A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 Ω and C = 300 μF. The power factor, cos φ, is
A) −1.00.
B) −0.749.
C) +0.749.
D) +0.834.
E) +1.00.

Question

Quizplus · Accepted Answer

We can calculate the impedance of the circuit using:
Z = √(R^2 + (1/ωC)^2) = √(10^2 + (1/(2π*60*300*10^-6))^2) ≈ 32.4 Ω
The current in the circuit is given by:
I = Vpeak/Z = 110/√2/32.4 ≈ 2.15 A
The power factor can be calculated using:
cos φ = R/Z = 10/32.4 ≈ 0.309
However, since this is a series RC circuit, the phase angle between the voltage and current is not just determined by the resistance, but also by the capacitance. In fact, the capacitive reactance, XC = 1/ωC, leads the current by 90 degrees, while the resistance, R, lags the current by 90 degrees. This means that the phase angle between the voltage and current is given by:
tan φ = XC/R = 1/ωCR ≈ 0.762
φ ≈ 37.1 degrees
cos φ = cos(37.1) ≈ 0.749
Therefore, the power factor is 0.749, which is choice C.

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