedance. The impedance of the circuit can be calculated as:
Z = √(R2 + (XL - XC)2)
where XL is the inductive reactance and XC is the capacitive reactance. The inductive reactance can be calculated as:
XL = 2πfL
and the capacitive reactance can be calculated as:
XC = 1 / (2πfC)
Substituting the given values into the equations, we get:
XL = 2π(7.50 Hz)(0.150 H) ≈ 2.83 Ω
XC = 1 / (2π(7.50 Hz)(25.0 μF)) ≈ 2.12 Ω
Z = √((1000 &x3A9;)2 + (2.83 &x3A9; - 2.12 &x3A9;)2) ≈ 1414.21 &x3A9;
Substituting the values into the power factor equation:
PF = cos(φ) = R / Z = 1000 &x3A9; / 1414.21 &x3A9;
Calculating the power factor:
PF = 0.71
Therefore, the correct answer is option (c) 0.71.