A series circuit contains a 20- $\Omega$ resistor, a 200- $\mathrm { mH }$ inductor, a $10 - \mu \mathrm { F }$ capacitor, and an ac power source. At what frequency should the power source drive the circuit in order to have maximum power transferred from the driving source?
A) $0.28 \mathrm { kHz }$
B) $0.11 \mathrm { kHz }$
C) $0.45 \mathrm { kHz }$
D) $0.96 \mathrm { kHz }$
E) $0.17 \mathrm { kHz }$

Question

Quizplus · Accepted Answer

For maximum power transfer in an RLC series circuit, the circuit must be at resonance, where the inductive reactance ($X_L$) equals the capacitive reactance ($X_C$). The resonance frequency ($f$) can be found using the formula $f = \frac{1}{2\pi\sqrt{LC}}$, where $L$ is the inductance in henries (H) and $C$ is the capacitance in farads (F). Substituting $L = 200 \, \text{mH} = 0.2 \, \text{H}$ and $C = 10 \, \mu\text{F} = 10 \times 10^{-6} \, \text{F}$, we find $f = \frac{1}{2\pi\sqrt{0.2 \times 10 \times 10^{-6}}}$, which calculates to approximately $0.11 \, \text{kHz}$.

A Series Circuit Contains a 20- Ω\OmegaΩ Resistor, a 200- mH\mathrm { mH }mH

A Series Circuit Contains a 20- $\Omega$ Resistor, a 200- $\mathrm { mH }$