The reactance of a capacitor is $4.0 \mathrm { k } \Omega$ at a frequency of $0.60 \mathrm { kHz }$. What is the capacitance?
A) $2.6 \mu \mathrm { F }$
B) $0.066 \mu \mathrm { F }$
C) $0.093 \mu \mathrm { F }$
D) $0.42 \mu \mathrm { F }$

Question

Quizplus · Accepted Answer

The reactance $X_C$ of a capacitor is given by the formula $X_C = \frac{1}{2\pi fC}$, where $f$ is the frequency in hertz and $C$ is the capacitance in farads. Rearranging this formula to solve for $C$ gives $C = \frac{1}{2\pi fX_C}$. Substituting the given values ($f = 0.60 \times 10^3$ Hz, $X_C = 4.0 \times 10^3$ Ohms) into the formula yields $C = \frac{1}{2\pi \times 0.60 \times 10^3 \times 4.0 \times 10^3}$ farads, which calculates to approximately $0.066 \mu F$.

The Reactance of a Capacitor Is 4.0kΩ4.0 \mathrm { k } \Omega4.0kΩ

The Reactance of a Capacitor Is $4.0 \mathrm { k } \Omega$