Ohm's Law
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mivey said:
It is also called "dynamic resistance" and is defined as the slope of the v/i curve at the operating point, that is,
r = dv/di
(it is "r", not "dr")
This concept is widely used in small signal AC analysis and active devices such as transistors and vacuum tubes.
ELA
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rattus said:
LarryFine said:
Rattus and others posturing here: Maybe we should just start a poll on who is the smartest participant here?
I thought Larry explained very well that the circuit behaves as if!
It is often useful to "think of" circuit behavior in simpler terms to help our understanding of what is going on. No need to jump on someone for that.
Thinking in strict theory will get you into trouble if you miss a decimal point on your calculator.
gar
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080628-1248 EST
larry:
See http://dictionary.reference.com/browse/impedance
for their definition of impedance.
You would not normally consider a capacitor to have an impedance dependent capacitor charge. If it did, then it would be described as a voltage variable capacitor.
In normal useage impedance will apply to steady-state conditions with single frequency (sine wave) excitation. In the battery, switch, resistor and capacitor example this is really a transient DC type circuit. The way to view this capacitor is that v = q/C where v is the capacitor voltage, q is the capacitor charge, and C the capacitance of the capacitor. Current is the rate of flow of charge, or i = dq/dt, In turn q = the integral of i dt. Thus, v capacitor = integral of i dt/C + an initial constant.
As charge flows thru the resistor this increases the voltage on the capacitor, but now the current thru the resistor is (Vbat - Vcap)/R. Therefore the higher the voltage on the capacitor the less charging current and in turn the capacitor voltage changes more slowly.
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larry:
See http://dictionary.reference.com/browse/impedance
for their definition of impedance.
You would not normally consider a capacitor to have an impedance dependent capacitor charge. If it did, then it would be described as a voltage variable capacitor.
In normal useage impedance will apply to steady-state conditions with single frequency (sine wave) excitation. In the battery, switch, resistor and capacitor example this is really a transient DC type circuit. The way to view this capacitor is that v = q/C where v is the capacitor voltage, q is the capacitor charge, and C the capacitance of the capacitor. Current is the rate of flow of charge, or i = dq/dt, In turn q = the integral of i dt. Thus, v capacitor = integral of i dt/C + an initial constant.
As charge flows thru the resistor this increases the voltage on the capacitor, but now the current thru the resistor is (Vbat - Vcap)/R. Therefore the higher the voltage on the capacitor the less charging current and in turn the capacitor voltage changes more slowly.
.
LarryFine
Master Electrician Electric Contractor Richmond VA
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- Henrico County, VA
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- Electrical Contractor
That I understand. What I was saying, and what ELA caught (Thanx!), is that, since the resistor's impedance can be considered constant, and the only other element in the loop is the cap, the latter certainly looks like its impedance is increasing as it approaches the source voltage.gar said:
Of course, if that source voltage varies, as it would if it were AC, the apparent impedance of the cap changes proportionately with the difference between the source's voltage and the cap's voltage, at any one moment in time. Apparent impedance, as in that's how it seems to affect the current.
Correct me if I'm wrong (as if I could stop you :grin
: A capacitor's charging current peaks during the greatest voltage difference between the source and the cap, and not during the source's voltage peak. A series resistor limits the charging current, but doesn't the current peak still occur at the same time?The timing difference between the supply's peak voltage point and the cap's peak voltage point, in relation to the period of a complete wave, seems to me to be what we commonly refer to as the leading phase of capacitive loads, unless I'm missing something.
Why can't a cap exhibit an impedance? Sources certainly do. A 12v car battery definitely has a lower impedance than a 12v photo battery does.
gar
Senior Member
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- Ann Arbor, Michigan
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080628-1949 EST
larry:
I believe what you are doing is trying to creating a colloquial definition for impedance. There is a lot of loose usage of the word impedance, and I tend to do this also.
I think the dictionary definition I referenced above is fairly useful. I have looked at a couple of sources and as is usual the definitions given are not addressing the issue directly by saying impedance is ---, and including all the conditions.
In "Analysis of A-C Circuits", by Melville B. Stout, University of Michigan, copyright 1952. This was not broadly published.
Page 16. Impedance is defined as
Z = sq-root ( R^2 + X^2 )
By implication this is defined for a sinusoidal signal and of a specific single frequency. Further it is assuming a steady-state condition.
Another source
"Radio Engineering Handbook", by Keith Henny, Editor-in-Chief, McGraw-Hill, 1941.
Page 34.
"22. Impedance. The resistance to the flow of electric current having the value i = Io sin wt depends upon the circuit element through which the current is passing. ---- "
Again the use of a steady-state sine wave.
These definitions of impedance do not encompass a transient or DC condition.
In the series RC example the impedance of the series combination is defined by Stout's definition. Also true if we look at the capacitor alone where Z = sq-root ( X^2 ) or just X.
Z is a function of frequency and in the limit near zero frequency it is virtually all capacitive reactance, and near infinite frequency all resistive.
I won't comment on your phase points at this time. However, here is a senior class question by A. D. Moore. What is the maximum possible phase shift of an RC circuit?
A big part of Moore's class was devoted to manual graphical field mapping. He had a speciality of analog computing of fields via a three dimensional fluid flow. This predated computers. Very tough on students, especially in back seats, and ones that did not respond to questions unless specifically mentioned by name. You needed to be prepared before class. He did not worry about hurting your self-esteem.
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larry:
I believe what you are doing is trying to creating a colloquial definition for impedance. There is a lot of loose usage of the word impedance, and I tend to do this also.
I think the dictionary definition I referenced above is fairly useful. I have looked at a couple of sources and as is usual the definitions given are not addressing the issue directly by saying impedance is ---, and including all the conditions.
In "Analysis of A-C Circuits", by Melville B. Stout, University of Michigan, copyright 1952. This was not broadly published.
Page 16. Impedance is defined as
Z = sq-root ( R^2 + X^2 )
By implication this is defined for a sinusoidal signal and of a specific single frequency. Further it is assuming a steady-state condition.
Another source
"Radio Engineering Handbook", by Keith Henny, Editor-in-Chief, McGraw-Hill, 1941.
Page 34.
"22. Impedance. The resistance to the flow of electric current having the value i = Io sin wt depends upon the circuit element through which the current is passing. ---- "
Again the use of a steady-state sine wave.
These definitions of impedance do not encompass a transient or DC condition.
In the series RC example the impedance of the series combination is defined by Stout's definition. Also true if we look at the capacitor alone where Z = sq-root ( X^2 ) or just X.
Z is a function of frequency and in the limit near zero frequency it is virtually all capacitive reactance, and near infinite frequency all resistive.
I won't comment on your phase points at this time. However, here is a senior class question by A. D. Moore. What is the maximum possible phase shift of an RC circuit?
A big part of Moore's class was devoted to manual graphical field mapping. He had a speciality of analog computing of fields via a three dimensional fluid flow. This predated computers. Very tough on students, especially in back seats, and ones that did not respond to questions unless specifically mentioned by name. You needed to be prepared before class. He did not worry about hurting your self-esteem.
.
Not at all:
Not at all:
I strongly disagree, you only increase misunderstanding by misusing terms which are precisely defined.
It is not a change of impedance, it is a reduction of voltage across the series resistor that causes the current to decrease.
Furthermore,
Impedance must be considered to be a constant to be a useful circuit parameter.
Impedance is not defined in time-domain problems such as a capacitor charging from a step function voltage. Impedance is only defined for steady state solutions with RMS values.
gar has already said this, but I had to say it again.
Not at all:
ELA said:
I strongly disagree, you only increase misunderstanding by misusing terms which are precisely defined.
It is not a change of impedance, it is a reduction of voltage across the series resistor that causes the current to decrease.
Furthermore,
Impedance must be considered to be a constant to be a useful circuit parameter.
Impedance is not defined in time-domain problems such as a capacitor charging from a step function voltage. Impedance is only defined for steady state solutions with RMS values.
gar has already said this, but I had to say it again.
LarryFine
Master Electrician Electric Contractor Richmond VA
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- Henrico County, VA
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- Electrical Contractor
We've always been taught that it's 90 degrees.gar said:
LarryFine
Master Electrician Electric Contractor Richmond VA
- Location
- Henrico County, VA
- Occupation
- Electrical Contractor
Oops!
LarryFine
Master Electrician Electric Contractor Richmond VA
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- Henrico County, VA
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- Electrical Contractor
You mean it's not the reduction of current that causes the voltage across the resistor to decrease??? :-?rattus said:
gar
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larry:
Here is the trick to the question ---
The wording RC circuit does not limit the circuit to a single resistor and capacitor.
Thus, Hewlett and Packard started their company with an oscillator based on an RC circuit with a 180 degree phase shift from a 3 or 4 stage variable capacitor tuned RC circuit. One other inovation of that oscillator was a tungsten filament bulb used for voltage stablization as the RC circuit gain changed from one end of the range to the other.
.
larry:
Here is the trick to the question ---
The wording RC circuit does not limit the circuit to a single resistor and capacitor.
Thus, Hewlett and Packard started their company with an oscillator based on an RC circuit with a 180 degree phase shift from a 3 or 4 stage variable capacitor tuned RC circuit. One other inovation of that oscillator was a tungsten filament bulb used for voltage stablization as the RC circuit gain changed from one end of the range to the other.
.
ELA
Senior Member
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- Electrical Test Engineer
rattus said:
Misusing the term "As If" ? What part of that do you not understand?
I think you should read a little more closely. Wouldn't it have been easier to have recognized your error in reading than to continue to posture?
Or is it that if we do not think like just Rattus does that you will continue to beat it to death until we do:roll:
rattus said:
Was that for added value or that it had to come from you?
ELA said:
I do not understand why one would use such an analogy instead of explaining what really happens. It would be more meaningful to use the analogy of a tire being inflated from a fixed pressure source. When the pressures equalize, the air stops flowing. When the voltages equalize, the current stops flowng.
No error in reading. It is simply wrong to speak of impedance in time domain problems. It is not a matter of my opinion; it is simply a matter of TRVTH.
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rattus said:
Now who is not speaking in absolutes? :grin:
LarryFine
Master Electrician Electric Contractor Richmond VA
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- Henrico County, VA
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- Electrical Contractor
I agree that the voltage causes the current to flow, but it's the resultant current that causes the voltage drop to occur.rattus said:
My point is that the varying voltage drop across the fixed series resistor behaves as if the capacitor's impedance varies with the voltage difference between the supply and the cap.
I'm not saying it's a great point, nor even an accurate one; just that it's mine. That's all we have in life sometimes.
quogueelectric
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Would you prefer mayonaise or mustard??rattus said:
mivey
Senior Member
I would say rattus is going to go hungry because how would you prove him wrong? It is like the Monty Python question "what is your favorite color?"quogueelectric said:
The question as posed:
The definition according to rattus is whatever he wants it to be. Now had the question been asked differently, there may be a meal in the making. For example:ELA said:
Can the voltage change and current change happen simultaneously if the source and device do not occupy the same space? (some relativity silliness)
The events will never be exactly coincident in an absolute sense, but we are not working at that level. Without more parameters, simultaneity is in the eye of the beholder, so to speak.
In my opinion, I can continuously flip two light switches simultaneously. I can build a timing circuit that would disagree. Einstein would also disagree, from an absolute standpoint.
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