Engineering Circuit analyse -- LR circuit frequency response

[8700]

Homework Statement

Find X [/B]

Homework Equations

V₁(t)=8cos(12000t)
V₀(t)=Xcos(12000t+θ)

The Attempt at a Solution

[/B]
I've tried quiet a lot actually, but all in vain. Seems like I am either misunderstanding something, or i am just too tired to think at the moment. Either way, I am frustated!

 

[berkeman]

Homework Statement

Find X [/B]

View attachment 108908

Homework Equations

V₁(t)=8cos(12000t)
V₀(t)=Xcos(12000t+θ)

The Attempt at a Solution

[/B]
I've tried quiet a lot actually, but all in vain. Seems like I am either misunderstanding something, or i am just too tired to think at the moment. Either way, I am frustated!

What technique would you expect to use for this type of problem? If the inductor were replaced with a resistor, what would your answer be?

Have you worked with Phasors? What about Differential Equations? You will probably use one of those techniques to solve this, depending on what you have been learning in class...

 

[8700]

we have mostly been working with phasors, which is those tools i am using.

I know that the following.

v(t)=Re{Ve^jωt}=V_Acos(ωt+Φ)

and

V=V_Ae^jΦ=V_A∠Φ

somehow I can't seem to get further then this.

I am considering to use the transfer function, and use that to solve for X

 

[berkeman]

we have mostly been working with phasors, which is those tools i am using.

I know that the following.

v(t)=Re{Ve^jωt}=V_Acos(ωt+Φ)

and

V=V_Ae^jΦ=V_A∠Φ

somehow I can't seem to get further then this.

I am considering to use the transfer function, and use that to solve for X

If the inductor were replaced with a resistor, what technique would you use?

And with the inductor put back in place, how can you use phasor impedances to do a similar calculation?

 

[8700]

Hmm I would probably use the voltage divider

Could I not do that with the transfor function?

 

[berkeman]

Hmm I would probably use the voltage divider

Could I not do that with the transfor function?

 

[8700]

I take that as an yes :D

 

[berkeman]

I take that as an yes :D

Yep. And if you want to see some good examples of how to work with them, just do a Google Images search on Phasor Voltage Divider...