What size capacitor should be placed in series with a $30 - \Omega$ resistor and a $40 - \mathrm { mH }$ inductive coil if the resonant frequency of the circuit is to be $1.0 \mathrm { kHz }$ ?
A) $3.3 \mu \mathrm { F }$
B) $2.0 \mu \mathrm { F }$
C) $0.63 \mu \mathrm { F }$
D) $6.0 \mu \mathrm { F }$
E) $4.5 \mu \mathrm { F }$

Question

Quizplus · Accepted Answer

The resonant frequency $f$ of an LC circuit is given by $f = \frac{1}{2\pi\sqrt{LC}}$, where $L$ is the inductance in henries and $C$ is the capacitance in farads. Rearranging for $C$, we get $C = \frac{1}{(2\pi f)^2L}$. Substituting $f = 1000 \, \text{Hz}$ and $L = 40 \times 10^{-3} \, \text{H}$, we find $C \approx 0.63 \, \mu\text{F}$.

What Size Capacitor Should Be Placed in Series with A 30