An LRC series circuit consists of an 85.0-Ω resistor,a 14.0-μF capacitor,a 1.50-mH inductor,and a variable frequency ac source of voltage amplitude 13.25 V.At what angular frequency will the inductive reactance be 4.00 times as large as the capacitive reactance? A) 1.38 × 10⁴ rad/s B) 6.90 × 10³ rad/s C) 3.45 × 10⁴ rad/s D) 2.20 × 10⁴ rad/s E) 1.10 × 10⁴ rad/s

Question

Quizplus · Accepted Answer

The inductive reactance $X_L = \omega L$ and the capacitive reactance $X_C = \frac{1}{\omega C}$, where $\omega$ is the angular frequency, $L$ is the inductance, and $C$ is the capacitance. Given that $X_L = 4X_C$, we can set up the equation $\omega L = 4 \left(\frac{1}{\omega C}\right)$. Solving for $\omega$ gives $\omega = \sqrt{\frac{4}{LC}}$. Substituting $L = 1.50 \times 10^{-3}$ H and $C = 14.0 \times 10^{-6}$ F into the equation yields $\omega \approx 1.38 \times 10^{4}$ rad/s.

An LRC Series Circuit Consists of an 85