X/R ratio

[mull982]

Can the X/R ratio be determined from the difference in angles between the voltage and current waveform? I know the power factor is determined from the cosine of this angle but could not remember is the X/R value could be determined by this angle as well.

If I call correctly it may be the sin or tangent of the angle between the voltage and current waveforms???

Can someone help jog my memory?

 

[beanland]

Phase angle

Phase angle

The phase angle between the voltage and current is mostly created by the load. If you had a purely resistive load and measured the phase angle between the voltage and current, you can back-calculate the source X/R ratio. However, if you have no control over the load, you have too many unknowns.

If you have a purely resistive load (water heater?), then you have an "R-load" in series with an "X-source" and "R-source". The voltage difference between load off and load on tell you about the total impedance in the source. The phase angle between the current and the voltage will tell you about the reactance in the source.

 

[kingpb]

Can the X/R ratio be determined from the difference in angles between the voltage and current waveform? I know the power factor is determined from the cosine of this angle but could not remember is the X/R value could be determined by this angle as well.

If I call correctly it may be the sin or tangent of the angle between the voltage and current waveforms???

Can someone help jog my memory?

The angle between voltage and current is the PF. Knowing the power factor and the load (VA) you can ultimately detrmine the r and x components by using P and Q which then can give you the X/R ratio.

It will require the use of current vector and conjugate of the current vector, if that jogs your memory.

 

[mull982]

I was reading somewhere where it said that an X/R ratio of 1.7 corrosponded to an angle of 60 degrees between the current and voltage waveforms. I couldn't remember how this relationship was derived.

The Tangent of 60 degrees is 1.73. Is this possibly the relationship??

 

[mull982]

I did some researching online and was able to find the answer.

Power Factor=Cos(Tan^-1(X/R))

Looking at this equation, the value inside the fist set of parenthesses represents the angle between the voltage and current waveform. Therefore looking at this in reverse you can prove that the X/R ratio is the Tangent of the phase angle between the voltage and current waveforms.

 

[bob]

Can the X/R ratio be determined from the difference in angles between the voltage and current waveform? I know the power factor is determined from the cosine of this angle but could not remember is the X/R value could be determined by this angle as well.

If I call correctly it may be the sin or tangent of the angle between the voltage and current waveforms???

Can someone help jog my memory?

X/R is generally related to fault calculations. The X and R are the physical characteristics of the system.
http://www.powerstudies.com/articles/ImportanceofX-over-RRatios.pdf
Check here. Also google X/R ratio.