# what does "d" signify in v=dw/dq, i=dq/dt

Discussion in 'General Electronics Chat' started by johnsmithne, May 5, 2016.

1. ### johnsmithne Thread Starter New Member

Mar 14, 2016
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Hi, new to electronics and just wondering what "d" signifies (v=dw/dq, i=dq/dt), it’s beginning to bug me. Why write it in if it doesn't have a purpose, I'm guessing at polarity, but as I say that is a guess. So if someone could enlighten me, Thanks.

2. ### wayneh Expert

Sep 9, 2010
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Derivative. For instance dx/dt is the change in x ( delta x) over delta y, in the limit where both approach zero.

3. ### profbuxton Member

Feb 21, 2014
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The "d" is calculus notation for change or differentiation. V="change of" W with respect to "change of" Q.
It is standard notation of a differential expression.

4. ### johnsmithne Thread Starter New Member

Mar 14, 2016
5
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Thank you Wayneh. I won't pretend to understand what that means, but at least now I have a starting point and I can look it up and work it out. Thanks again.

5. ### ErnieM AAC Fanatic!

Apr 24, 2011
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Here that "d" is not a variable but an operator for a calculus process to get what is basically the rate of change of an expression or function. It is a shorthand way, and it left out the dependent variable, or what the function changes by.

The full expression may perhaps better be written as:

i = d/dt ( q(t) )

Where q is some function of t or time. Now the d thingies stand out better as an opperator.

6. ### johnsmithne Thread Starter New Member

Mar 14, 2016
5
1
Tha
Thanks. Bought an arduino 3 months ago and it still in it box. Thought I had better study some basic electronics first, now I'm studying mathematics. Going to have to get my head around calculus. Have to say, total intrigued by it all, hopefully in 3 more months I will understand that concept. Thanks for the help.

Have to say this site is a great learning resource.

7. ### wayneh Expert

Sep 9, 2010
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I never tried it, but I believe self-teaching could be a difficult way to learn calculus. It was hard enough with a teacher. But maybe a well-written introduction would be better than a so-so teacher. Hmmm...

It's often useful to think of the derivative, such as dy/dx, as the slope of the curve when you plot the function y = ƒ(x). If that's a straight line, then dy/dx = ∆y/∆x = slope of y versus x. For anything else, the derivative is an instantaneous measure of the slope at a particular spot on the curve.

8. ### ElectronicMotor Member

May 1, 2016
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Lower case version of 'delta', Greek symbol 'd', Capital Case 'Δ', meaning 'Change'.
In the case of dv / dt, it is a ratio of an infinitely small change in quantity of voltage, measured over an infinitely small change in quantity of time.
Strangely, using Newtons method, v(t) = t[squared] + c so dv(t) / dt = 2.t. Somehow, an infinitely small value divided by another infinitely small value can have a finite value ?

Last edited: May 5, 2016
9. ### MrChips Moderator

Oct 2, 2009
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John, I am going to assume that you are an old timer just getting into electronics and didn't do Calculus in school.

As others have already stated, d is a substitute for Δ, (Greek letter meaning delta), and represents "change".

Suppose you want to build a flight of steps and you want a certain slope or incline. In layman's terms the incline is calculated as "raise over run".
That is, we divide the height of the riser by the depth of the tread.

incline = riser / depth

If we use symbols,
x = depth
y = riser

then

incline = y/x

Now, suppose your house is built on a hill.
We can compute the slope or incline up the hill from the public road in the similar manner:

incline = difference in elevation / distance to the house on a horizontal plane

This is similar to:

incline = y/x

Now, suppose the hill has a varying slope and we a want to measure the slope where it passes that tree.
We take a yardstick (or metre rule) and measure the slope at the vicinity of the tree.

Here we use

incline = Δy/Δx

where Δy is the difference in elevation and Δx is the distance along the horizontal.

(For the very observant reader, note that the Δx measurement must be made on a level plane.)
I know this isn't the greatest analogy but it's the best I can come up with.

In Calculus, we make Δy and Δx as small as possible, down to an inch, centimetre or even millimetre.
As we make the measurements to the smallest amount that is practical, we replace Δy and Δx with dy and dx,

Hence the slope = dy/dx represents the exact slope at that precise location.

The point here is the slope = dy/dx changes from place to place and represents the mathematical expression that describes how the slope varies along the entire path.

Hope this helps.

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10. ### GopherT AAC Fanatic!

Nov 23, 2012
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Yes, that infinitely small value is the slope of what would be a line between those two points that are separated by an infinitely small distance.

11. ### GopherT AAC Fanatic!

Nov 23, 2012
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I'm guessing john is a chemist. d=polarity (dipole). Welcome to the club.

12. ### nsaspook AAC Fanatic!

Aug 27, 2009
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Here is an ebook that explains all.

Last edited: May 5, 2016
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13. ### #12 Expert

Nov 30, 2010
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From an even less educated point of view...
dy/dx is the slope of the line, or the tangent of the angle.
If you don't know calculus, R=E/I
If you do know calculus, R = dE/dI
Most of the time, you can hack out the result with algebra, and rarely, a bit of trig.
Call me uneducated.
I only passed one semester of calculus and my brain never converted to thinking in those terms.

Ack! I put a plus sign where I meant an equal sign.
Corrected.

Last edited: May 5, 2016
14. ### Brownout Well-Known Member

Jan 10, 2012
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Interesting take. I would say R = dE/dI is a general formula that works for nonlinear resistance as well for linear resistance. R = E/I is a special case for linear resistance only.

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15. ### GopherT AAC Fanatic!

Nov 23, 2012
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But, for any two set of pair of infinitely close points, it is linear.

16. ### Brownout Well-Known Member

Jan 10, 2012
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Naturally, since that's a basic property of a derivative.

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17. ### ErnieM AAC Fanatic!

Apr 24, 2011
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The difference between two closely (or even widely) spaced points, oft known as the slope, is a number, a single number. It is never a line.

Lines take two points.

The calculus behind a lot of electronics can in many cases be skipped by using algebra and sticking to special cases. But take something like a basic capacitor where:

i = C dV/dt

When V is Sinusodial signal the derivative is also a sinusoid, not a straight line in any way shape or form.

d/dt Vm sin(wt) = wVm cos(wt) = wVm sin(wt + pi/2) where pi/2 is equivalent to a 90 degree phase shift.

That is why you can use -jwC as the impedance of a capacitor when doing phaser analysis, it is one special case of a result obtained thru calculus.

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18. ### shortbus AAC Fanatic!

Sep 30, 2009
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I'm even less educated and can beat that, only "calculus" I know about is the ones on my hands from a life of hard work.

19. ### BR-549 Well-Known Member

Sep 22, 2013
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nsaspook, Great Prologue.

20. ### wayneh Expert

Sep 9, 2010
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True, but the concept of a tangent line to visualize a slope can be a useful notion. It's hard for people to wrap their head around an instantaneous slope.

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