## 500 ohms

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One of the lessons I learned from my high school electronics teacher was DC analysis, or how to combine multiple resistors to obtain the value you needed.

He would stand in the door way and hand out a quiz as you entered the room, this quiz sheet had a few resistors in come series/parallel combo, your task was to solve for the equivalent resistance, voltage drop, current, and power dissipation , each day there would be one more resistor then yesterdays quiz.  This lesson was used in lab, if a circuit needed a 10k resistor, there were never enough 10k's for everyone to have, so you had to build your resistor from what was available.  I never knew if that was by design or not.

The other day, while setting up a test environment for one of our building automation controllers, we needed a 500 ohm resistor to test the range of one the universal inputs (voltage, current or resistance).

Problem, we needed 500 ohms, we only had available that day a hand full of 120 ohm resistors, I said it was possible, all I got were stares from the other engineers/techs in the room.

Can you solve the problem?  Build a 500 ohm resistor using some number of 120 ohm resistors.

How many does it take?

Have fun.

Jim

(Possum Lodge oath) Quando omni flunkus, moritati.

"I thought growing old would take longer"

Last Edited: Wed. Jul 24, 2019 - 03:46 PM

10 resistors:

One set: 4 in series to get 480 ohms

Other set: 6 in parallel to get 20 ohms

Put these two sets in series to get 500.

If you don't know my whole story, keep your mouth shut.

If you know my whole story, you're an accomplice. Keep your mouth shut.

Last Edited: Wed. Jul 24, 2019 - 03:56 PM

Very good, my solution only used 8!

(Possum Lodge oath) Quando omni flunkus, moritati.

"I thought growing old would take longer"

Just some random jottings..

Series

1 = 120

1 + 1 = 240

1 + 1 + 1 = 360

1 + 1 + 1 + 1 = 480

Parallel

1 / 1 = 60

1 / 1 / 1 = 40

1 / 1 / 1 / 1 = 30

1 / 1 / 1 / 1 / 1 = 24

1 / 1 / 1 / 1 / 1 / 1 = 20

Torby already discounted 20 + 480

So I figure you probably want to eat as big a chunk out of it with series but 480 is "too much" as it requires too many parallel for the last 20

3 Series gets you to 360 so you have 140 to go with 5 of your 8 left but 120 + 20 to make 140 is already discounted in Torby's answer.

140 could be 60 + 40 + 40 but all that takes 8 alone?

I'm going to keep shuffling the numbers but so far nothing immediately obvious springs out - look forward to seeing the 8 resistor solution!

I have it down to 8, trying for lower

120+120+120  ==>360

120||120 ===>60

120||(120+120)==>80

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

Last Edited: Wed. Jul 24, 2019 - 04:35 PM

avrcandies wrote:

120+120+120  ==>360

120||120 ===>60

120||(120+120)==>80

Bingo!

(Possum Lodge oath) Quando omni flunkus, moritati.

"I thought growing old would take longer"

Last Edited: Wed. Jul 24, 2019 - 04:44 PM

Ah ha so that's how you split the 140? As 60+80. Ingenious.

I guess the "clever bit" is the creation of the 80.

clawson wrote:
I guess the "clever bit" is the creation of the 80.

One of the "tricks" leaned was given two parallel resistors  R1 = 1/2 R2, equivalent resistance is 1/3 the larger (R2)

So given three identical resistors, place two in series, and wrap the third around those.

Jim

(Possum Lodge oath) Quando omni flunkus, moritati.

"I thought growing old would take longer"

Interesting. So in general, R//(nxR) = R - R/(n+1). This is pretty easy to deduce, but it never occured  to me that it might actually be useful to know.

120 is a "good" number for this kind of problem because it has so many integral divisors: 2, 3, 4, 5, 6, 8, 10, 12 etc...

El Tangas wrote:
it never occured  to me that it might actually be useful to know.

Mr Farber is smiling!

Jim

(Possum Lodge oath) Quando omni flunkus, moritati.

"I thought growing old would take longer"

Use four 120 ohm resistors in series to make 480 ohms.

In the real world 480 ohms is as good as 500 ohms. Unless you have a very specific application, then use a 500 ohm 1% resistor.

The chances are overwhelming that in your case, 480 ohms is just as good as 500 ohms.

If your teacher refuses to accept that, in the real world, 500 ohms is 480 ohms, then, go to a different school, because your teacher is a pedantic jerk and you're paying too much money in tuition to have to deal with this kind of nonsense.

The fact that everyone here disagrees with me on this doesn't change the fact that it's true.

I still like the question of "imagine a cube where each edge is made of resistors".  All are one ohm.  What is the resistance from, say, the lower front left corner to the upper right back corner?  Have fun putting that into serial and parallel designs...  S.

Edited to add:  Incidentally, a 'most obfuscated' way of making 500 ohms out of 120 ohm resistors involves cubes... and about sixty of them.  S.

Last Edited: Wed. Jul 24, 2019 - 09:41 PM

Simonetta wrote:

The fact that everyone here disagrees with me on this doesn't change the fact that it's true.

I am sure everyone can agree that you can suck the fun out just about anything too.

Jim

I would rather attempt something great and fail, than attempt nothing and succeed - Fortune Cookie

"The critical shortage here is not stuff, but time." - Johan Ekdahl

"Step N is required before you can do step N+1!" - ka7ehk

"If you want a career with a known path - become an undertaker. Dead people don't sue!" - Kartman

"Why is there a "Highway to Hell" and only a "Stairway to Heaven"? A prediction of the expected traffic load?"  - Lee "theusch"

Speak sweetly. It makes your words easier to digest when at a later date you have to eat them ;-)  - Source Unknown

Atmel Studio6.2/AS7, DipTrace, Quartus, MPLAB, RSLogix user

ki0bk wrote:

avrcandies wrote:

120+120+120  ==>360

120||120 ===>60

120||(120+120)==>80

Bingo!

Now compute the tolerance  of the 500 Ohms given that the 120 Ohm resistors have a tolerance of +/- 1%.

With resistors having +/- 1% tolerance, the equivalent resistance would be in the range 495-505 Ohm.

KerimF wrote:

With resistors having +/- 1% tolerance, the equivalent resistance would be in the range 495-505 Ohm.

I dunno about that....since each resistor has a plus minus window if all the resistors were on the low side for example I would think that the over all resistance would be the accumulation of each...making the final value a much wider window...

Jim

I would rather attempt something great and fail, than attempt nothing and succeed - Fortune Cookie

"The critical shortage here is not stuff, but time." - Johan Ekdahl

"Step N is required before you can do step N+1!" - ka7ehk

"If you want a career with a known path - become an undertaker. Dead people don't sue!" - Kartman

"Why is there a "Highway to Hell" and only a "Stairway to Heaven"? A prediction of the expected traffic load?"  - Lee "theusch"

Speak sweetly. It makes your words easier to digest when at a later date you have to eat them ;-)  - Source Unknown

Atmel Studio6.2/AS7, DipTrace, Quartus, MPLAB, RSLogix user

Now compute the tolerance  of the 500 Ohms given that the 120 Ohm resistors have a tolerance of +/- 1%.

If all the resistors are 1% low, you get 495 ohms.  If all are 1% high, you get 505 ohms.

If your teacher refuses to accept that, in the real world, 500 ohms is 480 ohms, then, go to a different school,

Maybe they were plotting a way to get you to transfer ? ​​​​​​​

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

jgmdesign wrote:

KerimF wrote:

With resistors having +/- 1% tolerance, the equivalent resistance would be in the range 495-505 Ohm.

I dunno about that....since each resistor has a plus minus window if all the resistors were on the low side for example I would think that the over all resistance would be the accumulation of each...making the final value a much wider window...

Jim

If you do the calculations, using the lowest a highest values, you will see that the total tolerance is actually the same as individual resistors.

But in practice, I think the tolerance will improve with more resistors because the error "cancels out", that is, maybe one resistor is 121 ohm, but the other is 119 so they ballance?

maybe one resistor is 121 ohm, but the other is 119 so they ballance?

Have you been to Monte Carlo?

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

jgmdesign wrote:
I am sure everyone can agree that you can suck the fun out just about anything too.
Everyone needs a hobby.

 "Experience is what enables you to recognise a mistake the second time you make it." "Good judgement comes from experience.  Experience comes from bad judgement." "Wisdom is always wont to arrive late, and to be a little approximate on first possession." "When you hear hoofbeats, think horses, not unicorns." "Fast.  Cheap.  Good.  Pick two." "We see a lot of arses on handlebars around here." - [J Ekdahl]

Chuck99 wrote:
Now compute the tolerance  of the 500 Ohms given that the 120 Ohm resistors have a tolerance of +/- 1%.

From High School physics I learned that:

For addition and subtraction the tolerance remains the same

For multiplication and division you add the tolerance.

With parallel resistors you have both both multiplication and division.

Plus the values of the "stages" are not the same.

It can get messy!

avrcandies wrote:
Have you been to Monte Carlo?

I've heard about the technique... but no.

The next step would be to make something like a 2 Watt 500 ohm resistor out of 1/4 watt 120 ohm resistors.

And the next step would be to make a program that calculated all values with n resistors like :

1:

120

2:

60, 240 (perhaps also 120 depending of connection rules).

3:

.....

I know it will explode in size but only "new" should be remembered (unless power is involved).

Back in the late 80's when I had a VLSI class I had a plan to make a program that should find different logic gates with n NFET and m PFET, but because you also can make transmission gates I never got to it. (using a transmission gate you can make a EOR with only 6 transistors where with normal logic it takes 8).

El Tangas wrote:

But in practice, I think the tolerance will improve with more resistors because the error "cancels out", that is, maybe one resistor is 121 ohm, but the other is 119 so they ballance?

In practice often all resistors from one bath are biased by similar values.

I was never very good at math puzzles.

The cube problem sounds like my dad's infernal "wheel circuits" in Circuits 101. "Wheel circuits are not to be confused with real circuits." -- Prof Eric S. Ruby

If you don't know my whole story, keep your mouth shut.

If you know my whole story, you're an accomplice. Keep your mouth shut.

awit wrote:

In practice often all resistors from one bath are biased by similar values.

Often they have a nice gaussian distribution with no bias: https://www.youtube.com/watch?v=...

In that case, the error distribution should narrow the more resistors are combined.

Scroungre wrote:

I still like the question of "imagine a cube where each edge is made of resistors".  All are one ohm.  What is the resistance from, say, the lower front left corner to the upper right back corner?  Have fun putting that into serial and parallel designs...  S.

Um. I'm getting a completely unbelievable result on the order of 5 teraohms. Incorrect.

If you don't know my whole story, keep your mouth shut.

If you know my whole story, you're an accomplice. Keep your mouth shut.

Sorry I can't help, I only have 121 ohm 1% resistors.

--Mike

EDIT: see Preferred Numbers

Last Edited: Thu. Jul 25, 2019 - 06:01 PM

The govt has banned standard 100W bulbs, now they are planning on banning resistors.  Current Representative Griswold McJello said "With this new legislation outlawing the use of resistors in new circuit designs, we enter an era of higher efficiency that will stand the test of time.  We were dumbedfounded to learn that resistors burn up megawatts of power every day.  Until now, leadership in this area has been lacking, and we join with those who are bold enough to envision a resistor-free future.

* note this is not a true story (in case you were wondering)

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

avr-mike wrote:

Sorry I can't help, I only have 121 ohm 1% resistors.

Good point.  120R are part of the E192 series at 0.5%.

avrcandies wrote:

* note this is not a true story (in case you were wondering)

Yet...

 "Experience is what enables you to recognise a mistake the second time you make it." "Good judgement comes from experience.  Experience comes from bad judgement." "Wisdom is always wont to arrive late, and to be a little approximate on first possession." "When you hear hoofbeats, think horses, not unicorns." "Fast.  Cheap.  Good.  Pick two." "We see a lot of arses on handlebars around here." - [J Ekdahl]

Torby wrote:

Scroungre wrote:

I still like the question of "imagine a cube where each edge is made of resistors".  All are one ohm.  What is the resistance from, say, the lower front left corner to the upper right back corner?  Have fun putting that into serial and parallel designs...  S.

Um. I'm getting a completely unbelievable result on the order of 5 teraohms. Incorrect.

Build one?  (I'd suggest using 1k or 10k resistors and scale (because 1 ohm resistors aren't everyone's cup of tea (great for theory, not so much for practice (I do have one one ohm resistor around here - it's about the size of a beer can (It's also rated for 100W(!)))))).  Show your work...

Also incidentally, that experiment will tell you how to make 500 ohms out of 120 ohm resistors in a very cheerfully silly way.  S.

avrcandies wrote:

The govt has banned standard 100W bulbs, now they are planning on banning resistors.  Current Representative Griswold McJello said "With this new legislation outlawing the use of resistors in new circuit designs, we enter an era of higher efficiency that will stand the test of time.  We were dumbedfounded to learn that resistors burn up megawatts of power every day.  Until now, leadership in this area has been lacking, and we join with those who are bold enough to envision a resistor-free future.

* note this is not a true story (in case you were wondering)

We Are AVR Freaks Of Borg.  We Have Room Temperature Superconductors.  Resistance Is Futile.

A resistor in electricity is equivalent to friction in the physics of movement.

No heat loss in friction results no control in the movement of the living things

I don't know about that.  Back about 20 years ago when the record industry was fighting Napster someone pointed out that "pirates" could copy music by connecting a recorder to the output of the analog-digital-analog converter.  The record industry execs talked seriously for a while about getting federal legislation to ban analog-digital and digital-to-analog converters.

Last Edited: Thu. Jul 25, 2019 - 09:41 PM

It's ok, switched capacitors are equivalent to resistors, right? We'll be fine even with the resistor ban.

avr-mike wrote:
Nerd Sniping
The explainxkcd page has an interesting comment about half-way down:

Amazing. From the first comment the discussion is diverted from discussing the comic, to discussing the problem presented in the comic. The commentators have been nerd sniped by a demonstration of nerd sniping. Randall is just that good. 108.162.216.86 17:55, 30 April 2014 (UTC)

So nerd-sniping is a fractal phenomenon.

 "Experience is what enables you to recognise a mistake the second time you make it." "Good judgement comes from experience.  Experience comes from bad judgement." "Wisdom is always wont to arrive late, and to be a little approximate on first possession." "When you hear hoofbeats, think horses, not unicorns." "Fast.  Cheap.  Good.  Pick two." "We see a lot of arses on handlebars around here." - [J Ekdahl]

El Tangas wrote:

It's ok, switched capacitors are equivalent to resistors, right? We'll be fine even with the resistor ban.

You are right.

But how could the various internal resistances be banned

And what about the source that drives a switched capacitor? I guess you agree with me that it has to be a current source. If we put aside the internal resistance (which cannot be banned), the current source that I think of now is the solar cell only

avrcandies wrote:

The govt has banned standard 100W bulbs, now they are planning on banning resistors.  Current Representative Griswold McJello said "With this new legislation outlawing the use of resistors in new circuit designs, we enter an era of higher efficiency that will stand the test of time.  We were dumbedfounded to learn that resistors burn up megawatts of power every day.  Until now, leadership in this area has been lacking, and we join with those who are bold enough to envision a resistor-free future.

* note this is not a true story (in case you were wondering)

Wouldn't surprise me any. Once had a guy explaining to me that we should only use low-value resistors so electricity flows more efficiently.

If you don't know my whole story, keep your mouth shut.

If you know my whole story, you're an accomplice. Keep your mouth shut.

Torby wrote:
Wouldn't surprise me any. Once had a guy explaining to me that we should only use low-value resistors so electricity flows more efficiently.

Would it not be more efficient use of electricity to use high value resistors, i.e less power used?

I don't know why I'm participating in this silly discussion!?!  (what have I started?)

Jim

(Possum Lodge oath) Quando omni flunkus, moritati.

"I thought growing old would take longer"

ki0bk wrote:
Would it not be more efficient use of electricity to use high value resistors, i.e less power used?
But then the electricity companies would have to lobby those in power to ban the high value resistors.

Ross McKenzie ValuSoft Melbourne Australia