Answer :
Final answer:
The phase angle in a circuit consuming 3200W of real power and 3700VA of apparent power is approximately 30.1 degrees, calculated using the power factor.
Explanation:
Phase angle can refer to several different concepts depending on the context in which it is used. In physics, engineering, and mathematics, phase angle often refers to the angular displacement or phase shift between two sinusoidal waveforms or oscillations.
In signal processing and communications, phase angle refers to the relative timing or alignment of different components of a signal. For example, in modulation techniques such as phase modulation (PM) or frequency modulation (FM), the phase angle of the modulating signal determines the phase shift of the carrier signal.
A circuit consumes 3200W of real power while the apparent power is 3700VA. To determine the phase angle, we use the concept of power factor (cos φ), which is the ratio of real power to apparent power. The power factor can be calculated as Power Factor = Real Power / Apparent Power = 3200W / 3700VA.
Therefore, Power Factor = 0.864. To find the phase angle, we use the inverse cosine (arccos) of the power factor, which is arccos(0.864). Phase Angle, φ = arccos(0.864) = 30.1 degrees. This means the phase angle between the voltage and current in this circuit is approximately 30.1 degrees.
