RLC Transfer Function for Voltage Across the Capacitor

[dashkin111]

Homework Statement

We have a series RLC circuit with x(t) as the voltage source. We are to find the frequency response function H(w) from the input x(t) to the output y(t)=Vc(t) - ie the voltage across the capacitor.

Homework Equations

The Attempt at a Solution

My answer is:

$$H(\omega) = \frac{1}{1+j \omega R C - \omega ^{2} L C }$$

I just got it from doing the impedance of the capacitor over the total impedance. First does this look correct?

My second question arises in a more "general" approach of going at transfer function problems. Do I always just do the impedance part we are looking at divided by the impedance of the whole circuit?

 

[mjsd]

Homework Statement

We have a series RLC circuit with x(t) as the voltage source. We are to find the frequency response function H(w) from the input x(t) to the output y(t)=Vc(t) - ie the voltage across the capacitor.

Homework Equations

The Attempt at a Solution

My answer is:

$$H(\omega) = \frac{1}{1+j \omega R C - \omega ^{2} L C }$$

I just got it from doing the impedance of the capacitor over the total impedance. First does this look correct?

yes.

My second question arises in a more "general" approach of going at transfer function problems. Do I always just do the impedance part we are looking at divided by the impedance of the whole circuit?

not entirely sure what you mean by "general" approach; but it usually depends on the circuit