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

[kl055]

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

Homework Statement

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.

Homework Equations

PROBLEM

SOLUTION

The Attempt at a Solution

 

[tiny-tim]

welcome to pf!

hi kl055! welcome to pf!

why is tan θ(ω) = ωL/R?

and what θ(ω) represent? how does it relate to the current?
…
Also, is it true that tan [-θ(ω)+90°] = R/Lω?]

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)

 

[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.

 

[kl055]

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

 

[rude man]

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

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

 

[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.