LRC series circuits: 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?

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. For $X_L$ to be 4 times $X_C$, we set up the equation $4\left(\frac{1}{\omega C}\right) = \omega L$. Solving for $\omega$ gives $\omega = \sqrt{\frac{4}{LC}}$. Substituting $L = 1.50 \times 10^{-3} H$ and $C = 14.0 \times 10^{-6} F$, we find $\omega$ that matches the value in choice A.

LRC Series Circuits: an LRC Series Circuit Consists of an 85.0-Ω