A 200-Ω resistor, 40.0-mH inductor and a 2.00-μF capacitor are connected in series with a 120-V rms source at 1000 Hz. What is the phase angle of this circuit?
A) 49.3°
B) 90.0°
C) 40.7°
D) 0°
E) 45.0°

Question

Quizplus · Accepted Answer

We can use the impedance triangle to find the impedance of the circuit:

- The resistance has an impedance of R = 200 Ω. 
- The inductive reactance has an impedance of XL = ωL = 2πfL = 251.3 Ω (where f=1000 Hz). 
- The capacitive reactance has an impedance of Xc = 1/(ωC) = 398.1 Ω.

Using the Pythagorean theorem, we can find the total impedance:

Z = sqrt(R^2 + (XL - Xc)^2) = 294.1 Ω

The phase angle is given by:

θ = arctan((XL - Xc)/R) = 40.7°

Therefore, the answer is C.

A 200-Ω Resistor, 40