A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 Ω and L = 10.0 mH. The power factor, cos φ, is
A) −1.00.
B) −0.936.
C) +0.943.
D) +0.936.
E) +1.00.

Question

Quizplus · Accepted Answer

To find the power factor, we need to calculate the impedance of the circuit, which is given by:

$Z = \sqrt{R^2+(2\pi fL)^2}$
where f is the frequency of the generator.

Plugging in the given values, we get:

$Z = \sqrt{10^2 + (2\pi 	imes 60 	imes 0.01)^2} = 12.42$ Ω

The current in the circuit is given by:

$I = \frac{V_{peak}}{Z} = \frac{110}{12.42} = 8.86$ A

The phase angle between the voltage and current is given by:

$\phi = 	an^{-1}\left(\frac{2\pi fL}{R}ight) = 	an^{-1}\left(\frac{2\pi 	imes 60 	imes 0.01}{10}ight) = 1.19$ rad

The power factor is then given by:

$\cos\phi = \cos(1.19) = 0.936$

Therefore, the answer is D.

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