Series and Parallel RLC parameters

[baby_1]

Homework Statement

I want to find different parameters of series and parallel RLC
for series RLC we have this transfer function

and we know that transfer function of second order system is something like this:we can assume H0=1

but

is wrong(when you use only denominator you find out that

).However the same approach works fine for parallel RLC.

what is my mistake?

Homework Equations

The Attempt at a Solution

 

[NascentOxygen]

For a series RLC, from the denominator I find $Q=\omega_o\frac L R$

What is your transfer function for the series circuit?

 

[baby_1]

Hi,
Sorry , I mean that this approach works for Series RLC but not works for parallel RLC
Here is my calculation

we know that

So in deliminator

, but with numerator it is different

The same approach