The phase angle of an RLC series circuit with an inductive reactance of 200 Ω and a capacitive reactance of 100 Ω is 40.0°. What is the value of the resistor in this circuit?
A) 100 Ω
B) 119 Ω
C) 156 Ω
D) 200 Ω
E) 265 Ω

Question

Quizplus · Accepted Answer

The phase angle of an RLC series circuit with an inductive reactance (XL) and a capacitive reactance (XC) can be calculated using the formula:

Φ = arctan((XL - XC)/R)

We know Φ = 40.0°, XL = 200 Ω, and XC = 100 Ω.

Substituting these values into the formula and solving for R, we get:

R = (XL - XC)/tan(Φ) = (200 - 100)/tan(40.0°) ≈ 118.95 ≈ 119 Ω

Therefore, the best choice is B, 119 Ω.

The Phase Angle of an RLC Series Circuit with an Inductive