Deriving v(t) from i(t) in a Series Circuit: Finding V Across Z | Homework Help

[rubber314chic]

Homework Statement

I've been given a series circuit with a .5H inductor .01F cap, .5H inductor and 10Ω resistor in series.

This circuit is connected to a source i(t) = 10cos(10t) and I need to find v(t) across Z

Homework Equations

From the givens I've found the Z(s) to be s+100/s+10 and Z(jω) to be j((ω^2-100)/ω)+10

The Attempt at a Solution

I believe I need to use Ohm's law V=IR to find V. So if I multiply j((ω^2-100)/ω)+10 by 10cos(10t) I should get a v(t) but I think I'm doing something wrong with this.

 

[wukunlin]

what you need to do is make sure you are in the s-domain, so V(s) = I(s)Z(s), you need to perform laplace transform to the current output to obtain I(s), then you can multiply that with the frequency dependent impedance, then finally get your answer from the inverse laplace of the product