In the many years since I graduated -- once as recently as last year -- I have on occasion had a sudden need to compute the equivalent resistance of two parallel resistors. It's a simple operation: basically their product over their sum. But not something you can do quickly on a piece of paper. Nor is it something you can do quickly on one of those god damn brain-damaged calculators that have an '=' sign.
This is because it has a couple intermediate values. The natural thing to do is get their product, then get their sum, and then divide one by the other. I still don't know: How the hell do you do that correctly on a standard calculator?
I think it's something like
1) R1 * R2 = something you have to store somewhere
2) R1 + R2 = something you have to store somewhere else
3) Recall the first one and divide it by the second one
Probably it's easier to divide the result of (2), which you have on the screen, by the result of (1), which is in the storage location, of which many calculators only give you one, and then do
4) 1/x
to end up with the right result. I dunno. It's too much work. Especially on something a little more challenging than one simple-ass two-variable equation.
I cut my teeth on the machine pictured. No god damn '=' sign. The above operation is intuitive, run through the same way as algebra on a notepad.
[R1] [Enter] [R2] [*] [R1] [Enter] [R2] [+] [/]
That's it. Minimal keystrokes. Enter the two numbers and multiply, enter the two numbers and add, and divide. When running through some monstrous equation that results from ninety minutes of puzzling through control systems theory, it makes a huge, nay monstrous, difference not to have to keep writing down intermediate values or remembering which storage location has which value. With RPN, all you gots ta do is run through it left to right. Simple! Easy! Get to bed before sunrise! (We won't even talk about the awesome power of the EEX key, or of ENG notation.)
I wrote once about the devastating loss of my trusty HP11C. Well, finally I quit being such a cheapskate and found a replacement on eBay. It was delivered today. Am I happy now? Yes.
20 comments:
I remember having to do that input the numbers in first thing and then hit the process long, long, long ago, and I hated it. To me, it was not intuitive. But then, I didn't use my calculator to run long equations. I'm not a math person. :-)
NERD ALERT!
NERD ALERT!
NERD ALERT!
I understand you RPN guys have a religious fanaticism about the dreaded "=" sign but the reality is a bit different. See, no mathematician or scientist would ever write your expression as [R1] [Enter] [R2] [*] [R1] [Enter] [R2] [+] [/]
The mathematician or scientist would write the expression as
R1 * R2
---------
R2 + R2
which any 10th grader can solve.
It's not even very hard to do on a calculator.
( R1 + R2 ) / ( R1 + R2) =
or, to use your conventions,
[(] [R1] [*] [R2] [)] [/] [(] [R1] [+] [R2] [)] [=]
Easy as pi.
I never saw a calculator with parentheses. Your keystrokes will be interpreted as ((R1 * R2) / R1) + R2 = something else entirely. The equation any 10th grader can solve is more easily done via RPN unless the 10th grader takes his pencil and circles the parts he needs to do first. Most efficient process in that case would be:
1) R1 + R2 =
2) 1/x
3) * R1 =
4) * R2 =
This would give you the right answer but it's hella more trouble to try and emulate paper and pencil on a calculator, than to simply run it through a computing machine designed for the task.
I'll allow you're right IF you have a calc with parens AND have practiced enough to avoid misplacing those inelegant extra keystrokes.
(Ain't religious debates fun?)
Every scientific calculator I've owned since about 1980 has had parens. Even the $10 solar Casio in my hand right now.
BTW, the keystrokes I gave are correct.
So they do! I guess my gripes either predate that feature or were based on the calcs people tend to have when I need to borrow one. Or something. At this time I don't know why I never noticed the parentheses, but my fingers are happier using the RPN stack in any case.
What does "the equivalent resistance of two parallel resistors" mean?
(Also, how did you get your blog roll on a different page?!?! I can't figure that out.)
I understand the preference, Don. Posty froths at the mouth when I talk about RPN. (Yes, I enjoy putting a quarter in him.) And, counting keystrokes, I see that the RPN entry is a couple fewer than arithmetic entry.
There's nothing inherently wrong with RPN except for one sneaky little difficulty: it's not what most people trained on through their entire schooling which means it is very, very easy to have a mathematician get an answer of 3 instead of 1.2 for values of R1=2 and R2=3.
Any tool that adds a risk of error just by its use worries me.
Most Serene Babe: The equivalent resistance of two parallel resistors refers to a very convenient simplification. After a few attempts just after getting home at 11:30pm, however, I have determined I am too drunk to type it out without making it seem more complicated than it is. Dang. Mayhap I will try again tomorrow.
Dick: Is Posty for or against? Neither would surprise me, as it is a subject to excite strong opinions.
Your example of a person getting 3 when paralleling 2 and 3 has to be of a mathematician. No engineer could possibly make such a mistake, even by mere inspection, the math itself be damned.
RPN is right up there with Glenn Beck in the Post universe.
"No engineer could possibly..."
<snerk>
Engineers are among the most literal people I know. Give one an arithmetic or full scientific calculator and that string of instructions and I'll bet Pareto rules. 80% will follow the key entries punch for punch ... and come up with the wrong answer.
Alright, I made up the statistic, but _some_ would. And many, many clerks would for sure.
We have tools so we don't train kids to estimate answers any more. The fact that using a "different" calculator can cause such errors worries me more and more because so many ordinary users wouldn't recognize that the answer is wrong.
I don't see how being proficient on either an RPN calc or on a calc with parens makes any difference with regards to judging that 2 in parallel with 3 cannot be 3; or how use of one leads to more math errors in comparison to the other.
Engineers are not quite that literal. They rely on informed judgment. This is one of the many things that separates them from the more literal mathematicians.
The string of instructions was illustrative. No competent engineer will follow it mindlessly.
I acknowledge your disdain for RPN, as snerkily expressed with the comparison to Beck. I will surrender enough ground to agree the two methods can be equivalent, but you're not going to get anywhere claiming superiority without any backing. Your concern that "the answer is wrong" escapes me. To use RPN, one must know what one is doing; and from there it is found by those who have converted to be superior to the task. Kind of like Linux as opposed to Windows when doing certain things.
"To use RPN, one must know what one is doing..."
Exactly.
I don't have disdain for RPN, merely for its evangelists like Bob. It is he who places both his calculator and Beck on a pedestal. And I don't even claim superiority for arithmetic methods. Your analog of *nix to Windows is a good one.
"The string of instructions was illustrative. No competent engineer will follow it mindlessly."
Actually, I think most engineers would follow a string of instructions key for key very deliberately, even if they expect a bad outcome, for exactly the reason of testing the outcome. And what happens as soon as we stop talking about someone we can expect to recognize the right answer or at least to know what the answer should be, within an order of magnitude? The store clerk or accountant or game warden might never know the answer the calculator gave them is wrong.
(Using R1=2 and R2=3 was likewise intended for the simplicity of the numbers, not because it was a typical problem.)
Ahh. I just noticed an error I made by assuming facts not in evidence. I wrote, "RPN is right up there with Glenn Beck in the Post universe."
The fact not in evidence is that the Post universe is the universe inhabited by Bob Post, P.E., my classmate at Stevens, best man, and racing partner.
He really truly doesn't get my opposition to RPN.
I understood that, if not the peanut gallery, which probably can't hear for the roar of crickets.
I never got my PE and am not going to, but a time may still come when I wish I had.
I like the clicky buttons on the HP calcs of that era.
Cut my calculating teeth on an algebraic calculator. Would've died for an HP but my grandparents bought me a TI programmable and thus was life writ.
Despise Beck.
Amused by Posty.
Have taken Dick to task for obscure references to things well known to but the elite few.
Happy you got your 11C.
Dick's example of literal engineers appears to reference people who, while possibly possessing engineering degrees, nevertheless do not possess engineering minds. Testers would follow instructions click for click. Engineers would dig in to understand the underlying principles, then figure out the coolest way to get to the answer using those principles.
Yes, I am generalizing and snooting at the same time.
No, I do not wish to be snarky.
It's 88 degrees out, sunny, and I have things to do.
Ta!
It's 88 degrees out, sunny, and you are such a tease.
Forecast:
Sat - 68d, 60% chance of precip
Sun - 70d, 50% chance of precip
Mon - 65d, 20% chance of precip
Tue - 70d, partly cloudy
Nominal:
85d and dry
I don't have a P.E. and have never felt it hampered my consultancy. I don't sign off on sewers and don't testify in court if I can avoid it.
While I understand the defense of engineers since I R one, too, I still stand by my belief that most engineers want to follow the directions because that's what the directions are there for. It's not until it's obvious the directions will fail that the good engineer digs in to the underlying principles to get the right answer.
I like the clicky buttons, too.
Oh yeah: To SereneBabe:
What does "the equivalent resistance of two parallel resistors" mean?
Voltage applied across an electrical circuit (which is pretty much any electrical thing) creates current. It is current flow that one way or another does actual work.
Current doesn't just take the path of least resistance. It takes every available path. But how much current takes which path depends on the resistance of that path. So a beefy resistor gets just a little current, and a motor made of wound-up wire which is hooked up to the same voltage source gets a lot (we're never-minding electromagnetism and reluctance and setch here).
Turns out just about every useful electrical circuit has multiple paths, so while you want to know how much current goes down each, you also want to know how much goes down all of it together. So those different paths get lumped together into one "equivalent" circuit, making the computation easier or more useful or whatever.
My example was of wanting to know the equivalent circuit when hooking two resistors up to the same source, i.e. in parallel (side by side). That's the equivalent resistance of two parallel resistors.
Why? A common occurrence in my little world is, in the service of some debug activity, a need to replace a resistor with a value of say 10k (i.e. 10,000 ohms) with one of say 6.8k (6800 ohms) and being in a stupid lab with no stupid parts trays and therefore having to make one out of whatever other stupid parts I can find. Quick benchtop calculations are a must in this scenario.
Yes, $43.6B in net revenue and I am sometimes scrounging around a dinky lab for parts that cost under a penny.
That was fun to write but I have no idea if it makes sense outside my brain.
Also yeah: To SereneBabe:
how did you get your blog roll on a different page?!?!
It's a whole nother blog with its own URL. I dragged a blog list gadget over to the left above the blog posts gadget and let it grow as big as it needs to. Beneath the list are the posts for that blog, but I've never written any, so there's nothing there but a little gadget that says "No posts" because I can't delete it. Then I just link to it from my main blog.
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