An LRC ac circuit has a reactance (due to its capacitance)of 17 kΩ,a reactance (due to its inductance)of 9.0 kΩ,and a resistance of 28 kΩ.What is the power factor of the circuit?
A) 0.96
B) 0.28
C) 1.04
D) 0.48

Question

Quizplus · Accepted Answer

The power factor (PF) is the cosine of the angle between the voltage and current in an AC circuit. In an LRC circuit, we need to consider the reactance due to both capacitance and inductance. The total impedance (Z) of the circuit is given by:

Z = sqrt((R^2) + ((Xc - Xl)^2))

where R is the resistance, Xc is the capacitive reactance, and Xl is the inductive reactance.

Substituting the given values, we get:

Z = sqrt((28000^2) + ((17000 - 9000)^2)) = 33541.02 Ω

The phase angle (θ) between voltage and current is given by:

θ = arctan((Xc - Xl)/R)

Substituting the given values, we get:

θ = arctan((17000 - 9000)/28000) = 38.66°

The power factor (PF) is the cosine of this angle, i.e., cos(θ). Substituting the value of θ, we get:

PF = cos(38.66°) = 0.96

Therefore, the best choice is A.

An LRC Ac Circuit Has a Reactance (Due to Its