A series $R L C$ circuit has a $100 - \Omega$ resistor, a $0.100 - \mu \mathrm { F }$ capacitor and a $2.00 - \mathrm { mH }$ inductor connected across a 120-V rms ac voltage source operating at $1000 / \pi \mathrm { Hz }$. What is the resonant frequency of this circuit?
A) $70.7 \mathrm { kHz }$
B) $17.9 \mathrm { kHz }$
C) $22.5 \mathrm { kHz }$
D) $11.3 \mathrm { kHz }$
E) $35.3 \mathrm { kHz }$

Question

Quizplus · Accepted Answer

The resonant frequency $f_0$ of an RLC circuit is given by $f_0 = \frac{1}{2\pi\sqrt{LC}}$, where $L$ is the inductance in henries (H) and $C$ is the capacitance in farads (F). Substituting $L = 2.00 \times 10^{-3}$ H and $C = 0.100 \times 10^{-6}$ F, $f_0 = \frac{1}{2\pi\sqrt{(2.00 \times 10^{-3})(0.100 \times 10^{-6})}} \approx 11.3 \, \text{kHz}$.

A Series RLCR L CRLC Circuit Has A 100−Ω100 - \Omega100−Ω Resistor, A

A Series $R L C$ Circuit Has A $100 - \Omega$ Resistor, A