- #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)

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- Thread starter eterna
- Start date

- #1

- 19

- 0

Can someone explain how wLT

could be written as wL

(w, L and T are all constants)

- #2

Simon Bridge

Science Advisor

Homework Helper

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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

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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- 0

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

Science Advisor

Homework Helper

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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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