The phase angle of an LRC 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 for an LRC series circuit can be calculated using the following formula:

tan θ = (XL - XC)/R

where XL is the inductive reactance, XC is the capacitive reactance, and R is the resistance.

Substituting the given values, we have:

tan 40.0° = (200 Ω - 100 Ω)/R

tan 40.0° = 100 Ω/R

R = 100 Ω/tan 40.0°

R = 119 Ω (rounded to the nearest whole number)

Therefore, the value of the resistor in this circuit is 119 Ω, which corresponds to choice B.

The Phase Angle of an LRC Series Circuit with an Inductive