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

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 (H) and $C$ is the capacitance in farads (F). Rearranging this formula to solve for $C$ gives $C = \frac{1}{(2\pi f)^2 L}$. Substituting $f = 1000$ Hz and $L = 40 \times 10^{-3}$ H into this formula yields $C \approx 0.63$ µF.

What Size Capacitor Should Be Placed in Series with a 30-Ω