Final answer:
The power factor of an AC motor with impedance ZL = (6.0+j4.0) Ω supplied by 220V, 60Hz source is determined by calculating the cosine of the arctan of the imaginary part over the real part of the impedance.
Step-by-step explanation:
The question is asking about the power factor of an AC motor with a given impedance of ZL = (6.0+j4.0) Ω when supplied by an RMS voltage of 220V at 60Hz. The power factor (PF) is a measure of how effectively electrical power is converted into useful work output and is a critical aspect of AC power systems. It can be calculated using the impedance values provided. The proper calculation involves finding the phase angle θ between the voltage and the current using the imaginary part and the real part of the impedance.
So, to calculate the power factor, we need to find the cosine of the phase angle, which is given by θ = arctan(imaginary part / real part). The power factor would then be cos(θ). In this case, the real part of the impedance (resistance R) is 6.0 Ω and the imaginary part (reactance X) is 4.0 Ω, so the power factor PF is cos(arctan(4.0/6.0)).