Impedance and resonant frequency for series RL with parallel C

[notnerd]

Homework Statement

Find the impedance (Z) of the circuit in the shown figure (R and L in series, and C in parallel with them). A circuit is said to be in resonance if Z is real, find ω in terms of R, L, and C?

Homework Equations

V_R= RIe^iωt
V_L= LiωIe^iωt
V_C= (Ie^iωt)/(iωc)

What I mean by I is I (not) H didn't know how to write it and i imaginary number, I hope the I wrote the equations clearly.

The Attempt at a Solution

What I think about is:
1. Find Z.
2. Put Z in term of x+iy.
3. If Z is real then y=0.
4. find ω from y=0.

If that correct I should find Z, but I'm not sure about it.
first I found Zseries for R & L = R+iωL
then Z = Zseries || Z_C
Am I right? or there are some specific formulas as if all R, L & C are in series?

 

[cnh1995]

first I found Zseries for R & L = R+iωL
then Z = Zseries || ZC
Am I right?

Yes.

2. Put Z in term of x+iy.
3. If Z is real then y=0.
4. find ω from y=0.

Right.

 

[cnh1995]

What I mean by I is I (not) H didn't know how to write it and i imaginary number, I hope the I wrote the equations clearly.

To avoid confusion with current, imaginary number 'i' in mathematics is denoted by 'j' in electrical circuit analysis. So the reactances become jX_L and -jX_c (Note 1/j= -j).