Calculating Power Factor in an AC circuit, given voltage and current

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Discussion Overview

The discussion revolves around calculating the power factor in an AC circuit, focusing on the relationship between voltage and current in phasor form, phase shifts, and the implications of these factors on circuit behavior. The scope includes theoretical aspects and mathematical reasoning related to power factor calculations.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant expresses uncertainty about calculating the phase shift and converting voltage and current to phasor form, indicating a need for clarification on these steps.
  • Another participant describes the rotational nature of voltage and current representation in the phasor domain, stating that the power factor is defined as cos(ϕ), where ϕ is the phase angle.
  • A participant acknowledges realizing that the power factor can be determined by subtracting the voltage angle from the current angle and taking the cosine of that difference.
  • Further discussion includes a participant's reasoning about the nature of loads (capacitive vs. inductive) based on phase angles, suggesting that a positive phase angle indicates an inductive load, while questioning the resistive nature of another load despite its phase angle.
  • One participant affirms another's reasoning, indicating some level of agreement on the interpretation of phase angles and their implications for load characteristics.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the calculation of phase shifts and the implications of phase angles on load characteristics. While some agreement exists on the definitions and calculations, the discussion remains unresolved regarding the nature of specific loads and their phase relationships.

Contextual Notes

Participants reference the need for clarity on phase shift calculations and the interpretation of phase angles in relation to load types, indicating potential limitations in their understanding of these concepts.

bardia sepehrnia
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Poster has been reminded to post schoolwork in the Homework Help forums
Homework Statement
Calculate the power factor for each case:
v(t) = 540 cos(ωt + 15◦) V, i(t) = 2 cos(ωt + 47◦) A
v(t) = 155 cos(ωt − 15◦) V, i(t) = 2 cos(ωt − 22◦) A
Relevant Equations
Vrms=V/sqrt(2)
Irms=I/sqrt(2)
1612536386045.png


My attempt at solving this question:
1612536445654.png
I realized my attempt is wrong however I just don't know how to proceed in the first step. How can I calculate the phase shift? and find Voltage and Current in phasor form??If I know that, then I can use power factor formula: pf=Pav/V*I
 
Last edited:
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The plane in which voltages and currents are represented rotates with ω radians per seconds. The angles between voltages and currents are constant and rotate all the time with the same velocity. Power factor it is the cos(ϕ).
 

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Yeah, I realized I just had to subtract the voltage angle from the current one and take cosine of that. Thank you.
 
Babadag said:
The plane in which voltages and currents are represented rotates with ω radians per seconds. The angles between voltages and currents are constant and rotate all the time with the same velocity. Power factor it is the cos(ϕ).
can you also help me with this one pls?
1612564193381.png

I understand that the first 2 are capacitive as power factors are leading. In C, I think I understand why it's inductive because first if we change current equation to cosine, then: i(t)=4.2 sin(ωt-(pi/2)), and the phase angle is 0-(-pi/2)=pi/2, and positive phase angle indicates that the load is inductive. If that reasoning is true, then d, should i also be inductive, but it is resistive. I thought the phase angle has to be for the load to be resistive.
 
You are right.
 

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Thank you very much!
 

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