A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 $\Omega$ and C = 300 $\mu$F.The power factor, cos $\phi$, is:
A)(-1.00.)
B)(-0.749.)
C)+0.749.
D)+0.834.
E)+1.00.

Question

A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0  $\Omega$  and C = 300 $\mu$F.The power factor, cos $\phi$, is:
A)(-1.00.)
B)(-0.749.)
C)+0.749.
D)+0.834.
E)+1.00.

Quizplus · Accepted Answer

The power factor, cos $\phi$, is given by $ R / Z $, where $ Z $ is the impedance of the circuit. The impedance $ Z $ is calculated as $ \sqrt{R^2 + (X_C)^2} $, where $ X_C = 1/(2\pi f C) $. Substituting the given values, we find $ X_C \approx 8.84 \Omega $ and $ Z \approx 13.34 \Omega $. Thus, the power factor is $ 10 / 13.34 \approx 0.749 $.

A 600-Hz Ac Generator with a Peak Voltage of 110 V