What resistance is needed in series with a $10 - \mu \mathrm { F }$ capacitor at $1.0 \mathrm { kHz }$ for a total impedance of 45 $\Omega$ ?
A) $1.8 \Omega$
B) $61 \Omega$
C) $42 \Omega$
D) $29 \Omega$

Question

Quizplus · Accepted Answer

The total impedance $Z$ in a series RC circuit is given by $Z = \sqrt{R^2 + (X_C)^2}$, where $X_C = \frac{1}{2\pi fC}$ is the capacitive reactance. Given $C = 10 \mu F = 10 \times 10^{-6} F$, $f = 1.0 kHz = 1000 Hz$, and $Z = 45 \Omega$, we first calculate $X_C$: $X_C = \frac{1}{2\pi \times 1000 \times 10 \times 10^{-6}} = \frac{1}{2\pi \times 10^{-2}} \approx 15.92 \Omega$. Then, solving for $R$ in the equation $45 = \sqrt{R^2 + (15.92)^2}$, we find $R \approx 42 \Omega$.

What Resistance Is Needed in Series with A 10−μF10 - \mu \mathrm { F }10−μF

What Resistance Is Needed in Series with A $10 - \mu \mathrm { F }$