Math

[no one ever]

Just a quick 'help me out' question...

Wikipedia defines the equation of parallel resistors as 1/R₁+1/R₂... or is it R₁R₂/R₁+R₂?

and series capacitors go by the same formula?

[qwixzh]

parallel resistor should be r1r2/ (r1 +r2) or 1/{(1/r1) + (1/r2)}

parallel caps ......just add the values

hope this helps

[mojotron]

if you write it:

1  =   1    +    1
--       --         --
R       R1        R2

Then,


1  =   R2    +    R1
--       --            --
R       R1R2       R1R2

Then,

1  =   (R2    +    R1)
--              ------
R              R1R2
     
Then,


R   =       R1R2
--           --------
1        (R2    +    R1)

Then,

R   =       R1*R2
           ------------
           (R2    +    R1)

[Nasse]

It is not easy to do such calculations with average "four function" cheap calculator, or Windows calculator, if you dont put on "scientific" mode on and use memory function, write it on paper or use the ))(( buttons. There are some online calculators too, just looked and my favorite one RPN (reverse polish notation) calculator link was down... Maybe we could make an example calculation with real values so you can check if you typed it ok. I swear I saw a spiffy link of online calculator for parallel resistors, that picks values from standard available values, or I was just dreaming, but dont remember where it was.

Just spend silly amount of money for two quite expensive calculators (Hewlett-Packard) for two of my doughters, they have busy time at school just now. They were not a tiny bit interested when I suggested I should teach how to use those new calculators...

EDIT
Nice RPN calculatorhttp://www.arachnoid.com/lutusp/calculator.html

The link is working now (the main site was updating perhaps)

[R.G.]

Resistors add in series. Conductances add in parallel.

1/R = conductance.

So if you have three resistances in parallel, you can solve it easily by adding (1/R1) + (1/R2) + (1//R3). That gives you the total conductance, which is 1/(the parallel resistance).

So to do any number of parallels on a calculator, do
(enter r1)
1/x
+
(enter r2)
1/x
+
...


then take 1/x on the total to get the parallel resistance.

[no one ever]

reciprocal the sums of each value's reciprocal?


thanks.


So capacitors in series go by the same formula?

[mojotron]

Caps in series - use the same formula for resistors in parallel

Caps in parallel - use the same formula for resistors in series

replacing the "R"s for "C"s

For RC networks in parallel and series... well, that's when the fun begins... 

[no one ever]

For RC networks in parallel and series... well, that's when the fun begins... 

i'll save that particular lesson for another day. 


while i'm on the subject, are there many formulas/functions in EE-ing that require calculus?

[KMS]

Actually, all the formulas are the result of calculus, well not all of them.  Ohms Law is not. But calculus is the axis for all of Engineering and you won't ever degree without it.   The answer to your questions is....Yes.

[no one ever]

Actually, all the formulas are the result of calculus, well not all of them.  Ohms Law is not. But calculus is the axis for all of Engineering and you won't ever degree without it.   The answer to your questions is....Yes.

well i know that it took advanced critical thinking and reasoning from extremely talented, gifted, and rare individuals to control this thing called "electricity"... but i mean things like formulas to calculate phase shift degrees and other advanced thingies.

because i know nothing of calculus. (in algII/trig currently)



ps. R.G... have you gotten any of my pm's? sent you two... regarding the vibe.   

[Rick]

Yes, I still remember the formula from this line from the course book: (it sounds a bit twisty but if you say it out loud a few times you will probably remember it for ever).

Parallel resistors:  The reciprocal of the reciprocal of the sum of the resistances!

Just get a simple calculator and make sure it has the reciprocal function (1/x), makes it easier or rather faster than doing 1 divided by r many times for a bunch of resistors.

1/r+1/r+1/r = then flip it one last time with the (1/x) button and you have it!

For paralleling only two identical resistors (and only two) you get half the value of one of the resistors.
10ohms || 10ohms = 5ohms

I know this has been explained all over already, but I think some may remember it better this way.
...Rick

[mojotron]

For RC networks in parallel and series... well, that's when the fun begins... 

i'll save that particular lesson for another day. 


while i'm on the subject, are there many formulas/functions in EE-ing that require calculus?

Academically, electrical engineering is mostly math - from figuring out the parasitic loss within the material formation of a device (transistor...), to modeling the transfer functions of networks of different devices, to figuring out the penetration (skin depth) of an electromagnetic field on a material, to working out Maxwell's equations to relate electrical/magnetic properties to physics. But, an understanding of how it all ties together comes from a strong interest in building things and solving problems - it's a very creative and rewarding field to study. A vast majority of that math is based on calculus.

When I was in college, I used to think Maxwell, Newton, Leibniz... were simply from a time when people were just plain smarter - but once I turned off the calculator and spent some time studying I started to understand the logic and realized that the math is just a descriptive tool/language...

[d95err]

If you're really lazy - this helps:

http://www.diystompboxes.com/analogalchemy/emh/emh.html

[StephenGiles]

I've said this before, but how has "mathematics" taken on a singular abbreviation?? Just curious really.
Stephen

[no one ever]

I've said this before, but how has "mathematics" taken on a singular abbreviation?? Just curious really.
Stephen

why is abbreviation such a long word? 

[Paul Perry (Frostwave)]

I used to think Maxwell, Newton, Leibniz... were simply from a time when people were just plain smarter -

No, there's always been a pretty wide range of talent. But, to get somewhere in maths, you need a good attention span. Incidentally, Maxwell played guitar (unfortunately, an acoustic) and invented  the first photographic color slide projector. http://en.wikipedia.org/wiki/James_Clerk_Maxwell

[Transmogrifox]

Actually, all the formulas are the result of calculus, well not all of them.  Ohms Law is not. But calculus is the axis for all of Engineering and you won't ever degree without it.   The answer to your questions is....Yes.

...speaking of Maxwell's equations, actually, Ohms law is derived using calculus.  Since thinkers such as Maxwell have done the groundwork, we don't need to even think twice about the calculus done that gives us the confidence in the integrity of the simple algebraic and arithmetic operations we do in circuit design.

So when it comes to the more mathematically involved operations such as frequency response and phase functions, we still don't actually need to do much calculus.  I can't think of any application in analog guitar pedal design that requires chugging through convolution, Laplace transforms and inverse Laplace transforms, or the likes. 

Here's an example:

The current/voltage relationship in a capacitor is expressed by the following in the time domain:

I(t) = C*d V(t)/dt

Impedance is generally expressed as Z= V(t)/I(t)
This is a hard one to express in the time domain for a capacitor, but it is fortunate that we have Fourier transformations.  The Fourier transform of this equation (presented without going through the mathematical process to get there) is this:

I = jwC*V

==> V/I = 1/jwC

Where w=2*pi*f, which is the radian frequency, or 2*pi*frequency
j = square root of negative one (imaginary number which mathematicians and physicists reference as "i")

Now this is easy.  We can just treat the capacitor in an equation like a resistor for circuit analysis just by saying that the impedance of the capacitor is Zc=1/jwC

For the Laplace transform representation, we can say jw=s assuming sigma is 0 (sigma is a parameter in the Laplace transform that effectively adds a 3rd dimension to the frequency response plot, but it is set to 0 for the frequency response that is relevant to the real deal).

So Zc=1/sC

Now we can find the magnitude of the capacitors impedance at any frequency (we see that it does change with frequency).  So now it's just down to algebra again.

When talking about phase response, we do need to understand complex (real vs. imaginary) numbers because we need to deal with that "j" term for phase.  Again, these operations are broken down to algebra and simple trigonometry.  Sometimes the algebra gets nasty, but not as bad as it would be if we were doing it all in the time domain with calculus.

As and added bonus, the graphical plot of the frequency response is so much more intuitively meaningful than time domain equations.

The moral of the story is this:
You don't need to know anything more than algebra and complex numbers to do frequency and phase response....until you get into RF, microwave, radio transmission, and stuff that generally doesn't find its way into stompboxes.

Most of my designing is experimentation on the breadboard.  With this method, the circuit does all the math for me.  As long as I have a good intuitive understanding of what each circuit element does, how they will interact, and what components change parameters that I would like to change then I let my ears tune the circuit to the proper values.   The #1 skill that you need in engineering is the ability to think logically.  I don't think such a skill is out of the reach of an unschooled person.

[StephenGiles]

I've said this before, but how has "mathematics" taken on a singular abbreviation?? Just curious really.
Stephen

why is abbreviation such a long word? 

It's just that we say Maths in the UK, Math sounds odd although it could be short for Mathew.
Stephen

[no one ever]

It's just that we say Maths in the UK, Math sounds odd although it could be short for Mathew.
Stephen

Calling a Matthew "Math" would be absurd around these American parts, tomato tomahto I guess.

Transmogrifox... I applaud your post...  however evident it is to me that only algebra and other mildly complex methods of logic are required to mathematically solve your way through a quandary/design, it is equally evident that it will be a while before I learn to know which equation/function/transformation to use in any given scenario (that is, the likes of Fourier and Laplace's transformations) .

[StephenGiles]

"Calling a Matthew "Math" would be absurd around these American parts, tomato tomahto I guess."

No, we have some Mathews with just one "t" who sometimes coin the name Mathew Pathew!!!

I just stick parts in a breadboard until the bugger works.........I finished with sums in 1965 - but don't let me stop you.
Stephen