How Does Phasor Simplification Apply to wLT /_ theta?

[eterna]

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

 

[Simon Bridge]

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?

 

[eterna]

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
$wL e^{(wt+\theta)}Ie^{(wt+\theta-90)}$...?

 

[Simon Bridge]

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.