A 120- $\mathrm { V }$ rms voltage at $60 \mathrm {~Hz}$ is applied across an $R C$ circuit. The rms value of the current in the circuit is $0.60 \mathrm {~A}$, and it leads the voltage by $60 ^ { \circ }$. What is the capacitance in this circuit?
A) $15 \mu \mathrm { F }$
B) $17 \mu \mathrm { F }$
C) $13 \mu \mathrm { F }$
D) $14 \mu \mathrm { F }$
E) $16 \mu \mathrm { F }$

Question

Quizplus · Accepted Answer

The phase angle $\phi = 60^\circ$ indicates that the current leads the voltage, which is characteristic of an RC circuit. The impedance $Z$ can be calculated using Ohm's Law, $V = IZ$, where $V = 120 \, \mathrm{V}$ and $I = 0.60 \, \mathrm{A}$. Thus, $Z = \frac{V}{I} = \frac{120}{0.60} = 200 \, \Omega$. The phase angle in an RC circuit is given by $\tan(\phi) = \frac{1}{\omega RC}$, where $\omega = 2\pi f$ and $f = 60 \, \mathrm{Hz}$. Given $\tan(60^\circ) = \sqrt{3}$, we can solve for $C$ using the relationship between the impedance, the resistance $R$, and the capacitive reactance $X_C = \frac{1}{\omega C}$. Rearranging the formula to solve for $C$ and substituting the known values, we find that $C$ is approximately $15 \mu \mathrm{F}$, making option A correct.

A 120- V\mathrm { V }V Rms Voltage At 60 Hz60 \mathrm {~Hz}60 Hz

A 120- $\mathrm { V }$ Rms Voltage At $60 \mathrm {~Hz}$