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

The impedance of the RC circuit can be calculated as follows:

Z = √(R² + (1/ωC)²) = √(10² + (1/(2π×60×300×10⁻⁶))²) = 52.4 Ω

The current through the circuit can be calculated using Ohm's law:

I = Vpeak/Z = 110/52.4 ≈ 2.10 A

The reactance of the capacitance can be calculated as follows:

Xc = 1/(ωC) = 1/(2π×60×300×10⁻⁶) ≈ 88.5 Ω

The resistance and reactance can be used to calculate the phase angle:

φ = arctan(Xc/R) = arctan(88.5/10) ≈ 1.40 radians

The power factor can be calculated as follows:

cos φ = cos(1.40) ≈ 0.999

Therefore, the power factor is approximately +0.749.

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