AC Circuits Terminology: Phase shift vs Phase Angle

We talked about AC circuits and phase shifts were discussed. Voltage changes "lag behind" current changes so that's how we get phase shifts. It's like a sinusoid so fine. Then we talked about impedance.

There's a real and "imaginary" component to impedance, graphed on x-axis and y-axis respectively. Fine, but now the prof starts saying phase angle which he refers to the angle each impedance vector makes with the x-axis. Lots of people are telling me phase angle is the same as the phase shift. Convincing arguments too since impedance relates current and voltage, and phase shift would relate to two phase angles. I thought the phase angle is for an impedance vector at a particular frequency at a given time while the phase shift is the difference between two phase angles.

So, is a phase angle and phase shift actually the same in AC circuits???

Good question war485, these terms are often mixed up, and yes they are different.

 We talked about AC circuits and phase shifts were discussed. ..... It's like a sinusoid so fine.
So in alternating circuits the instantaneous voltage or current may be represented by

V = V0 cos(ωt)

as a function of time.

Now you are actually taking the cosine of an angle so (ωt) is really an angle, say θ.

This angle is called the phase angle and it tells us "How far along the cycle the voltage wave is, relative the the voltage at zero, V0".

(Note
1) This applies to all waves, not just electrical ones
2) I have used cos since it is not zero at θ = zero)

The times t1 and t2 correspond to two angles θ1 and θ2

The difference between these angles is called phase difference.

Now consider a second wave, counted from the same (arbitrary) zero point in time.
There is no reason for this wave to peak at the same instant as the first, even if it is of the same frequency.

If the second wave does have the same frequency, the difference in time and therefore θ = ωt , is the difference in angle is $\varphi$ = (θ2 - θ1) between the time of occurrence of the peak value for the second wave and the peak of the first.

$\varphi$ is called the phase shift of the second wave relative to the first.

Since θ2 = (θ1 + $\varphi$)

we can write V = V2cos(θ1 + $\varphi$)

To plot it on the same axes as the first wave.

Note
The phase shift may be positive or negative and this corresponds to a shift forwards or backwards along the horizontal axis.
I have used cos rather than sin since it peaks at zero. We need to compare (positive) peaks since the waves may be sloping backwards or forwards where they cross zero. The peaks are the only values that occur exactly once in a cycle. Every other point in the cycle occurs more than once.

Does this help?
 It's clear but there's 2 follow-up questions in my mind. In your example, you had: V = V2cos(θ1 + φ) So you are saying that: θ2 = θ1 + φ = (ωt) + φ = a new phase angle? Relating this back to impedance, curious, "if" the frequency was the same for both the current and voltage, does that mean impedance still have the same frequency? i.e. take one impedance vector at some instant time. Because I never hear anyone talk about impedance with phase shifts, just phase angles. Thanks for taking the time to clear out the terms!

AC Circuits Terminology: Phase shift vs Phase Angle

 you are saying that: θ2 = θ1 + φ = (ωt) + φ = a new phase angle?
Yes.

Remember the phase angle tells you how far along its cycle a particular wave is and the second wave will be at a different point in its cycle at any matching t. t is common to both waves and ω is the same since they are of the same frequency.

 Because I never hear anyone talk about impedance with phase shifts, just phase angles.
That's just loose talk. The correct term is phase difference between current and voltage.

You will also see the term phase shift ( of 180°) applied to a single wave on reflection.

 Tags ac circuit, phase angle, phase shift