Something Different:

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drbond24 said:
What caused the 30 degree lag?
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Bondo, it does not matter what caused the lag.

These are functions of time. They are NOT RMS equations.

The evaluation of the sine functions returns REAL not complex numbers--no phase angles either.

You need to review instantaneous equations in Ch. 1 of your AC Circuits text.
 
Hameedulla-Ekhlas said:
you asked the value of v(t) and i(t) which is already had given as a number and you did not mention the ratio. Ok but any way, thanks for all and you are right.
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I was actually responding to Steve66's claim that he could compute the impedance from the values of voltage and current.
 
rattus said:
Bondo, it does not matter what caused the lag.

These are functions of time. They are NOT RMS equations.

The evaluation of the sine functions returns REAL not complex numbers--no phase angles either.

You need to review instantaneous equations in Ch. 1 of your AC Circuits text.
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Chapter 1 says v(t) is an independant voltage source that maintains the same voltage across its terminals regardless of the current through it and i(t) is an independant current source that maintains the same current output regardless of the voltage across it. Are these the definitions you were thinking of in the first post?
 
drbond24 said:
Chapter 1 says v(t) is an independant voltage source that maintains the same voltage across its terminals regardless of the current through it and i(t) is an independant current source that maintains the same current output regardless of the voltage across it. Are these the definitions you were thinking of in the first post?
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Not exactly. We can consider v(t) to be an AC voltage source across a load; then i(t) would be the resulting AC load current.

But, by using lower case and "(t)" we indicate that both are functions of time, that is,

v(t) = Vm[sin(wt)]
and
i(t) = Im[sin(wt + phi)] where phi is the lead or lag angle.

The evaluation of these functions at any instant of time yields a real number--that is all. A plot of v and i vs wt yields two sine waves displaced by the angle phi. But, the voltages and currents so plotted are REAL numbers--no phase angle.

Clearly, the ratio of v and i is not constant unless phi = 0.

The point is that the idea of impedance as a function of time is nonsense.
 
rattus said:
...the idea of impedance as a function of time is...
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On the above quoted part, I'll agree with you. This can be shown by writing out the formula as complex exponential functions...

SomethingDifferent2.gif


Note how the time variable cancels out of the formula.
 
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Hameedulla-Ekhlas said:
Could you please post a circuit diagram for this v(t) / i(t).
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Ham, there are an infinite number of possibilities, but for the case where i lags v by 45 degrees, you can try a series RL circuit where R = wL. Bear in mind though, that we are discussing v(t) and i(t). We haven't learned about RMS values or phasors yet.
 
rattus said:
Ham, there are an infinite number of possibilities, but for the case where i lags v by 45 degrees, you can try a series RL circuit where R = wL. Bear in mind though, that we are discussing v(t) and i(t). We haven't learned about RMS values or phasors yet.
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Mmm. R = wL, v(t) and i(t) are constants. vL = L di/dt I will think all about these...
 
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Hameedulla-Ekhlas said:
Mmm. R = wL, v(t) and i(t) are constants. vL = L di/dt I will think all about these...
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Ham, v(t) and i(t) are not constants; they are functions of time.

For the RC series circuit example, you could use any values of R and C you wish, e.g.,

R = 1/wC would provide a 45 degree leading current, but that would not be obvious if v(t) is a step function.
 
Finis:

Finis:

With one vote for meaningless, another for nonsense, and in the absence of any proof to the contrary, we must conclude that the notion of z(t) is,

"Meaningless nonsense".
 
rattus said:
Ham, v(t) and i(t) are not constants; they are functions of time.

For the RC series circuit example, you could use any values of R and C you wish, e.g.,

R = 1/wC would provide a 45 degree leading current, but that would not be obvious if v(t) is a step function.
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rattus: Please see this example, is that what you mean

28aurlt.png
 
rattus said:
Bondo, I think the words mean essentially the same thing.
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Their definitions do overlap; what I'm saying is that v(t) / i(t) provides perfectly good numbers that can be plotted on a graph and show a periodic curve that varies to +/- infinity and has asymptotes everywhere that i(t) = 0. It exists and can be calculated with math. If for no other reason than to give a math student something to do, it can be shown that the ratio exists and is defined. Therefore it isn't nonsense. Perhaps useless would be a better word? I agree with your statement that it isn't useful in circuit analysis.
 
drbond24 said:
Their definitions do overlap; what I'm saying is that v(t) / i(t) provides perfectly good numbers that can be plotted on a graph and show a periodic curve that varies to +/- infinity and has asymptotes everywhere that i(t) = 0. It exists and can be calculated with math. If for no other reason than to give a math student something to do, it can be shown that the ratio exists and is defined. Therefore it isn't nonsense. Perhaps useless would be a better word? I agree with your statement that it isn't useful in circuit analysis.
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Why not just plot the tangent as I had to many moons ago? The tangent is meaningful.
 
rattus said:
Why not just plot the tangent as I had to many moons ago? The tangent is meaningful.
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Hmmm... plotting tangent = meaningful?
Yet plotting v(t)/i(t), a variation on plotting tangent, ≠ meaningful?

If that be the case, I have to surmise I missed a lesson :roll:
 
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