Power: A series circuit consists of a 50-Hz ac source, a 40-Ω resistor, a 0.30-H inductor, and a 60-μF capacitor. The rms current in the circuit is measured to be 1.6 A. What is the power factor of the circuit?

Question

Quizplus · Accepted Answer

The power factor is given by the cosine of the phase angle between the voltage and current in the circuit. The phase angle is given by the arctangent of the ratio of the inductive reactance to the capacitive reactance. The inductive reactance is given by 2πfL, where f is the frequency and L is the inductance. The capacitive reactance is given by 1/(2πfC), where C is the capacitance. In this case, the inductive reactance is 2π(50 Hz)(0.30 H) = 94.2 Ω and the capacitive reactance is 1/(2π(50 Hz)(60 μF)) = 53.1 Ω. Therefore, the phase angle is arctan(94.2 Ω/53.1 Ω) = 60.0°. The power factor is then cos(60.0°) = 0.5.

Power: a Series Circuit Consists of a 50-Hz Ac Source