Understanding Power Factor and Load Impedance

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SUMMARY

Power factor (PF) is defined as the ratio of average power to apparent power, expressed mathematically as PF = cos(theta v - theta i), where theta v represents load voltage and theta i represents load current. The power factor angle corresponds to the angle between the voltage and current vectors, not directly to load impedance. The relationship between power factor and load impedance is established through the angle between the impedance and resistance vectors, which is equivalent to the power factor angle. Understanding these relationships is crucial for analyzing AC circuits effectively.

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  • Basic understanding of AC circuit theory
  • Familiarity with vector representation of voltage and current
  • Knowledge of impedance and resistance concepts
  • Mathematical proficiency in trigonometry
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  • Learn about phasor diagrams and their application in power factor analysis
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Homework Statement



I understand power factor is defined as (average power)/(apparent power) or cos(theta v - theta i) where theta v = load voltage and theta i = load current. Also the power factor angle is equal to the load impedance.

I don't understand how the 2 definitions of power factor equal each other or why the power factor angle equals the load impedance.

I know it's a tall order but I would appreciate it if somebody could answer these questions. Alternatively a good website or book that explains this fully.
 
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Your first statement means PF = Cos of the angle between V (the supply voltage) and the current vectors.
It does not equal the impedance but the angle between the impedance and the resistance vectors is the same as in my first sentence.
Hope this helps you to picture the vectors and the angle
 
See if this helps
FIG+5.jpe
 
This is what I was after.
 

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