# Homework Help: Find the impedance and ω for (R and L in series, & C in || )

1. Oct 2, 2016

### notnerd

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
VR= RIeiωt
VL= LiωIeiωt
VC= (Ieiωt)/(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.

3. 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 || ZC
Am I right? or there are some specific formulas as if all R, L & C are in series?

2. Oct 2, 2016

Yes.
Right.

3. Oct 2, 2016

### cnh1995

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