Delta symbol used in formulas
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billsnuff
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In general it means the difference in or change in
Seems like it means : how does the voltage at the end of a conductor change with the difference in current at the beginning of a conductor.
If I had to guess, the input current which is abbreviated I(initial) is inversely proportional to the voltage V (terminal) or sometimes abbreviated E (terminal).
It would make more sense though if the question read:
how does the voltage at the end of a conductor change relative to the input voltage with respect to the length. however thats a completely different question but more common.
PS> The "triangle" is actually a "delta" symbol. Delta is the greek letter "D" in their alphabet. It stands for a change of any type. For example if the temperature is 55 and it increases to 60, the Delta "T" would be 5 degrees.
Similarly, if the initial V (voltage) is 120V and the terminal voltage is 115V, the Delta V would be 5 volts. Sometimes this is referred to as the "potential difference". So more appropriately the potential difference is 5 Volts, ie. delta V.
If I had to guess, the input current which is abbreviated I(initial) is inversely proportional to the voltage V (terminal) or sometimes abbreviated E (terminal).
It would make more sense though if the question read:
how does the voltage at the end of a conductor change relative to the input voltage with respect to the length. however thats a completely different question but more common.
PS> The "triangle" is actually a "delta" symbol. Delta is the greek letter "D" in their alphabet. It stands for a change of any type. For example if the temperature is 55 and it increases to 60, the Delta "T" would be 5 degrees.
Similarly, if the initial V (voltage) is 120V and the terminal voltage is 115V, the Delta V would be 5 volts. Sometimes this is referred to as the "potential difference". So more appropriately the potential difference is 5 Volts, ie. delta V.
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I always assume it means change when used in electrical formulae. Often the Delta symbol, not being a standard part of a QWERTY keyboard, is just shown as a capital D. If you use your character map however, you can show it by selecting and copying it.
Δ = Delta = D
So Rint = DV/DI is telling you that you can calculate the internal resistance in something by looking at the change in voltage divided by the change in current. So if you have a device that you do not know the internal resistance of and you cannot measure it directly, you can determine it by changing the voltage by a known amount, observing the change in current, and dividing the first value by the second.
Δ = Delta = D
So Rint = DV/DI is telling you that you can calculate the internal resistance in something by looking at the change in voltage divided by the change in current. So if you have a device that you do not know the internal resistance of and you cannot measure it directly, you can determine it by changing the voltage by a known amount, observing the change in current, and dividing the first value by the second.
GeorgeB
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The only ting I'll add to Jreaf's post is that, in my experience, lower case d is always used, dV/dI. This probalby comes from the derivative terminology.
wiigelec
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From a purely mathematical standpoint:
Rint = dV/dI
If you were to plot V and I with V on the y-axis and I on the x-axis, R would be the tangential slope at any instantaneous point on that plot.
http://en.wikipedia.org/wiki/Differential_calculus
If the plot for V versus I is a straight line, R is constant, otherwise R is a function of (dependant on) V and I and is not constant...
Rint = dV/dI
If you were to plot V and I with V on the y-axis and I on the x-axis, R would be the tangential slope at any instantaneous point on that plot.
http://en.wikipedia.org/wiki/Differential_calculus
If the plot for V versus I is a straight line, R is constant, otherwise R is a function of (dependant on) V and I and is not constant...
Right. If you have a constant or linear resistance, then you only need to use R=V/I. If you did calculate delta V/ delta I, it would be the same as V/I, and it doesn't matter which points you use.
For a non-linear resistance (a diode for example), the resistance graph is a curve, and delta V/ delta I is the AC resistance, or the "small signal resistance". Its value depends on which points you use for the calcualation.
For example, think about an audio signal superimposed on a DC voltage, and passed through a diode. To the audio signal, the DC resistance of the diode doesn't matter, but the AC resistance does matter.
gar
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110411-1600 edt
In my first calculus book "Elements of The Differential and Integral Calculus", by Granville, Smith, and Longley, 1934, the delta symbol is introduced in Chapter III with the definition:
delta y denotes an increment of y
This does not imply infinitesimal.
However, if you take a fraction such as delta y/ delta x and evaluate this as delta x approaches 0, and further add the condition of the limit as delta x approaches 0, then this becomes the definition of the derivative of y over x. This is written as
dy/dx = the limit as delta x approaches 0 of delta y / delta x
Shown more accurately on page 21 of the above book.
So delta means a difference and not necessarily small. But if you then study how a function varies as the independent variable approaches 0, then you have obtained the derivative of that function. And yes in this class of math you can divide by zero and get a finite value. But you divided by zero by determining what happens as you make the increment in the independent variable smaller and smaller.
As was mentioned above if you have the equation r = e/i and apply this to a constant value resistor independent of the value of i you will find that for any small change in i that you get a directly proportional small change in voltage.
If you consider a diode and perform an experiment where there are small changes in current at different current levels the result will be different ratios of voltage change to current change as the current is changed. This is a non-linear resistor.
.
In my first calculus book "Elements of The Differential and Integral Calculus", by Granville, Smith, and Longley, 1934, the delta symbol is introduced in Chapter III with the definition:
delta y denotes an increment of y
This does not imply infinitesimal.
However, if you take a fraction such as delta y/ delta x and evaluate this as delta x approaches 0, and further add the condition of the limit as delta x approaches 0, then this becomes the definition of the derivative of y over x. This is written as
dy/dx = the limit as delta x approaches 0 of delta y / delta x
Shown more accurately on page 21 of the above book.
So delta means a difference and not necessarily small. But if you then study how a function varies as the independent variable approaches 0, then you have obtained the derivative of that function. And yes in this class of math you can divide by zero and get a finite value. But you divided by zero by determining what happens as you make the increment in the independent variable smaller and smaller.
As was mentioned above if you have the equation r = e/i and apply this to a constant value resistor independent of the value of i you will find that for any small change in i that you get a directly proportional small change in voltage.
If you consider a diode and perform an experiment where there are small changes in current at different current levels the result will be different ratios of voltage change to current change as the current is changed. This is a non-linear resistor.
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