Something Different:

[steve66]

But Steve, there is no way that the ratio of v(t)/i(t) could be 0.866 -j0.5 because the ratio, v(t)/i(t), at any point in time, is a single real number.

Who says it has to be a single real number. And now you are adding another constraint to the original question by adding "at any point in time."

Furthermore, the ratio would have to be constant before it could be called "impedance", and it is not.

0.5 ohms of R in series with 0.866 ohms of Xc is just as constant as the number 4 is.

I could pass off our differences on the original question, since it has become obvious that the question you asked is not the question you wanted to ask.

However, your conclusion:

Simply put, impedance and reactance are undefined for instantaneous equations. You must use RMS values in a steady state analysis.

is utter nonsense. And you complained about someone else confusing people with their unproven theories.....

Since the impedance determines the magnitude, shape, and phase of the current, is should be blatantly obvious that it also determines the instantaneous values that make up that current.

 

[rattus]

Who says it has to be a single real number. And now you are adding another constraint to the original question by adding "at any point in time."

Whoever invented trigonometry says so.

-1 LTE sin(wt) LTE +1

These are real numbers! There is no j operator. Then the ratio of two sinusoids at any point in time must be a single real number. These are the numbers you pull off your calculator. Just numbers, nothing else.

0.5 ohms of R in series with 0.866 ohms of Xc is just as constant as the number 4 is.

Indeed it is, but

- inf LTE sin(wt)/sin(wt -30) LTE +infinity

Clearly, this is not a constant.

Since the impedance determines the magnitude, shape, and phase of the current, is should be blatantly obvious that it also determines the instantaneous values that make up that current.

Maybe so, but you cannot use reactance and impedance in instantaneous equations. We went through this same discussion a couple of years ago if you remember.

Reactance and impedance are used with RMS voltages and currents which are constants whereas any function of time varies. Clearly v(t) and i(t) are not constants and their ratio cannot be constant except in one special case.

 

[steve66]

We went through this same discussion a couple of years ago if you remember.

Yes, and back then your claim was that phasors could not be used to determine instantaneous values of current or voltage.

Now you have added impedence and reactance.

You didn't have a clue then, and you don't have a clue now. Its so staggering simple, yet you just don't get it.

Give me a voltage, and an impedence (like you did in post #22 for example). Then I will calculate the current for any instant in time. Yet, you will say it can't be done.

Give me a voltage and current, and I will give you the impedence. Again, you will spew argument after argument that it can't be (even though every 1st semester student learns this.)

You will ignore all correct answers and explinations that have any use to calculating or predicitng what will happen in an electrical circuit, and just repeateldy claim that everyone else is wrong.

I give up. You are hopeless.

 

[rattus]

Give me a voltage and current, and I will give you the impedence. Again, you will spew argument after argument that it can't be (even though every 1st semester student learns this.)

Alright,

v(t) = 1.0v
i(t) = 0.0a

again for the same circuit, let

v(t) = 0.0v
i(t) = 1.0a

which result provides the impedance?

 

[Hameedulla-Ekhlas]

Alright,



which result provides the impedance?

Rattus:
Can we call v(t)/i(t) = instantanteous impedance ?

 

[Smart $]

...

Maybe so, but you cannot use reactance and impedance in instantaneous equations. ...

Yes, you can. But to do so, you have to use an instantaneous equation. You wouldn't use a Vrms value in an instantaneous power equation, would you?

For example, say your circuit impedance is 2 ohms reactive, operating at 1.414Vrms and .707Arms with current lagging voltage by 30?.

v(t) = |v|cos(ωt)
i(t) = |i|cos(ωt-π/6)

...and |v| = 2 and |i| = 1​

then

v(t)/i(t) = z(t) = |z|cos(θ)-tan(ωt+θ) ...when θ<0
v(t)/i(t) = 2Ω*cos(π/6)-tan(ωt-π/6)​

...and as I said before |z| = |v|/|i| in units of ohms.

 

[Hameedulla-Ekhlas]

Yes, you can. But to do so, you have to use an instantaneous equation. You wouldn't use a Vrms value in an instantaneous power equation, would you?


...and as I said before |z| = |v|/|i| in units of ohms.

Smart$:
In post 69 I had given an example of transmission line and it was a good example.

 

[Smart $]

Smart$:
In post 69 I had given an example of transmission line and it was a good example.

A good example of a transmission line

Can you make the connection to what we have been discussing though???

 

[rattus]

Yes, you can. But to do so, you have to use an instantaneous equation. You wouldn't use a Vrms value in an instantaneous power equation, would you?

For example, say your circuit impedance is 2 ohms reactive, operating at 1.414Vrms and .707Arms with current lagging voltage by 30?.

v(t) = |v|cos(ωt)
i(t) = |i|cos(ωt-π/6)

...and |v| = 2 and |i| = 1​

then

v(t)/i(t) = z(t) = |z|cos(θ)-tan(ωt+θ) ...when θ<0
v(t)/i(t) = 2Ω*cos(π/6)-tan(ωt-π/6)​

...and as I said before |z| = |v|/|i| in units of ohms.

Smart, why did I not learn this in engine school? Could it be because your Machivellian math yields a non-constant impedance which at best is useless and at worst confusing.

Someone may come to believe this nonsense.

Now do something useful and plot your z(t) as a function of time to demonstrate its wild excursions.

 

[Hameedulla-Ekhlas]

A good example of a transmission line

Can you make the connection to what we have been discussing though???

Can we not call v(t)/i(t) an instantaneous impedance?

 

[Hameedulla-Ekhlas]

A good example of a transmission line

Can you make the connection to what we have been discussing though???

Ok if you dont like that than see this example and by solving, it can explain all the result of v(t)/i(t) in different situation

In a RLC circuit, if we have t<0 or t = 0 that v(t)/i(t) = R and if we have t > 0 than the inductance and capacitance also exist.

We say v(t) / i(t) = R for t < 0 or t = 0
v(t) / i(t) = z only for t > 0

 

[Smart $]

Smart, why did I not learn this in engine school?

I don't know. Isn't that a question better answered by you and or your school

Could it be because your Machivellian math yields a non-constant impedance which at best is useless and at worst confusing.

Again, I don't know. But I'm going to go out on a limb and surmise that you believe it is :roll:

Someone may come to believe this nonsense.

Quite likely.

Now do something useful and plot your z(t) as a function of time to demonstrate its wild excursions.

I already have, and you know it, too. So quit wasting my time with repetitious demands. The reality of it is: it is what it is and I'm not trying to make it into anything other than what it is.

 

[Smart $]

Ok if you dont like that than see this example and by solving, it can explain all the result of v(t)/i(t) in different situation

In a RLC circuit, if we have t<0 or t = 0 that v(t)/i(t) = R and if we have t > 0 than the inductance and capacitance also exist.

We say v(t) / i(t) = R for t < 0 or t = 0
v(t) / i(t) = z only for t > 0

This is an elementary learning block in the analysis of signal (or wave) propagation. It has some significance to the discussion at hand, but I doubt most readers will get the gist of it. I have almost completely forgotten everything I learned about it. Ol' use it or lose it has crept in along the way :roll:

 

[Hameedulla-Ekhlas]

This is an elementary learning block in the analysis of signal (or wave) propagation. It has some significance to the discussion at hand, but I doubt most readers will get the gist of it. I have almost completely forgotten everything I learned about it. Ol' use it or lose it has crept in along the way :roll:

Smart$:Yes, I think this circuit can explain what is v(t)/i(t) but I am really wondering, no one gave me the definition or explaination of instantaneous impedance.

 

[Smart $]

Smart$:Yes, I think this circuit can explain what is v(t)/i(t) but I am really wondering, no one gave me the definition or explaination of instantaneous impedance.

Perhaps... but it subscribes to the theory of charge compression and decompression at the leading/trailing edges of the signal. Power engineering [normally] does not integrate the notion when limited to a local event. One reason being the frequency is on the lower end of the bandwidth scale. Another is we typically evaluate from an in-progress viewpoint. The concept you are putting on the table is more related to startup surge. Ad to that the measurements are typically of a fixed location rather than moving along the circuit path as the signal travels to and from source to load.

As for a definition of instantaneous impedance, I'm doubt you will find a widely-accepted one. Since the discussion began with considering v(t)/i(t), I'd say that it will prove to be as widely accepted as you are going to get.

One previously elusive point that you bring to the table is impedance analysis of reactive components in a DC circuit. AC rms and average values do not apply here, yet ohmage plotted vs. time is not constant here either. Yet aren't AC rms and average values based on DC equivalent?

 

[Hameedulla-Ekhlas]

Perhaps...

AC rms and average values do not apply here, yet ohmage plotted vs. time is not constant here either.

One previously elusive point that you bring to the table is impedance analysis of reactive components in a DC circuit.

It was also step function exmaple.

The solution for what is v(t) / i(t) and why R or z is the analysis of time domain and step fuction. This example is a linear circuit and without any intial capacitor charge. The unique solution is

We say v(t) / i(t) = R for t < 0 or t = 0
v(t) / i(t) = z only for t > 0

Yet aren't AC rms and average values based on DC equivalent?

Since the mean value is an average of squared values, the square root of the mean is the single value that is equivalent to a steadystate dc value.

v(t) / i(t) = ?

One more thing let me mention that since v(t) / i(t) is the time domain step fuction analysis.

We say v(t) / i(t) = R for t < 0 or t = 0

But for t > 0 v(t) / i(t) = z I have doubt in this. Because since we are in time domain and we have all R, L and C. R is ohm, L is mh, and C is micro F.
Now in frequency domain we change easily C and L to Xc or XL by only multiplying the jwL or jwC. How can you add in time domain C, L and R to say that v(t) / i(t) = z ? I may be confused or any idea. Hope to give some explaination.

But what I have seen the instantaneous impedance in signal analysis which is also called characteristic impedance. Even in signal or transmission line j cancells and we get simple real number with unit ohm

 

[skeshesh]

Now in frequency domain we change easily C and L to Xc or XL by only multiplying the jwL or jwC. How can you add in time domain C, L and R to say that v(t) / i(t) = z ? I may be confused or any idea. Hope to give some explaination.

But what I have seen the instantaneous impedance in signal analysis which is also called characteristic impedance. Even in signal or transmission line j cancells and we get simple real number with unit ohm

I was resisting throughout this discussion to dust off books from college since I'm buried in work but I think I'm going to try in the next few days or the weekend.

As a quick (and admittedly unverified) response, I believe the fourier transform to go from time to frequency domain requires evaluating a Riemann summation, and the way we solve this to arrive at the general definition of the Fourier Transform is by letting the limit of integration (in this case time) to go to infinity. If the function fluctuates greatly in time it becomes very difficult to evaluate the transform so I believe classic definition of 'impedance' is based on steady state, in other words having the same function for all t>0.

Having said this there are applications where impedance at different periods are evaluated seperately, i.e. sub-transient and transient fault analysis, etc. As Laszlo pointed out in either this or another recent topic, how instantaneous is instantaneous? One could argue even using the most advanced equipment you are still looking at a defined period of time and hence you are again looking at the same definition of impedance.

 

[rattus]

Waiting:

Waiting:

Alright,

v(t) = 1.0v
i(t) = 0.0a

again for the same circuit, let

v(t) = 0.0v
i(t) = 1.0a

which result provides the impedance?

Steve must be busy. Anyone else care to answer? bondo, cf?

Let me try to explain another way:

In a linear analysis, impedance must be constant.

Then in general, the following must be true if v(t)/i(t) is a valid expression,,

1) i(t)*K = v(t)--for any instant of time

but there is no value of K which will satisfy eqn. 1, therefore we must conclude that the ratio, v(t)/i(t) is not a valid expression for impedance.

Now I have tried to emphasize that one must evaluate i(t) and v(t) and then divide the results. No one has asked for anything else. No effective value, no average value, no form factor, nothing. Just a simple ratio.

Furthermore, to be of use, such a ratio must be valid for all waveforms, and it is only for sinusoids that impedance is defined--just another nail in the coffin of z(t).

 

[Hameedulla-Ekhlas]

Steve must be busy. Anyone else care to answer? bondo, cf?

Let me try to explain another way:

In a linear analysis, impedance must be constant.

Then in general, the following must be true if v(t)/i(t) is a valid expression,,

1) i(t)*K = v(t)--for any instant of time

z(t).

but there is no value of K which will satisfy eqn. 1,

v(t) = 1.0v
i(t) = 0.0a -------------------------this condition eq-1

again for the same circuit, let

v(t) = 0.0v
i(t) = 1.0a ---------------------------this condition eq-2

ratuss: Is that what you mean by eq-1

 

[Hameedulla-Ekhlas]

1) i(t)*K = v(t)--for any instant of time

z(t).

Now in this circuit for t > 0, the value of v(t) / i(t) = ? for v(t) = 12 t > 0