Calculating the Power Factor and Power

The power factor at 60.0 Hz is found from

We know $Z\text{= 531 Ω}$ from Example 23.12, so that

This small value indicates the voltage and current are significantly out of phase. In fact, the phase angle is

The phase angle is close to $\text{90º}$, consistent with the fact that the capacitor dominates the circuit at this low frequency (a pure RC circuit has its voltage and current $\text{90º}$ out of phase).

The average power at 60.0 Hz is

$I_{\text{rms}}$ was found to be 0.226 A in Example 23.12. Entering the known values gives

At the resonant frequency, we know $\text{cos}\varphi =1$, and $I_{\text{rms}}$ was found to be 6.00 A in Example 23.13. Thus,

$P_{\text{ave}}=(3\text{.}\text{00}\text{A})(\text{120}\text{V})(1)=\text{360}\text{W}$ at resonance (1.30 kHz)

Both the current and the power factor are greater at resonance, producing significantly greater power than at higher and lower frequencies.