# What is the variable theta of omega in a series RL cct?

1. May 20, 2013

### kl055

What is the variable "theta of omega" in a series RL cct?

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

Hi

I'm not looking for a complete solution to this problem. My question concerns just one specific part of the solution to part A:
why is tan θ(ω) = ωL/R?

and what θ(ω) represent? how does it relate to the current? I took the introductory EC course almost two years ago so I need a refresher. Which section should I review? (I am using Electric Circuits 9ed by Nilsson)

I was able to complete the entirety of part A except for that part.

Also, is it true that tan [-θ(ω)+90°] = R/Lω? If so, then my answer is correct because I got that answer, but in cosine form. So the +90 would validate my answer.

2. Relevant equations
PROBLEM

SOLUTION

3. The attempt at a solution

Last edited: May 20, 2013
2. May 21, 2013

### tiny-tim

welcome to pf!

hi kl055! welcome to pf!
it's simple trig …

Acosφ + Bsinφ = A(cosφ + (B/A)sinφ)

and cos(φ+θ) = cosφcosθ - sinφsinθ = cosθ(cosφ - tanθsinφ)

so if we define θ so that tanθ = -B/A,

then Acosφ + Bsinφ = (A/cosθ)cos(φ+θ)

(and tan(90°- θ) = cotθ = 1/tanθ)

3. May 21, 2013

### rude man

Show us your computation of K1.

That way I can show you why θ(ω) = tan-1(ωL/R).
θ(ω) is part of the phase angle between voltage and current. It's the part that's a function of frequency wheras phi and -90 deg. are constant angles, independent of frequency.

4. May 21, 2013

### kl055

I did a partial fraction expansion, solved the system of equations, then rewrote K1 using trig laws.

5. May 21, 2013

### rude man

So you're happy with what you did, no more questions?

6. May 21, 2013

### kl055

Yes. I don't have a problem with the math but I was wondering how to conceptually interpret the theta angle. You mentioned the "phase angle between voltage and current" which indicates that I need to review the phasor section of the textbook. Thanks for the help.
I've got quite a bit of reading to do =/
I'll post here again if I have trouble with the textbook's explanation.