What resistance is needed in a series circuit with a $20 - \mathrm { mH }$ coil and $1.0 - \mu \mathrm { F }$ capacitor for a total impedance of $100 \Omega$ at $1.5 \mathrm { kHz }$ ?
A) $18 \Omega$
B) $82 \Omega$
C) $0.16 \mathrm { k } \Omega$
D) $57 \Omega$

Question

Quizplus · Accepted Answer

The impedance of a series LC circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $X_L = 2\pi f L$ and $X_C = \frac{1}{2\pi f C}$. At $1.5 \mathrm{kHz}$, $X_L = 188.5 \Omega$ and $X_C = 106.1 \Omega$. Solving for $R$ in $100 = \sqrt{R^2 + (188.5 - 106.1)^2}$ gives $R \approx 57 \Omega$.

What Resistance Is Needed in a Series Circuit with A 20