If we want to be able to trust the math, then the math needs to be correct. atan2() will only give us the correct angle for all four quadrants if the sign of each argument is maintained. You can't "factor it out". If you do, then there's no point using atan2() -- just use the normal atan() function.

Nope, I messed it up. I was too focused on getting the curly braces to render that I didn't pay close enough attention to the bigger picture. I've corrected that above. Thanks for catching it.

Hi,

Yeah that's one thing i hate about Latex. Makes really nice math text, when it works right

Oh, about the -atan2(y,x), I did not 'factor out' the negative sign, if that's what you mean. I generalized it for a capacitor with a resistor only. I dont see any reason why we can't do this when we are concentrating on one thing only, and the numbers are bound to the problem (sometimes referred to as binding).
I think -atan2(y,x) is wrong, but when the signs are unchangeable, we can write -atan2(1,2) for example. But for more generality, when we write
-atan(n,m) when 'n' and 'm' are clearly taken to be both positive and the angle is always negative, then we can write it as -atan2(n,m). If either n or m or both can change sign, that would not be valid. I can give a few examples...(I am going to make this up randomly to keep it simpler)...
ph=atan2(-R/w,(R+w)/(w*C*L))
The imag part is negative, but all the variables are either 0 or greater than zero. This allows us to simplify.
First, 'w' is in the denominator of both imag and real parts, so it can be eliminated (but only because w>0):
ph=atan2(-R,(R+w)/(C*L))
That changes nothing.
Next, we can see that if R, w, C and L are all positive, then we have the case:
ph=atan2(-a,b)
where both a and b are positive (0 is a special case). Since 'y' is negative and 'x' is positive, the angle MUST be negative for all a and all b. Thus we can write:
ph=-atan2(a,b)

So although -atan2(a,b) is not correct all by itself, when we deal with real components we usually have positive values for R, C, and L and w, and if one or more is zero we have to check for a special case and state what it is if we want to be clear. This means:
ph=-atan2(a,b)
when it is clear that a and b are both positive and originally we had atan2(-a,b).

An example that would not work...
ph=-atan(R,K) or ph=-atan(K,R) would not work if we did not know the sign of K was fixed (we assume R is positive).

It's also true that if we do this reduction and R is not a more typical positive value, we have to be more careful. With:
ph=atan2(R,K) with R possibly being negative or positive, we cannot generalize to anything like ph=-atan2(...,...).

And that means the generalization could also be bound to the problem at hand, which for this discussion was an R and C in series.

Here is an actual example from a real circuit:
The imag part is: -(w*C*R1^2*R2)/(w^2*C^2*R1^2*R2^2+R2^2+2*R1*R2+R1^2)
and the real part is: (R1*R2+R1^2)/(w^2*C^2*R1^2*R2^2+R2^2+2*R1*R2+R1^2)
We can see that in the typical case we would assume w>0 and R1>0 and R2>0 and C>0, and that the denominators are the same, so this reduces to:
imag: -w*C*R1^2*R2
real: R1*R2+R1^2
and using the atan2() function this means we have the form:
atan2(-a,b)
where both a and b must be positive, and that reduces further to:
-atan2(a,b)
We do have to be careful though because in many cases we do include w=0 and that could lead to another result. In the case at hand we get lucky:
atan2(-a,b)=0
-atan2(a,b)=0
if w goes to zero.

I hope I did all the calculations correctly, but these kinds of generalizations are kind of typical because we usually want to get the expression into the simplest form possible. By stating -atan2(...,...) we are suggesting that the angle is always negative.
I think a lot of math software would automatically reduce the larger example above to -atan2(...,...) and then even reduce it more to:
-atan(a/b)
in cases where a and b are both positive and can never be negative (and zero is a special case of course). This probably depends on the math software.

If you spot any mistakes please let me know.

 

He's a rather infamous UFO researcher and retired Electrical Engineer.

UFO's and Bigfoots should be both in the same category I think

It always amazes me how much we see on TV about these subjects without one single solid absolute proof of either.
What do we have proof of?
Little dots on a screen, green lights, flying things that we can't identify yet or even be sure they are actually flying, blurred images of what might be some sort of animal in the woods behind a thick swatch of trees and bushes, animal calls from deep in the woods. Ha ha.
Yet there are countless, truly countless, TV shows about this stuff.

How did we get into this subject anyway. The phase of a circuit is real, the other stuff isn't

 

As soon as he says, "the flow of voltage", my Spidey Senses started twanging.

It looks like he is describing a circuit in sinusoidal steady state.

Because the video starts in mid-presentation, we don't know what the point was that he was trying to really make using the exponential curves. There seemed to be a fair bit of technobabble there. I suspect he was trying to describe how the transient response settles into the steady-state response and was probably trying to come up with an hand-wavy explanation off the cuff.

In sinusoidal steady state, the voltage and current in a capacitor are always shifted by 90°. He is only talking about the voltage across the capacitor and the current through the capacitor.

I'm not a fan of using the term "displacement" in this context -- "shifted" or "offset" are better choices. But that's not a hill worth dying on.

At the end, he flubs up pretty good -- leaving his absolute disregard for proper tracking of units aside, he initially says that the source voltage is 70.7 V. At first it looked like he was going to buy that, but then did catch that it was obviously wrong and changed it to 7.07 V. But then he completely failed to realize that this is just as obviously wrong.

The lesson here is that you need to always, always, always ask if your answer makes sense. If you are given two sides of a right triangle, you KNOW that the hypotenuse can be no smaller than the longest side and no longer than the sum of the two sides, so any answer that is not in the range of 10 V to 20 V must be wrong. It sounds like a couple of the students were catching on that the answer didn't make sense right at the end, but it cut off before we could see how that ended up.

But we need to give some grace because it is easy to make silly mistakes and not catch them when you are doing things on the fly in front of an audience. You are juggling a number of tasks and things fall through the cracks.
I think the confusion in that presentation is pretty common when someone mixes transient RC behavior with steady state AC phasor analysis, because they are actually two different mathematical models even if they involve the same circuit. In transient analysis you are dealing with exponential time domain solutions, while in phasor form you assume sinusoidal steady state where derivatives turn into complex frequency terms, so the phase shift between voltage and current depends on impedance, not a fixed rule like “always 90 degrees”. That is why the statement about a constant 90 degree lag across a capacitor is only true in the ideal pure capacitive case, not when resistance is present in the circuit. When I see this kind of mix up, I usually think it would help to have a clearer breakdown of the math behind each case, and can actually be useful because it shows step by step MATLAB based solutions for circuit problems, including control systems and signal analysis, which forces you to separate transient response from frequency domain behavior. I find that approach helpful because once you see both models side by side, the contradiction disappears and it becomes clear what assumptions are being made in each method.

I think your confusion is justified honestly. A lot of presentations mix together:

• transient RC behavior (time-domain exponential charging/discharging)
• and steady-state sinusoidal AC phasor analysis

…as if they’re the same thing, when they really describe different situations.
The “current leads capacitor voltage by 90°” statement is only strictly true for an ideal capacitor under pure sinusoidal steady-state AC. Once resistance is involved in an RC circuit, the phase relationship between source voltage and current is no longer exactly 90°. The phase angle becomes frequency-dependent and is somewhere between 0° and 90°.
For a series RC circuit:

• resistor voltage is in phase with current
• capacitor voltage lags current by 90°
• total circuit voltage is the vector/phaser sum of both

So the source voltage does not generally lag/lead by exactly 90° relative to current.
And yes, transient exponential charging behavior is a completely different analysis using differential equations in the time domain, not phasors. People sometimes blur the intuition between the two, which can make explanations sound contradictory or sloppy.
So based on your description, it does sound like the presenter may be mixing concepts together a bit.