An ac circuit has a 100- $\Omega$ resistor in series with a $4.9 - \mu \mathrm { F }$ capacitor and a $700 - \mathrm { mH }$ inductor. At what frequency does the circuit act like a pure resistance?
A) $86 \mathrm {~Hz}$
B) $0.29 \mathrm { MHz }$
C) $12 \mathrm { MHz }$
D) $1.9 \mathrm { MHz }$
E) $0.54 \mathrm { kHz }$

Question

Quizplus · Accepted Answer

The circuit acts like a pure resistance at the resonant frequency, where the inductive reactance equals the capacitive reactance. The resonant frequency $f$ is given by $f = \frac{1}{2\pi\sqrt{LC}}$, where $L$ is the inductance in henries and $C$ is the capacitance in farads. Substituting $L = 0.7 \, \text{H}$ and $C = 4.9 \times 10^{-6} \, \text{F}$, we find $f \approx 86 \, \text{Hz}$.

An Ac Circuit Has a 100- Ω\OmegaΩ Resistor in Series with A

An Ac Circuit Has a 100- $\Omega$ Resistor in Series with A