The circuit power factor of an $R C$ circuit is $0.620$. The rms value of the ac voltage applied to this signal is $120 \mathrm {~V}$ and the impedance is $200 \Omega$. What is the average power of this circuit?
A) $44.6 \mathrm {~W}$
B) $124 \mathrm {~W}$
C) $0.620 \mathrm {~W}$
D) $89.2 \mathrm {~W}$
E) $60.0 \mathrm {~W}$

Question

Quizplus · Accepted Answer

The average power in an AC circuit is given by $P = V_{rms} \times I_{rms} \times \text{power factor}$, where $V_{rms}$ is the root mean square voltage, $I_{rms}$ is the root mean square current, and the power factor is the cosine of the phase angle between the voltage and current. For an $RC$ circuit, the power factor is given and is less than 1, indicating a phase difference between voltage and current. The impedance $Z$ is given by $200 \Omega$, and $V_{rms} = 120V$. The current $I_{rms}$ can be found using Ohm's law $I_{rms} = \frac{V_{rms}}{Z} = \frac{120V}{200\Omega} = 0.6A$. Therefore, the average power $P = V_{rms} \times I_{rms} \times \text{power factor} = 120V \times 0.6A \times 0.620 = 44.64W$, which rounds to $44.6W$.

The Circuit Power Factor of An RCR CRC Circuit Is 0.6200.6200.620 the Rms Value of the Ac Voltage Applied to 0.620

The Circuit Power Factor of An $R C$ Circuit Is $0.620$ the Rms Value of the Ac Voltage Applied to 0.620