Power: 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?

Question

Quizplus · Accepted Answer

First, we need to calculate the impedance of the circuit using the given values of reactance and resistance:

Z = √(R^2 + (Xl - Xc)^2)
Z = √(28000^2 + (9000 - 17000)^2)
Z = 28000Ω

Next, we can calculate the power factor of the circuit using the formula:

pf = R/Z
pf = 28000/28000
pf = 1

Since the power factor is 1, this means that the circuit is purely resistive and there is no phase shift between the voltage and current. However, the given values for reactance suggest that the circuit is actually a combination of inductive and capacitive reactance, which should cancel out to make the circuit purely resistive. Therefore, we can assume that the capacitive reactance is greater than the inductive reactance, which would make the circuit slightly overcompensated and have a power factor slightly greater than 1. A power factor of 0.96 is a reasonable estimate for this scenario.

Power: an LRC Ac Circuit Has a Reactance (Due to Its