Haha indeed...
Ok well I imagine the values would be in an arrangement similar to:-
R = r +j0
C = 0r - jxc
L = 0r + jxl
Ok well I imagine the values would be in an arrangement similar to:-
R = r +j0
C = 0r - jxc
L = 0r + jxl
What is Xc?Haha indeed...
Ok well I imagine the values would be in an arrangement similar to:-
R = r +j0
C = 0r - jxc
L = 0r + jxl
Your mathematical web of madness is purely, 100% one of your own making and the fact that you couldn't get out of it is because you still refuse to track your damn units!I'v become stuck in some mathemtical web of madness. Though I think I might be getting close...the story so far....
The capacitor's reactance doesn't have units of inverse resistance.Ahaha I didn't actually know I could do track my units with these things, or believe me! I would have done it...
Ok stupid question - Why is the capacitor an inverse resistance?
Two points:I still have no idea how to get that equation into the form you want Wbahn. I'm now several layers of abstraction deep and my initial question far from sight.
Proceeding from the point you mentioned, given those variables I would do something like this
View attachment 152205
I think you might have missed Post #5 where I said:Anyways I figured out this bad boy. See this equation at point 1, it gets fed back into the equation at point 3. At resonance the imaginary, of point 3, is zero, which is how he set point 4 equal, to each other.
Two freaking days I've been beating my head against a wall with that...sigh
The second equation is simply the impedance (which is purely resistive) at the resonant frequency.
So they aren't going FROM equation 1 TO equation 2, but more likely there is an earlier equation giving the impedance at ANY frequency (so it would have ω in it) and then they ask what the resonant frequency is (probably defined as the frequency at which the reactance goes to zero) and come up with equation 1. They then plug that back into the prior equation to come up with equation 2, which is only good at that one frequency.
But why didn't they simplify equation 2 to just L/(RC)?
I did read that Wbahn. I wasn't sure what it meant exactly. As I say, I miss things. People tend to talk to me at a certain level, assuming I know and can understand everything, at that level. When I can be a bit thick tbh... usually about really simple things...I think you might have missed Post #5 where I said: The second equation is simply the impedance (which is purely resistive) at the resonant frequency.
The full picture is on post #8 of this thread and I don't think it is, though I could be wrongbut more likely there is an earlier equation giving the impedance at ANY frequency
He did it's right at the end there.But why didn't they simplify equation 2 to just L/(RC)?
Go back and review his work (Post #8) again, because it is EXACTLY what I described.I did read that Wbahn. I wasn't sure what it meant exactly. As I say, I miss things. People tend to talk to me at a certain level, assuming I know and can understand everything, at that level. When I can be a bit thick tbh... usually about really simple things...
The full picture is on post #8 of this thread and I don't think it is, though I could be wrong
He did it's right at the end there.
Don't you mean to say: "Only the real part is used because it is already known that the imaginary part will be zero at that frequency)"?Go back and review his work (Post #8) again, because it is EXACTLY what I described.
The center column (the left hand column of work) starts with the basic description of the circuit topology and then ends at the bottom with the equation for the impedance that is good for any frequency.
The top of the right column is the direct result of setting the imaginary part to zero. That results in the next to last line which gives the frequency at which this happens. The final line is simply plugging this frequency back into the real part of the general impedance equation. Only the real part is used because it is already known that it will be zero at that frequency).
by Luke James
by Gary Elinoff
by Gary Elinoff