Something Different:

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steve66

Senior Member
Location
Illinois
Occupation
Engineer
If v(t) and i(t) are sine waves, the result is the impedence.

We can see this by transforming v(t) and i(t) to their phasor equivalents, and using the definition of impedence.

BTW, in case this enters the converstation, I have a reference in one textbook that states that although impedence doesn't vary with time, it is normally treated as a phasor.

If v(t) and i(t) are not sine waves, say they are step functions, or a discontinuous function, I believe we can still use transforms (Laplace?) or convolution and find something similar to an impedence. But I haven't had to think about that since college.


Steve
 

Smart $

Esteemed Member
Location
Ohio
Who thinks that the expression,

v(t)/i(t)

has any meaning? If so, what meaning?
I sorta brought this up in the Power factor and VA vs Watts around post #20. The discussion on this jumps around as there are posts/replies to others intermixed. Anyway, I initially and errantly called it impedance... but later changed it to the resistance equivalent of impedance.
 

charlie b

Moderator
Staff member
Location
Lockport, IL
Occupation
Retired Electrical Engineer
Of course it has meaning. All expressions have meaning. The matter of whether its meaning is of engineering interest is another question. ;):grin:
 

rattus

Senior Member
Slow down now:

Slow down now:

You guys are talking impedance which is defined only for the steady state.

Let me rephrase the question:

Does the ratio, v(t)/i(t), have any meaning or is it utter nonsense?

Assume a linear load and sinusoidal voltages and currents.
 

steve66

Senior Member
Location
Illinois
Occupation
Engineer
You guys are talking impedance which is defined only for the steady state.

Let me rephrase the question:

Does the ratio, v(t)/i(t), have any meaning or is it utter nonsense?

Assume a linear load and sinusoidal voltages and currents.

Doesn't a linear load, and sinusoidal voltage and currents, require us to be at steady state?

Besides, even if we aren't at steady state, we can take transforms of v(t) and i(t). Maybe those are V(X) and I(X). So the ratio V(X)/I(X) gives us some other function, say Z(X).

Z(X) is now a "Transfer Function" of the given circuit. And given any v(t), we can calculate V(X) and find out what I(X) would be by I(X) = V(X)* Z(X). Of course, once we know I(X), we can always transform it back and get i(t).

And Z(X) can also be transformed back to the time domain to obtain z(t), for a general frequency -f. However, if our input is not constant, it might be very difficult to transform Z(X) back to z(t,f). Maybe impossible, maybe just beyond our ability to calculate, who knows which.

So, if you have a problem with calling z(t,f) an impedence, maybe because it can vary with frequency or time, I'll provide what might be a more technically correct answer:

The transform of v(t)/i(t) is the transfer function of a particular circuit. This "transfer function" allows us to calculate the circuit response to any input. And I will stop just short of saying we can transform the "transfer function" back to find an impedence.

Steve
 

Cold Fusion

Senior Member
Location
way north
...Does the ratio, v(t)/i(t), have any meaning or is it utter nonsense?

Assume a linear load and sinusoidal voltages and currents.
I worked on this a bit (less than two hours) during one of the previous threads:

(sin(wt))/(sin(wt + a)) = ???

And I didn't get anywhere. I couldn't find any relief with:
trig identies
conversion to Euler's formula
Maclaurin/Taylor series
I even looked at Fourier/Lapace transforms

My conclusion was (is): My math skills, while normally excellent for power systems other than utility distribution, are simply below that required to make useful sense out of this concept.

However, I'll be listening and ready to gain understanding on the math model and the applications to power engineeing. I half suspect I am missing some simple concept that will provide the link - just because it has never come up before.

cf
 

drbond24

Senior Member
Who thinks that the expression,

v(t)/i(t)

has any meaning? If so, what meaning?

In order to answer this, I need to know if you are a college professor. In my experience, college profressors never ask questions like this unless they have a trick up their sleeve. Therefore, if you are, I call shenanigans and patiently await you to get tired of people guessing wrong and explain it. If you are not, you apparently should be. :D
 

rattus

Senior Member
No tricks, no prof:

No tricks, no prof:

In order to answer this, I need to know if you are a college professor. In my experience, college profressors never ask questions like this unless they have a trick up their sleeve. Therefore, if you are, I call shenanigans and patiently await you to get tired of people guessing wrong and explain it. If you are not, you apparently should be. :D

Just a simple question. No need for fancy math. As Jack Webb would say, "Just the facts ma'am".
 
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