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

#### johnsmithne

Joined Mar 14, 2016
5
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.

#### wayneh

Joined Sep 9, 2010
17,262
Derivative. For instance dx/dt is the change in x ( delta x) over delta y, in the limit where both approach zero.

#### profbuxton

Joined Feb 21, 2014
421
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.

#### johnsmithne

Joined Mar 14, 2016
5
Derivative. For instance dx/dt is the change in x ( delta x) over delta y, in the limit where both approach zero.
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.

#### ErnieM

Joined Apr 24, 2011
8,355
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.

#### johnsmithne

Joined Mar 14, 2016
5
Tha
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.
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.

#### wayneh

Joined Sep 9, 2010
17,262
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.

#### ElectronicMotor

Joined May 1, 2016
53
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 ?

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#### MrChips

Joined Oct 2, 2009
28,473
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.

• Sinus23 and #12

#### GopherT

Joined Nov 23, 2012
8,009
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 ?
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.

#### GopherT

Joined Nov 23, 2012
8,009
I'm guessing john is a chemist. d=polarity (dipole). Welcome to the club.

#### nsaspook

Joined Aug 27, 2009
11,257
Here is an ebook that explains all.

The preliminary terror, which chokes off most fifth-form boys from even attempting to learn how to calculate, can be abolished once for all by simply stating what is the meaning—in common-sense terms—of the two principal symbols that are used in calculating. These dreadful symbols are: (1) d which merely means “a little bit of.” Thus dx means a little bit of x; or du means a little bit of u. Ordinary mathematicians think it more polite to say “an element of,” instead of “a little bit of.” Just as you please. But you will find that these little bits (or elements) may be considered to be indefinitely small.

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• atferrari and BR-549

#### #12

Joined Nov 30, 2010
18,224
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.

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#### Brownout

Joined Jan 10, 2012
2,390
If you don't know calculus, R=E/I
If you do know calculus, R + dE/dI
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.

• #12

#### GopherT

Joined Nov 23, 2012
8,009
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.
But, for any two set of pair of infinitely close points, it is linear.

#### Brownout

Joined Jan 10, 2012
2,390
But, for any two set of pair of infinitely close points, it is linear.
Naturally, since that's a basic property of a derivative.

• GopherT

#### ErnieM

Joined Apr 24, 2011
8,355
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.

• GopherT

#### shortbus

Joined Sep 30, 2009
9,858
From an even less educated point of view...
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. #### BR-549

Joined Sep 22, 2013
4,928

#### wayneh

Joined Sep 9, 2010
17,262
It is never a line.
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.

• atferrari