A $10 - \Omega$ resistor is connected in series with a $20 - \mu \mathrm { F }$ capacitor. What is the impedance at $1.0 \mathrm { kHz }$ ?
A) $8.0 \Omega$
B) $13 \Omega$
C) $15 \Omega$
D) $10 \Omega$

Question

Quizplus · Accepted Answer

The impedance $Z$ in a series RC circuit is given by $Z = \sqrt{R^2 + (X_C)^2}$, where $R$ is the resistance and $X_C$ is the capacitive reactance. The capacitive reactance $X_C = \frac{1}{2\pi fC}$, where $f$ is the frequency in hertz and $C$ is the capacitance in farads. For a $20 - \mu \mathrm{F}$ capacitor at $1.0 \mathrm{kHz}$, $X_C = \frac{1}{2\pi \times 1000 \times 20 \times 10^{-6}} = \frac{1}{0.04\pi} \approx 7.96 \Omega$. Thus, $Z = \sqrt{10^2 + 7.96^2} \approx 12.8 \Omega$, which rounds to $13 \Omega$.

A 10−Ω10 - \Omega10−Ω Resistor Is Connected in Series with A 20−μF20 - \mu \mathrm { F }20−μF

A $10 - \Omega$ Resistor Is Connected in Series with A $20 - \mu \mathrm { F }$