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?
A) 0.70
B) 0.66
C) 0.63
D) 0.59
E) 0.56

Question

Quizplus · Accepted Answer

To find the power factor of the circuit, we need to calculate the impedance and the phase angle of the circuit.

The impedance of the circuit is given by:

Z = sqrt(R^2 + (XL - XC)^2)
where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

Using the given values, we get:

Z = sqrt(40^2 + (2π*50*0.30 - 1/(2π*50*60*10^-6))^2)
   = 51.76 Ω

The phase angle of the circuit is given by:

θ = tan^-1((XL - XC)/R)

Using the given values, we get:

θ = tan^-1((2π*50*0.30 - 1/(2π*50*60*10^-6))/40)
   = 42.58°

The power factor of the circuit is cos(θ), which is:

cos(42.58°) = 0.70

Therefore, the best choice is A) 0.70.

A Series Circuit Consists of a 50-Hz Ac Source,a 40-Ω