To find power factor of the ac circuit given only the source and load voltages

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Discussion Overview

The discussion revolves around determining the power factor of an AC circuit using given source and load voltages. Participants explore various methods to analyze the relationship between these voltages and the implications for the load's characteristics, including resistance and reactance.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests starting with the vector sum of two voltages equaling the third to form a triangle representing the voltages.
  • Another participant notes that the load must consist of resistance and reactance, as the square of the source voltage does not equal the sum of the squares of the other two voltages.
  • Some participants propose that calculations are necessary to find the cosine of the angle (Cosθ) using either a vector diagram or algebraic methods.
  • One participant reports a calculated power factor of 0.83, while another claims to have calculated it as 0.453.
  • A participant expresses that there may be two correct answers based on different interpretations of the question regarding the load and its relationship to the supply voltage.
  • Another participant interprets the scenario as involving a lossy transmission line, which adds complexity to the analysis.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the question and the resulting calculations, indicating that multiple competing views remain without a clear consensus on the power factor values or the method of calculation.

Contextual Notes

There are unresolved assumptions regarding the nature of the load (inductive vs. capacitative) and the interpretation of the voltages in relation to the power factor calculation.

sathishj
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how to find power factor of the load, the three voltmeter readings are V1=220v,V2=122v,V3=136v
 

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Start with the vector sum of two of these voltages equalling the third, and determine the triangle representing this.
 
The load must be a combination of resistance,R, and reactance,X, because 220^2 does not equal 122^2 + 136^2
this means that for the load Vr^2 + Vx^2 = 136^2
this will give 2 equations which can be solved for the Vr in the load and the Vx for the load
 
No calculations are needed beyond what I outlined:
NascentOxygen said:
Start with the vector sum of two of these voltages equalling the third, and determine the triangle representing this.
 
Some calculation is needed to get a value for Cosθ, either from a vector diagram or by algebra.
Does anyone have an answer? I got 0.83. Purely for personal preference I took the reactive part of the load to be inductive but it could have been capacitative.
 
I get pf=0.453
 
NascentO
Here is what I did, I interpreted the question as asking for the power factor for the load connected to the supply voltage of 220V (this is what is usually meant for power factor).
The question however does say 'the load' and 'the load' is clearly marked onthe diagram.
I would say there are 2 correct answers !
Sorry! attachment not there... I will do it again
 
Last edited:
Attachment for power factor calculation
 

Attachments

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I interpreted it as a lossy transmission line. Otherwise, I agree with your answers.
 

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