A series RLC circuit has a 100-Ω resistor, a 0.100-μF capacitor, and a 2.00-mH inductor connected across a 120-V rms ac source operating at (1000/π) Hz. What is the rms voltage across the inductor?
A) 120 mV
B) 87.1 mV
C) 302 mV
D) 96.1 mV
E) 200 mV

Question

Quizplus · Accepted Answer

First, we can calculate the angular frequency of the circuit:
ω = 2πf = 2π(1000/π) = 2000 rad/s

Next, we can calculate the impedance of the circuit:
Z = √(R^2 + (X_L - X_C)^2) = √(100^2 + (ωL - 1/(ωC))^2) = 126.2 Ω

where X_L = ωL and X_C = 1/(ωC) are the inductive and capacitive reactances, respectively.

Using the voltage divider rule, we can find the rms voltage across the inductor as:
V_L = (X_L/Z) V_rms = (ωL/Z) V_rms = (2π)(2.00 mH)/(126.2 Ω) (120 V/√2) ≈ 96.1 mV.

Therefore, the answer is D.

A Series RLC Circuit Has a 100-Ω Resistor, a 0