The following table gives the reactance and rms voltage across the elements of a series RCL circuit:
-What is the power factor for this circuit?
A)0.40
B)0.57
C)0.81
D)1.4
E)5.5

Question

The following table gives the reactance and rms voltage across the elements of a series RCL circuit: 
-What is the power factor for this circuit?
A)0.40 
B)0.57 
C)0.81 
D)1.4 
E)5.5

Quizplus · Accepted Answer

We can use the formula for power factor (PF) in a series RCL circuit:

PF = cos(phase angle) = R/Z, where Z is the magnitude of the impedance

The impedance can be found using the Pythagorean theorem:

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

where Xl is the inductive reactance and Xc is the capacitive reactance.

Plugging in the given values:

Xl = 100 ohms
Xc = 50 ohms
R = 50 ohms

Z = sqrt[50^2 + (100 - 50)^2] = 86.6 ohms

PF = cos(arctan[(Xl - Xc)/R]) = cos(arctan[50/50]) = cos(45 degrees) = 0.707

This is closest to answer choice B, 0.57.

The Following Table Gives the Reactance and Rms Voltage Across