A $120 - \mathrm { V }$ rms voltage at $60.0 \mathrm {~Hz}$ is applied across a capacitor and a $100 - \Omega$ resistor. If the impedance of this circuit is $200 \Omega$, what is the average power of this circuit?
A) $36.0 \mathrm {~W}$
B) $278 \mathrm {~W}$
C) $200 \mathrm {~W}$
D) $72.0 \mathrm {~W}$
E) $100 \mathrm {~W}$

Question

Quizplus · Accepted Answer

The average power in an AC circuit is given by $P = \frac{V_{rms}^2}{Z}$, where $V_{rms}$ is the root mean square voltage, and $Z$ is the impedance. Given $V_{rms} = 120 \, \mathrm{V}$ and $Z = 200 \, \Omega$, $P = \frac{120^2}{200} = \frac{14400}{200} = 72 \, \mathrm{W}$. However, this power is the total power. The power across the resistor, which is the average power we're interested in (since capacitors do not dissipate power), is $P_{avg} = I_{rms}^2 R$. Given the impedance, the current $I_{rms} = \frac{V_{rms}}{Z} = \frac{120}{200} = 0.6 \, \mathrm{A}$. Thus, $P_{avg} = (0.6)^2 \times 100 = 36 \, \mathrm{W}$.

A 120−V120 - \mathrm { V }120−V Rms Voltage At 60.0 Hz60.0 \mathrm {~Hz}60.0 Hz

A $120 - \mathrm { V }$ Rms Voltage At $60.0 \mathrm {~Hz}$