Hameedulla-Ekhlas
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when waveforms are out of phase, it is due to lagging and leading ( inductance and capacitance )
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when waveforms are out of phase, it is due to lagging and leading ( inductance and capacitance )
Hameedulla-Ekhlas
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yes, I had not given that for daily use and I just gave that for a different question a different answer.
By the way, can you prove it back v(t)/i(t) from that complex equation.
Your point is simply wrong. Just because v(t)/i(t) = z(t) doesn't mean that v(0)/t(0) = z(0). The error here is you are trying to make a complex number fit on the real number line. Thats why you are getting a impedence that varies.
You won't see z written as a function of time in textbooks, because the time function goes away. z(t) = constant = z.
The correct way to do this problem is to transform to and back from the complex plane. Say v(t) =sin (wt) and i(t) = sin (wt+a).
V= 1 @0 and I = 1 @a. It follows from what we know about phasors that Z = 1 @-a. We can transform back Z to get z(t). z(t) is simply 1 ohm at an angle of -a, and we can simply call it z. That is the impedence.
I think you are forgetting that a phasor is simply a representation of time function. See if you can find any reference to "Steinmetz Algorithm".
Since z is a complex number, you cant simply divide the voltage at some time by the current at the same time and expect it to be z. v(0)/i(0) is not z.
Steve
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Only with a resistive load does this make any sense. In general it is still utter nonsense.
Impedance is the ratio of RMS voltage to RMS current, and it is undefined for instantaneous values.
z(t) is not mentioned in the texts because it does not exist!
v(t)/i(t) equals R +/- jX (thats an attempt to write "R plus or minus j reactance").
If you want to claim R +/- jX isn't an impedence, well....whatever.
Again, v(t)/i(t) = z does not mean the dividing the voltage at a specific time by the current at that same time is going to equal z. z can have a resistive component, and a reactive component. So not being able to get a constant when you plug in values of t simply means you are doing the math wrong.
Impedence is also the ratio of the Peak voltage to the peak current. Oh, and those are instantaneous values.
It doesn't take a genius to realize that any variable or constant can be plotted as a function of time. A constant is going to plot as a horizontal line (like our z does), but how does that mean "it doesn't exist"???
Steve
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I don't know Ham'. Perhaps... perhaps not. I don't even know if it is a valid equation. I can't see any purpose in taking the time to prove, disprove a complex equation when a much simpler one is readily recallable from [my] memory.
drbond24
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I have a new question!
Who thinks this thread had any meaning, or was it just utter nonsense? :grin::grin:
You may tally my vote in the 'utter nonsense' category.
:roll:
Who thinks this thread had any meaning, or was it just utter nonsense? :grin::grin:
You may tally my vote in the 'utter nonsense' category.
:roll:Note to all:
Note to all:
The values of v(t) and i(t) are real--not complex--numbers. e.g.
v(t) = Em*sin(wt)--ranges between +/-1
i(t) = Im*sin(wt + phi)--ranges between +/- 1
That is all, you can't just jump ahead and treat them as phasors and then jump back.
Clearly, the ratio cannot be a constant, therefore it cannot be an impedance. Clearly the ratio ranges between +/- infinity! Smart even plotted it for us.
Furthermore, such a ratio is meaningless. Utter nonsense!
Note to all:
The values of v(t) and i(t) are real--not complex--numbers. e.g.
v(t) = Em*sin(wt)--ranges between +/-1
i(t) = Im*sin(wt + phi)--ranges between +/- 1
That is all, you can't just jump ahead and treat them as phasors and then jump back.
Clearly, the ratio cannot be a constant, therefore it cannot be an impedance. Clearly the ratio ranges between +/- infinity! Smart even plotted it for us.
Furthermore, such a ratio is meaningless. Utter nonsense!
Would you feel better if I called everything a vector instead of a phasor? You can't seem to grap that a phasor (or a vector) is just a way to represent a number that has a phase angle associated with it. There is nothing magical about a vector or a phasor.
Clearly the ratio is a constant. That constant is R +jX. Smart's graph included the same mathmetical error you keep making. You keep trying to combine two independent numbers into one single real number.
I'd like to see some support for that statement.
I repeat, these numbers are neither vectors nor phasors. A rotating phasor is of the form,
Vm[cos(wt) +jsin(wt)]
which is NOT the expression we are using. There is no "j" operator; there is no imaginary part.
The one real number is the value of the expression. It does not carry a phase angle. The phase angle is part of the trig argument.
kingpb for one says it is meaningless.
Given:
v(t) = |v|cos(ωt)
i(t) = |i|cos(ωt+θ)
where θ = φi - φv
The following appears to be valid: i(t) = |i|cos(ωt+θ)
where θ = φi - φv
v(t)/i(t) = z(t) = |v|/|i|*cos(θ)+tan(ωt+θ) ...when θ>0
v(t)/i(t) = z(t) = |v|/|i| ...when θ=0
v(t)/i(t) = z(t) = |v|/|i|*cos(θ)-tan(ωt+θ) ...when θ<0
Ham' might be interested in proofing this claim. I haven't proofed it, but I have plotted it and the 'curves' were identical to plotting v(t)/i(t) for the example I used. Yet...v(t)/i(t) = z(t) = |v|/|i| ...when θ=0
v(t)/i(t) = z(t) = |v|/|i|*cos(θ)-tan(ωt+θ) ...when θ<0
...even if it is valid, it is not much different than simply writing the equation as:
v(t)/i(t) = z(t) = |v|cos(ωt)/|i|cos(ωt+θ)
btw, I'm not saying the above has any meaningful significance
...though...
Z = |v|/|i|
...is always significant
Hameedulla-Ekhlas
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Given:
v(t) = |v|cos(ωt)The following appears to be valid:
i(t) = |i|cos(ωt+θ)
where θ = φi - φv
v(t)/i(t) = z(t) = |v|/|i|*cos(θ)+tan(ωt+θ) ...when θ>0Ham' might be interested in proofing this claim. I haven't proofed it, but I have plotted it and the 'curves' were identical to plotting v(t)/i(t) for the example I used. Yet...
v(t)/i(t) = z(t) = |v|/|i| ...when θ=0
v(t)/i(t) = z(t) = |v|/|i|*cos(θ)-tan(ωt+θ) ...when θ<0
...even if it is valid, it is not much different than simply writing the equation as:
v(t)/i(t) = z(t) = |v|cos(ωt)/|i|cos(ωt+θ)
btw, I'm not saying the above has any meaningful significance
...though...
Z = |v|/|i|...is always significant
Yes, Smart$,
Not it is not like this. What rattus is saying, he is completely right that v(t) = i(t) R it is a Ohm 's Law.
One of our professor had come from Kansas University and he taught us some electrical topics. Now I opened his given material and it looks for me that rattus is correct. Let me make it a clear reason for that.
Give me time to proof for it that he is right.
Given:
v(t) = |v|cos(ωt)The following appears to be valid:
i(t) = |i|cos(ωt+θ)
where θ = φi - φv
v(t)/i(t) = z(t) = |v|/|i|*cos(θ)+tan(ωt+θ) ...when θ>0Ham' might be interested in proofing this claim. I haven't proofed it, but I have plotted it and the 'curves' were identical to plotting v(t)/i(t) for the example I used. Yet...
v(t)/i(t) = z(t) = |v|/|i| ...when θ=0
v(t)/i(t) = z(t) = |v|/|i|*cos(θ)-tan(ωt+θ) ...when θ<0
...even if it is valid, it is not much different than simply writing the equation as:
v(t)/i(t) = z(t) = |v|cos(ωt)/|i|cos(ωt+θ)
btw, I'm not saying the above has any meaningful significance
...though...
Z = |v|/|i|...is always significant
Smart, you are out of the ball park. The 'what if' waveforms are not sinusoidal, one is a step function, the other is an exponential.
Furthermore, the magnitudes of v and i change with time--not the same as Vrms/Irms or Vm/Im. You should write the expression as Vm*sin(wt), etc.
And, you are wasting your time trying to define z(t) which is not mentioned in any text I ever saw because it is utter nonsense.
The original question was:
It obviously has meaning, and everytime someone tries to explain that to you , you cry foul and respond by placing another new constraint on the origninal question.
Since the original question, you have since added that we:
-can't use chapter 1, were in chapter 2,
- can't use any math that too advanced (I guess chapter 3 is out too)
- can't use phasors,
-can't use vectors,
- can't use impedence
- can't use any transforms,
- can't use complex numbers,
- can't use anything with a phase angle
- can't use any reacatance
....The list goes on and on.
Its basically gotten to the point where you are asking "does impedence have any meaning if I don't let you mention impedence".
So again, I have to agree with Spongebob that this thread is nonsense.
It obviously has meaning, and everytime someone tries to explain that to you , you cry foul and respond by placing another new constraint on the origninal question.
Since the original question, you have since added that we:
-can't use chapter 1, were in chapter 2,
- can't use any math that too advanced (I guess chapter 3 is out too)
- can't use phasors,
-can't use vectors,
- can't use impedence
- can't use any transforms,
- can't use complex numbers,
- can't use anything with a phase angle
- can't use any reacatance
....The list goes on and on.
Its basically gotten to the point where you are asking "does impedence have any meaning if I don't let you mention impedence".
So again, I have to agree with Spongebob that this thread is nonsense.
If I'm out of the ball park it's because I'm chasing down my homerun ball.
Don't know where you're coming up with one 'what-if' waveform being a step function, but you are correct about the exponential one. What do you think the tangent function is?
For complex number z = x + iy the complex modulus is |z| = |x+iy| = √(x?+y?). Just a different way to denote the modulus (m).
I realize it is a useless pursuit, but that doesn't mean it's nonsense or that I can't have some fun
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Something wrong here:
Something wrong here:
It is obvious that some do not understand the difference between steady state and instantaneous equations. The value of,
sin(wt + phi),
is just a number that you would read off your calculator or from the trig tables. The phase angle "phi" merely shifts the function in time and does not appear in the value. For example, at t= 0 and phi = 45 deg.,
sin(0 + 45) = sqrt(2)/2
That is all, just a real number with no phase angle in the result. No complex numbers either and no phasors which actually appear in Chapter 8.
Clearly this function ranges between +/- 1.
Therefore the ratio, sin(wt)/sin(wt + 45) ranges between +/- infinity. No other math is required. Since the value varies wildly, it is of no use in circuit analysis.
The concept of impedance is developed from the instantaneous equations with the aid of some higher math. It is only applicable to steady steady state equations.
Instantaneous equations, in general, require the application of differential equations which are messy. Steady state methods avoid this messiness.
Something wrong here:
It is obvious that some do not understand the difference between steady state and instantaneous equations. The value of,
sin(wt + phi),
is just a number that you would read off your calculator or from the trig tables. The phase angle "phi" merely shifts the function in time and does not appear in the value. For example, at t= 0 and phi = 45 deg.,
sin(0 + 45) = sqrt(2)/2
That is all, just a real number with no phase angle in the result. No complex numbers either and no phasors which actually appear in Chapter 8.
Clearly this function ranges between +/- 1.
Therefore the ratio, sin(wt)/sin(wt + 45) ranges between +/- infinity. No other math is required. Since the value varies wildly, it is of no use in circuit analysis.
The concept of impedance is developed from the instantaneous equations with the aid of some higher math. It is only applicable to steady steady state equations.
Instantaneous equations, in general, require the application of differential equations which are messy. Steady state methods avoid this messiness.
gar
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In an earlier post I created a time varying resistance by motor driving a variable resistor.
I can do the same with a variable capacitor and thus have a time varying reactive component.
.
In an earlier post I created a time varying resistance by motor driving a variable resistor.
I can do the same with a variable capacitor and thus have a time varying reactive component.
.
drbond24
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I love this post, and not just because I get honorable mention at the end.
I was cheering before I even read that. 
kingpb
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