Phasor simplification

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  • #1
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Homework Statement



Can someone explain how wLT /_ theta

could be written as wL /_ theta X T /_ (theta - 90)

(w, L and T are all constants)


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Simon Bridge
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Homework Statement



Can someone explain how wLT /_ theta

could be written as wL /_ theta X T /_ (theta - 90)

(w, L and T are all constants)

By wL /_ theta X T /_ (theta - 90)

do you mean ##\omega L \angle\theta\times T\angle (\theta-90^\circ)## ?

Following:
http://en.wikiversity.org/wiki/Phasor

You seem to be asking how we can say:$$\omega LT e^{i\theta} = \omega L e^{i\theta}Te^{i(\theta-\frac{\pi}{2})}$$ ... multiply it out and see what the phasor looks like.

Where did you get this relation from?
 
  • #3
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By wL /_ theta X T /_ (theta - 90)

do you mean ##\omega L \angle\theta\times T\angle (\theta-90^\circ)## ?

Following:
http://en.wikiversity.org/wiki/Phasor

You seem to be asking how we can say:$$\omega LT e^{i\theta} = \omega L e^{i\theta}Te^{i(\theta-\frac{\pi}{2})}$$ ... multiply it out and see what the phasor looks like.

Where did you get this relation from?

The book says that a sinusoidal voltage v(t)=Vcos(wt+ ##\theta##) can be defined by the phasor V=V##\angle \theta## where ##\theta## is the phase angle

The actual relation is
V=##wLI\angle \theta##
and that it can be written in the form
V=##(wL\angle\theta)## x ##I\angle(\theta-90)##

so then that should mean ##wLIe^{(wt+\theta)}## can be written in the form
##wL e^{(wt+\theta)}Ie^{(wt+\theta-90)}##...?
 
  • #4
Simon Bridge
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The book says that a sinusoidal voltage v(t)=Vcos(wt+ ##\theta##) can be defined by the phasor V=V##\angle \theta## where ##\theta## is the phase angle

So ##v(t)=Re[Ye^{\omega t}]## so ##Y=Ve^{j\theta}## and you write it as ##Y=V\angle\theta##

so then that should mean ##wLIe^{(wt+\theta)}## can be written in the form
##wL e^{(wt+\theta)}Ie^{(wt+\theta-90)}##...?

You should be able to translate the notation back into the cosine form to see what is happening.
I have a feeling your book is trying to talk about the phase difference between the voltage across an inductor and the current through it.
 

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